Genetic selection for feed intake and efficiency in beef cattle

DISSERTATION GENETIC SELECTION FOR FEED INTAKE AND EFFICIENCY IN BEEF CATTLE Submitted by Miranda M. Culbertson Department of Animal Sciences In partial fulfillment of the requirements For the Degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Fall 2019 Doctoral Committee: Advisor: Scott Speidel Co-Advisor: Mark Enns Milt Thomas Terry Engle Marshall Frasier Copyright by Miranda M. Culbertson 2019 All Rights Reserved ABSTRACT GENETIC SELECTION FOR FEED INTAKE AND EFFICIENCY IN BEEF CATTLE Feed costs are reported as the largest variable expense in beef production systems accounting for 50% to 70% of total production costs. Due to the large impact of feed costs on profitability, producers have become increasingly aware of the need to improve feed utilization in cattle. With the advent of technologies to measure individual feed intake in cattle, a phenotype is available for selection; however, how to implement this phenotype into a breeding objective or genetic evaluation is debatable. This dissertation examines some of these unanswered questions about feed intake and efficiency and its utility in for genetic selection. The objectives herein were 1) to evaluate the maternal genetic effects on dry matter feed intake (DMI), 2) to simulate data to examine the effects single trait selection on DMI or residual feed intake (RFI) on genetically correlated traits of weaning weight (WWT) and yearling weight (YWT), 3) to examine data generated by an ear tag accelerometer (CowManger; Agis Automatisering BV, Harmelen, Netherlands) while attached to steers located in a feedlot and on pastures to develop a proxy for measures of intake and 4) to examine the phenotypic relationship between grazing and feedlot intake. For the examination of maternal genetic effects on intake, the American Gelbvieh Association (AGA) and the Red Angus Association of America (RAAA) provided pedigree information in addition to DMI and WWT records. Dry matter intake records were limited to animals within an age range of 240 d to 365 d to limit data to only postweaning cattle. Embryo transfer calves were removed. Gelbvieh and Red Angus data were analyzed separately. ii The first analysis was a single trait model that examined the maternal genetic effects of DMI. Contemporary groups (CG) were formed using sex, pen, feed trial designation, trial length and year for both AGA and RAAA. The final data set for AGA consisted of 3,021 animals with DMI records and a 3-generation pedigree of 15,418 animals. For Red Angus, cattle with DMI records was 3,213 and a 3-generation pedigree of 13,747 animals. The heritabilities of DMI direct for Gelbvieh and Red Angus were moderate to high (0.45 ± 0.06 and 0.24 ± 0.06, respectively) but the DMI maternal heritability for Gelbvieh was 0.00 ± 0.00 and Red Angus DMI maternal heritability was very low at 0.05 ± 0.04. Resulting in little to no maternal effect for DMI. The second analysis was a multi-trait model estimating the correlation between DMI and WWT maternal. For the multi-trait model, fixed effects for weaning weight included age, age of dam and CG. The contemporary group for WWT was sex, breeder, weaning date, and herd. For Gelbvieh, the heritabilities for DMI, WWT direct and WWT maternal were 0.45 ± 0.05, 0.36 ± 0.06 and 0.15 ± 0.05, respectively. The heritabilities for Red Angus were 0.27 ± 0.05, 0.21 ± 0.06 and 0.16 ± .07 for DMI, WWT direct and WWT maternal, respectively. The genetic correlation between DMI and WWT maternal was low at 0.12 ± 0.13 and 0.12 ± 0.24, for Gelbvieh and Red Angus, respectively. These results suggested that WWT maternal would has minimal impact on the estimation of DMI EPD using a multivariate model. For the second objective of this dissertation, data were simulated to examine the effects on genetically correlated traits of WWT and YWT when single trait selection was conducted on DMI or RFI. Genetic parameters were established using published variance estimates weighted for the number of animals included in each estimation. Based on the weighted genetic parameters, a simulated population was established for three selection scenarios. The first and iii second scenario for selection was single trait selection for DMI and RFI, respectively. The third scenario used an economic selection index as criteria for replacements. With an annual replacement rate of 20% for females and 5% for males, 10 years of offspring data was generated. Replacements were chosen based on their breeding value for the trait of interest. At the conclusion of 10 years of simulated data, the scenarios for the selection of DMI and RFI saw a decrease in DMI of 0.85 kg/year and 0.19 kg/year, respectively. Both scenarios also resulted in a decrease for YWT of 27.83 kg/year from selection of DMI and 5.13 kg/year from the selection of RFI. Selection using the economic index showed a steady increase in YWT (14.84 kg/year) but also demonstrated an increase of DMI (0.42 kg/year). The three scenarios were all examined by the amount of profitability determined from fed cattle and feed prices. Of the three scenarios, the economic index showed the greatest amount of profit due to the increase in YWT. Although DMI increased with the index, the amount of increase in yearling weights was significant enough to outweigh the increase in feed costs. The third study of this dissertation examined a remote sensor technology as a potential proxy for DMI in addition to estimating a correlation between DMI measured in a feedlot versus grazing intake for cattle on pasture. Ninety-three steers were equipped with a CowManager ear tag accelerometer (CME) that measured the amount of time an animal spent ruminating, eating, and levels of activity. The steers were placed in a feedlot where their intakes were measured using the GrowSafe Feed Intake monitoring system. The data collected via CME and GrowSafe were analyzed to identify existing associations between the measurements. Based on the DMI measured by GrowSafe, the 15 highest and 15 lowest intake animals were identified. These low/high intake animals (LHI) were used to quantify grazing intake using the biomarker titanium dioxide (TiO2). No association between CME and DMI measured in the feedlot were found. iv Pearson’s correlations for CME measurements and DMI were low and ranged from -0.11 to 0.12. A regression analysis found no significant CME variable as explanatory variables for DMI. After a 54-d performance test, the steers were immediately transported to pasture where the steers were maintained for 43 days. Data from CME were continuously collected while cattle grazed on pasture. For the final 20 d, the LHI cattle were administered a bolus of 10 g of TiO2 each morning. During the 6 final days of this study, rectal fecal samples were collected twice daily with collection occurring 12 h apart. Every 24 h, time of collection was advanced 2 hours to minimize effects of diurnal variation. The fecal samples were analyzed for TiO2 concentration and based on these concentrations grazing dry matter intakes (GDMI) were estimated. The Pearson’s correlation between GDMI and DMI measured in the feedlot was 0.84 ± 0.10 (P < 0.05) with a Spearman rank correlation of 0.99 ± 0.03 (P < 0.05). This result suggested a strong relationship between grazing and feedlot DMI; however, it is less than 1 indicating some change in rank between DMI and GDMI. The correlation between GDMI and CME ranged from -0.22 to 0.19 with the largest correlation (-0.22) was between GDMI and time spent eating. All of these correlation estimates were not significantly different from zero (P > 0.05). This study was able to show the application of remote sensor technology for monitoring cattle maintained on rangeland, but the precision of measurements from CME failed to provide an indicator for GDMI. A strong relationship between feedlot measured DMI and DMI for grazing cattle was established in this study. v ACKNOWLEDGMENTS I would like to express my heartfelt gratitude to my advisors, Drs. Mark Enns and Scott Speidel, as well as committee member and mentor, Dr. Milt Thomas. It has been a long journey with unexpected setbacks to obtaining this degree and their guidance, assistance and encouragement throughout my program has been invaluable. I would also like to thank Drs. Terry Engle and Marshall Frasier for serving on my committee and providing valuable feedback to improve the quality of this research. I owe a huge debt of gratitude to my family for their endless support. This would not have been possible without it. In particular, I have to thank my mother for her unwavering support both emotionally and financially throughout this endeavor. A special thank you to my fellow graduate students. Not only was their friendship a crucial element to the graduate school experience but there was always a wealth of volunteers to help with projects when needed. Without their help, completing some these projects would not have been possible. Finally, I owe an enormous thank you to my cousin, Dr. Avery L. Culbertson. She convinced me it was never too late to go back to school and pursue a graduate degree. I owe this Ph.D. to her for her encouragement and endless words of support. vi TABLE OF CONTENTS ABSTRACT………………………………………………………………………………………ii ACKNOWDEDGEMENTS……………………………………………………………………...vi LIST OF TABLES……………………………………………………………………………......ix LIST OF FIGURES…………………………………………………………………………...…xii LIST OF EQUATIONS…………………………………………………………………………xiv CHAPTER I. INTRODUCTION AND OBSJECTIVES…………………………………………1 1.1 Introduction…………………………………………………………………………....1 1.2 Objectives……………………………………………………………………………..4 Literature Cited……………………………………………………………………………5 CHAPTER II. LITERATURE CITED………………………………………………………..…..8 2.1 Introduction……………………………………………………………………………8 2.2 Measuring Feed Intake………………………………………………………………...0 2.2.1 Equipment and Guidelines for Measuring Feed Intake……………………10 2.2.2 Feeding Trials for Feed Intake……………………………………………..15 2.2.3 Measuring Grazing Intake …………………………………………………17 2.3 Measures of Feed Intake and Efficiency……………………………………………..19 2.3.1 Feed Intake…………………………………………………………………19 2.3.2 Feed Conversion Ratios……………………………………………………21 2.3.3 Residual Feed Intake……………………………………………………….22 2.4 Biological Factors of Feed Efficiency……………………………………………….25 2.4.1 Mitochondrial Function……………………………………………………27 2.4.2 Biological Markers of RFI…………………………………………………29 2.5 Genetic Parameters of Feed Efficiency and Intake………………………………..…31 2.5.1 Heritability…………………………………………………………………31 2.5.1.1 Heritability for Feed Efficiency and Intake……………………...32 2.5.2 Genetic Correlations……………………………………………………….35 2.5.2.1 Genetic Correlations of Feed Efficiency and Intake……………..35 2.5.3 Genetic Improvement of Feed Efficiency and Intake……………………...40 2.6 Conclusion....................................................................................................................41 Literature Cited …………………………………………………………………………..42 CHAPTER III. ESTIMATION OF VARIANCE COMPONENTS DUE TO DIRECT AND MATERNAL EFFECTS FOR FEED INTAKE FOR RED ANGUS AND GELBVIEH CATTLE…………………………………………………………………………………56 3.1 Introduction…………………………………………………………………………..56 3.2 Materials and Methods……………………………………………………………….57 3.3 Results and Discussion….……………………………………………………………62 3.4 Conclusion……….…………………………………………………………………...67 Literature Cited …………………………………………………………………………..68 CHAPTER IV. A SIMULATION STUDY EXAMINING GENETIC SELECTION FOR FEED INTAKE AND RESIDUAL FEED INTAKE ON CORRELATED PERFORMANCE TRAITS IN BEEF CATTLE…………………………………………………………….70 4.1 Introduction…………………………………………………………………………..70 vii 4.2 Materials and Methods……………………………………………………………….71 4.2.1 Estimation of Weighted Means and Phenotypic Averages and Genetic (Co)variances…………………………………………………………….72 4.2.2 Simulated Data……………………………………………………………..79 4.3 Results and Discussion………………………………………………………………89 4.4 Conclusion…………………………………………………………………………...99 Literature Cited …………………………………………………………………………101 CHAPTER V. ESTIMATION OF FORAGE INTAKE FOR GRAZING BEEF CATTLE USING EAR TAG ACCELEROMETER TECHNOLOGY……………………………………107 5.1 Introduction…………………………………………………………………………107 5.2 Materials and Methods……………………………………………………………...108 5.3 Results and Discussion……………………………………………………………..118 5.4 Conclusion………………………………………………………………………….129 Literature Cited …………………………………………………………………………131 APPENDIX A: R CODE USED TO CREATE SIMULTED DATA FOR FEMALE BASE POPULATION…………………………………………………………………………134 APPENDIX B: R CODE USED TO CREATE SIMULTED DATA FOR SINGLE TRAIT SELECTION ON DRY MATTER INTAKE…………………………………………..139 APPENDIX C: R CODE USED TO CREATE SIMULATED DATA FOR SINGLE TRAIT SELECTION ON RESIDUAL FEED INTAKE……………………………………….199 APPENDIX D: R CODE USED TO CREATE ECONOMIC SELECTION INDEX PARAMETERS………………………………………………………………………...259 APPENDIX E: R CODE USED TO CREATE SIMULATE DATA FOR SELECTION USING AN ECONOMIC SELECTION INDEX……………………………………………….267 viii LIST OF TABLES Table Page Table 2.1: Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a range of studies prior to 2000 on growing animals across different breeds………………………………..……………32 Table 2.2: Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a range of studies after 2000 on growing animals across different breeds……………………………………………..33 Table 2.3: Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a lactating or dry mature animals across different breeds adapted from Berry and Crowley (2013)……………………34 Table 2.4: Number of studies (N), pooled heritabilities (pooled), minimum (min) and maximum (max) heritability estimates for average daily gain (ADG), weight (WT), dry matter feed intake (FI), residual feed intake (RFI), feed conversion ratio (FCR) adapted from Berry and Pryce (2013)………………………34 Table 2.5: Genetic correlations between feed efficiency traits…………………………………..36 Table 2.6: Genetic correlations (S.E.) for feed efficiency and postweaning traits………………37 Table 2.7: Genetic correlations between feed efficiency and carcass traits……………………..38 Table 3.1: Summary statistics for cattle with feed intake records for Gelbvieh and Red Angus cattle…………………………………………………………….....................63 Table 3.2: Weaning weight summary statistics for cattle with feed intake records for Gelbvieh and Red Angus cattle………………………………………………………63 Table 3.3: Direct and maternal variance components of dry matter feed intake for Gelbvieh and Red Angus cattle………………………………………………………65 Table 3.4: Estimated heritabilities (± S.E.) on the diagonal, above the diagonal is the residual correlation, and genetic correlations (± S.E.) below the diagonal for dry matter intake (DMI), weaning weight direct (WWTD) and weaning weight maternal (WWTM) for Gelbvieh and Red Angus cattle. …………………….67 Table 4.1: Weighted averages calculated from literature for residual feed intake (RFI), daily dry matter intake (DDMI), weaning weight (WWT), and yearling weight (YWT)………………………………………………………………75 ix Table 4.2: Number of estimates (Est.) from literature (n) and weighted estimates with standard error in parenthesis for genetic variance (diagonal), genetic correlation (above diagonal), residual correlation (below diagonal), and heritability (h2) for residual feed intake (RFI), average daily dry matter intake (DDMI), weaning weight (WWT) and yearling weight (YWT) with sources cited………………………………………………………………………….78 Table 4.3: Number of females for each age group used as a base population for a simulation study (n=10,000)………………………………………………………...80 Table 4.4: Ten-year average for cattle and commodity prices…………………………………...87 Table 4.5: Regression coefficients for the selection index for dry matter intake………………..88 Table 4.6: The phenotypic average for each year's progeny from 3 simulation scenarios with selection on average daily dry matter intake (DDMI), residual feed intake (RFI) and an economic selection index. Included are the progeny averages of DDMI and genetically correlated traits included in each simulation (weaning weight and yearling weight)………………………………91 Table 4.7: Number of simulated progenies produced each year for three simulations scenarios…………………………………………………………………………...…92 Table 4.8: Changes in estimated costs and incomes from the simulation of selection on average daily dry matter intake (SDDMI), residual feed intake (SRFI) or an economic index (SESI) on the average per head basis from year 1 to year 10……………………………………………………………………………………..98 Table 5.1: Composition of rations fed to cattle in Colorado State University Feed Intake Unit on an as fed basis………………………………………………...……110 Table 5.2: Summary statistics for cattle (n=98) at the conclusion of the 2017 performance test…………………………………………………………………….118 Table 5.3: Summary statistics for CowManager ear tag accelerometer measurements of time (in minutes) for eating (EAT), rumination (RUM), not active (NACT), active (ACT) and high active (HACT) on Angus cattle (n=98) during the 2017 performance test…………………………………………………..119 Table 5.4: Summary statistics for the 15 lowest and highest intake animals from the 2017 performance test…………..…………………………………………………119 Table 5.5: Pearson's correlations for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT) and dry matter intake (DMI) measured by a GrowSafe system. ……………………………………………………………121 x Table 5.6: Pearson's correlations for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT) and dry matter intake (DMI) measured by a GrowSafe system for a subset of cattle with the highest and lowest intake values. ……………………………………………………………………….123 Table 5.7: Phenotypic correlations for grazing intake estimated using TiO2 (GDMI, kg) and measurements using CowManager ear accelerometers. ………………….125 Table 5.8: Summary statistics for dry matter intake measured by a GrowSafe system and estimated dry matter intake with the use of a biomarker titanium dioxide on beef steers (n=32). ……………………………………………………...126 xi LIST OF FIGUES Figure Page Figure 2.1: Calan Gates are pictured on the left and animals equipped with electronic keys pictured on the bottom (http://www.animal.ufl.edu/facilities/bru/images/calang2.jpg)..................................11 Figure 2.2: Picture of GrowSafe System feed bunks at Colorado State University’s Feed Intake Unit.………….………………………………………………………...12 Figure 2.3: Picture of Insentec Monitoring System (http://www.hokofarmgroup.com/ric/feed-weigh.aspx).............................................13 Figure 2.4: SmartFeed feed monitoring system. On the left are the SmartFeed feed bunks in a feedlot and on the right is the SmartFeed trailer that can be transported to various locations (https://www.c-lockinc.com/shop/feed-intake-measurements/smartfeed/)................14 Figure 2.5: Picture of grazing cage (Nobel Research Institute, 2017)……………………...……18 Figure 2.6: Contributions of biological mechanisms to variation in residual feed intake as determined from experiments on divergently selected cattle (Richardson and Herd, 2004)……………………………………………………….26 Figure 4.1: Schematic representation of simulated data used to generate populations of cattle for single trait selection for either daily dry matter intake, residual feed intake, or an economic selection index……………………………….82 Figure 4.2: The simulated changes in phenotypic dry matter intake and yearling weight for three selection scenarios. SDDMI was the single trait selection of dry matter intake and the response to the genetically correlated trait yearling weight. SRFI was the selection of residual feed intake and the response of genetically correlated traits of dry matter intake and yearling weight. SESI was a simulation of selection using economic index values with genetically correlated traits of dry matter intake and yearling weight……...…90 Figure 4.3: The average per head progeny profit or loss for three simulation scenarios. SDDMI was a simulation for the single trait selection on average daily dry matter intake, SRFI was the simulation for selection on residual feed intake, and SESI is the simulation for use of an economic index for yearling weight and feed intake……………………………………………………..96 xii Figure 4.4: The profit or loss for the progeny from three simulation scenarios. SDDMI was a simulation for the single trait selection on average daily dry matter intake, SRFI was the simulation for selection on residual feed intake, and SESI is the simulation for use of an economic index for yearling weight and feed intake………………………………………………………………………97 Figure 5.1: Picture of Colorado State University’s Eastern Colorado Research Center diagraming the positioning of CowManager routers (Google Earth, 2019)……….112 Figure 5.2: Picture of GrowSafe System feed bunks (right side of picture) and concrete feed bunk (left side of picture) at Colorado State University’s Feed Intake Unit………………………………………………...…………………116 Figure 5.3: Plot from the principle component analysis for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT)………………………………122 xiii LIST OF EQUATIONS Equation Page Equation (2.1): Feed conversion ration….……………………………………………………….21 Equation (2.2): Residual feed intake……..………………………………………………………23 Equation (2.3): Heritability………………………………………………………………………31 Equation (3.1): Linear BLUP animal model with maternal effects…….………………………..60 Equation (3.2): Variances and means included in animal model with maternal effects…………60 Equation (3.3): Multi-trait BLUP animal model with maternal effects………………………….61 Equation (3.4): Variances and means included in multi-trait animal model with maternal effects………………………………………………………………………..…62 Equation (4.1): Multi-trait BLUP model……..………………………………………………….73 Equation (4.2): Variances included in multi-trait BLUP model…..……………………………..73 Equation (4.3): Weighted mean for phenotypes…………………………………………………74 Equation (4.4): Weight heritabilities……………………………………………………………..75 Equation (4.5): Weighting factor to weight heritabilities…….………………………………….76 Equation (4.6): Standard error for weighted heritabilities….……………………………………76 Equation (4.7): Fisher’s Z transformation for phenotypic and genetic correlations…..…………76 Equation (4.8): Standard errors for Fisher’s Z transformation…….……………………………77 Equation (4.9): The pooled Fisher’s Z…………………………………………………………..77 Equation (4.10): Transformation of pooled Z back to correlation……….………………………77 Equation (4.11): Generation interval…………………………………………………………….80 Equation (4.12): Positive-definite matrix A for Cholesky decomposition………………………84 Equation (4.13): Derivation of diagonal matrix elements of Cholesky factor…..……………….84 xiv Equation (4.14): Derivation of off diagonal matrix elements of Cholesky factor….……………84 Equation (4.15): Progeny observations……..……………………………………………………85 Equation (4.16): Economic selection index……………………………………………………...86 Equation (4.17): Animal profit calculation………………………………………………………87 Equation (4.18): Economic selection index used for simulation…..…………………………….88 Equation (4.19): Final economic selection index with weighting factors…..…………………...88 Equation (5.1): Grazing intake estimation via biomarker……….……………………………...113 Equation (5.2): Fecal output….………………………………………………………………...114 Equation (5.3): Full regression model for CowManager ear tag accelerometer….…………….117 xv CHAPTER I INTRODUCTION AND OBJECTIVES 1.1 Introduction Sustainability of any agricultural production system is dependent on the profitability of the production system. Traditionally, the beef industry has placed emphasis on improving output traits, such as growth and fertility, to improve profitability (Arthur et al., 2001; Hill, 2012) but profitability of any production system is dependent on both output and input traits. In economic environments of rising feed costs and resource constraints, producers in the beef industry have become increasingly aware of the need to improve input/cost traits, such as feed intake. Feed costs have been attributed to the largest production expense for cow/calf producers accounting for 50% to 70% of total production costs (Anderson et al., 2005). Decreasing feed costs while maintaining animal performance could have large impacts on the profitability of a beef operation. A 10% increase in performance (i.e. gain) has been reported to contribute an 18% increase in profits, as compared to a 10% improvement of feed efficiency (increasing performance while simultaneously decrease feed intake) which is reported to increase profits by 43% (www.beefefficiency.org). A report from the Alberta Agriculture and Forestry Ministry (2006) stated that a 5% improvement in feed efficiency would have 4 times the economic effect of a 5% improvement in average daily gain. Therefore, maintaining animal performance while decreasing feed costs could have large impacts on the profitability, and therefore the sustainability, of a beef operation and could make beef more competitive against other, cheaper proteins such as pork or poultry. 1 In addition to the economic benefits associated with reductions in of feed intake, there are environmental benefits to consider. The world population is estimated to reach 9.7 billion by 2050 which will require an increase in agricultural output of 70% with increasing constraints on resources (FAO, 2009). To sustain animal agriculture as a protein source for this growing population, cattle will have to be produced on fewer natural resources such as feed or forage. With increases in the human population, there are also concerns of intensifying climate change and ruminants have been associated with contributing 80% of livestock greenhouse gas emissions (Gerber et al., 2013). Feed intake has been shown to be positively correlated to greenhouse gas emission from beef cattle. Herd et al. (2014) found that methane production was positively correlated with DMI (0.65 ± 0.02) and that the reduction of feed intake while maintaining production through genetic selection would contribute to a reduction in greenhouse gases. Cottle (2011) proposed a selection index using feed intake for indirect selection for the reduction of greenhouse gases. Considering that cattle finished in a feedlot spend 50 to 70% of their lifespan grazing forage prior to feedlot entry (Capper, 2011), a reduction of forage intake would likely contribute to the reduction of greenhouse gases. Furthermore, reducing forage intake while maintain stocking rates on rangelands has the potential to improve pasture quality. When cattle require less feed for production, stress placed on pastures due to drought, overgrazing, or climate change can be mitigated. Due to the importance of feed costs to the sustainability and profitability of a beef operation, interest in selecting cattle that are more feed efficient has increased. Several breed associations have begun to publish expected progeny differences (EPD) for feed intake or traits of feed efficiency, such as residual feed intake (RFI). In order to select cattle that are more efficient, individual feed intake must be measured. Since the mid-1990’s, technological advances have 2 allowed for a large increase in the measurement of feed intake on group housed animals (Cruz et al., 2011; Hill, 2012, Arthur et al., 2014). The collection of feed intake measures is expensive, time consuming and testing facilities have a limited capacity for the measurement of individual feed intake (Wang et al., 2006; Nielsen et al., 2013). These limitations restrict the number of animals that can be measured annually and therefore limit the amount of data generated for genetic evaluations. Current individual feed intake measurements are obtained in feedlot environments and have a direct application to feedlot cattle. The translation and application of these feedlot-measured intakes outside of a feedlot environment is essentially unknown. This is significant given that approximately 50% of feed costs in the beef industry are attributed to the mature cow herd (Whisnant, USDA-NIFA-CRIS) which is generally maintained in much more extensive environments with forage-based diets, typically grazing on rangelands. To select for a cowherd that is more efficient in forage utilization, individual grazing intake needs to be measured. Currently there is no technology to effectively measure feed intake on a large population of grazing cattle. Methods used for estimation of dry matter intake (DMI) for grazing animals lack precision and are often tedious, expensive and time-consuming (Undi et al., 2008). Current techniques for measuring grazing DMI typically involve digestive markers, herbage disappearance measured on group housed animals, or equations predicting DMI based on net energy requirements (NRC 2000; Meyer et al., 2008; Undi et al., 2008). To date, there are large gaps of knowledge on feed intake as a phenotype, such as the relationship of feed intake measured in a feedlot to forage intake and the importance of maternal effects on feed intake. In addition, there is a debate as to the application of feed intake as an economically relevant trait and how it should best be used for selection decisions and for genetic 3 improvement. The overarching objective of this dissertation is to explore a novel approach to estimating forage intake, explore maternal effects on feed intake, and illustrate different approaches of genetic selection for feed efficiency. 1.2 Objectives The underlying theme of this dissertation is to further examine feed intake and its application to the beef industry. This will be accomplished through 3 projects: 1. To explore and estimate parameters for the maternal genetic effects of feed intake on beef cattle. 2. To determine the effects of direct selection on DMI, residual feed intake (RFI), or an economic selection index using simulated data to illustrate which selection method would be more desirable for production. 3. To develop a method or approximation for measuring intake on grazing beef cattle through measured behavior such as eating time or rumination. 4 LITERATURE CITED Alberta Agriculture and Forestry. 2006. Agri-Facts: Residual feed intake (net feed efficiency) in beef cattle. https://open.alberta.ca/dataset/91a77dec-f0a4-49c2-8c54f172fe568e2c/resource/721e982c-b90f-4605-9de0-a3b8bb312b1f/download/2006-42011-1.pdf. (Accessed April 30, 2017). Anderson, R. V., R. J. Rasby, T. J. Klopfenstein, and R. T. Clark. 2005. An evaluation of production and economic efficiency of two beef systems from calving to slaughter. J. Anim. Sci. 83: 694-704. Arthur, P. R., J. E. Pryce, and R. M. Herd. 2014. Lessons learnt from 25 years of feed efficiency research in Australia. Proc. 10th World Congr. Genet. Appl. to Livest. Prod., Vancouver, Canada. Arthur, P. R., J. A. Archer, R. M. Herd, and G. J. Melville. 2001. Response to selection for net feed intake in beef cattle. Proc. Assoc. Advmt. Anim. Breed Genet. 14: 135-138. Capper, J. L. 2011. The environmental impact of beef production in the United States: 1977 compared with 2007. J. Anim. Sci. 89: 4249-4261. Cottle, D. J. 2011. Use of residual feed intake as an indirect selection trait for reduction of methane emission on grazing beef cattle. Proc. Assoc. Advmt. Anim. Breed Genet. 19: 423-425. Cruz, G. D., J. B. Trovo, J. W. Oltjen, and R. D. Sainz. 2011. Estimating feed efficiency: Evaluation of mathematical models to predict individual intakes of steers fed in group pens. J. Anim. Sci. 89: 1640-1649. 5 FAO. 2009. How to feed the world in 2050. Food and Agriculture Organization of the United Nations, Rome, Italy. Gerber, P. J., H. Steinfeld, b. Henderson, A. Mottet, C. Opio, J. Dijkman, A. Falcucci, and T. Tempio. 2013. Tackling climate change through livestock – A global assessment of emissions and mitigation opportunities. Food and Agriculture Organization of the United Nations, Rome, Italy. Herd, R. M., P. F. Arthur, K. A. Donoghue, S. H. Bird, T. Bird-Gardiner and R. S. Hegarty. 2014. Measures of methane production and their phenotypic relationships with dry matter intake, growth, and body composition traits in beef cattle. J. Anim. Sci. 92: 5267-5274. Hill, R. A. 2012. Feed Efficiency in the Beef Industry. Wiley-Blackwell, Oxford, UK. p. 7-18. Meyer, A. M., M. S. Kerley, and R. L. Kaleenbach. 2008. The effect of residual feed intake classification on forage intake by grazing beef cows. J. Anim. Sci. 86: 2670-2679. National Program for Genetic Improvement of Feed Efficiency in Beef Cattle. USDA. http://www.beefefficiency.org (Accessed April 30, 2017). Nielsen, M.K., M.D. MacNeil, J.C.M Dekkers, D.H. Crews Jr., T. A. Rathje, R.M. Enns, and R.L. Weaber. 2013. Review: Life-cycle, total industry genetic improvement of feed efficiency in beef cattle: Blueprint for the Beef Improvement Federation. Prof. Anim. Sci. 29: 559-565. NRC. 2000. Nutrient requirements of beef cattle. 7th rev. ed. Natl. Acad. Press, Washington, DC. Undi, M., C. Wilson, K. H. Ominski and K. M. Wittenburg. 2008. Comparision of techniques for estimation of forage dry matter intake by grazing beef cattle. Can. J. Anim. Sci. 88:693701. 6 Wang, Z., J. D. Nkrumah, C. Li, J. A. Basarab, L. A. Goonewardene, E. K. Okine, D. H. Crews, Jr. and S. S. Moore. 2006. Test duration for growth, feed intake, and feed efficiency in beef cattle using the GrowSafe System. J. Anim. Sci. 84: 2289-2298. Whisnant, C. USDA-NIFA-CRIS Research. http://cris.csrees.usda.gov/cgibin/starfinder/6244/crisassist.txt (Accessed April 30, 2017) 7 Chapter II LITERATURE REVIEW 2.1 Introduction Sustainability and profitability of agricultural systems are dependent on both outputs and inputs. In the beef industry, producers have traditionally placed emphasis on improving output traits, such as fertility and live weight, to increase profitability (Arthur et al., 2001; Hill, 2012). However, increasing outputs often lead to increased inputs, such as feed costs (Meyer et al., 2008). Feed costs are the largest variable expense in the beef industry accounting for 50 to 70% of total production costs (Anderson et. al, 2005). It has been estimated that a 10% increase in weight gain would increase profits by 18%, this is in contrast to a 10% improvement in feed efficiency which has been estimated to increase profits by 43% (www.beefefficiency.org). This suggests improvement in feed efficiency would have a larger impact on profit as compared to the same magnitude of improvement on performance. This is further supported by the Alberta Agriculture and Forestry Ministry (2006) that reported that a 5% improvement in feed efficiency would have 4 times the economic effect of a 5% improvement in ADG. Therefore, decreasing feed costs without sacrificing animal performance could have large impacts to the profitability of a beef operation. There is debate as to the best phenotype for feed efficiency in cattle, how to incorporate it into a breeding program and what impacts selection on feed intake or efficiency would have on other performance traits (Berry and Pryce, 2014). The traditional phenotypic measures of feed efficiency in the beef industry were ratios of intake to production and generally on pens of cattle. 8 Also, direct selection of ratios is typically problematic due to inherent problems of selection for ratio measures (Gunsett, 1986). More recently, residual feed intake (RFI) has become the phenotype of interest for feed efficiency in livestock production because it considers production levels of the animals (Berry and Crowley, 2013). Due to the large influence of feed costs on production profits, interest in selecting for cattle that are more feed efficient has increased. However, to select for more feed efficient cattle, individual feed intakes must be measured. Currently, individual feed intake measurements are collected in feedlot environments and the application of these measurements outside of the feedlot has yet to be quantified (Berry and Crowley, 2013). Furthermore, the relationships between these feedlot-measured intakes and the cowherd grazing on rangeland are unknown. Approximately 50% of variable feed costs and 70 to 75% of total annual energy for maintenance in the beef industry are attributed to the mature cow herd (Whisnant, USDA-NIFA-CRIS; Ferrell and Jenkins, 1985). To select for a cowherd that is more efficient for forage utilization, grazing intake needs to be measured. Currently, there are no simple technologies to measure feed intake on a population of grazing cattle. The relationship between feed intake measured in current feed trials and intake from grazing cattle are unknown. 2.2 Measuring Feed Intake The ability to measure feed efficiency in cattle is dependent on the capability to measure individual feed intake (FI) and the quality of these records (Hill, 2012). Traditional methods for the collection of intakes per animal involved housing cattle individually. Research has shown an inadequacy of feed intake data for individually housed cattle for the purpose of genetic evaluations 9 (Hill, 2012) given that the collection of FI on individually housed animals severely limited the number of animals that could be measured and thus limited the ability for estimation of reliable genetic parameters of FI. Since the mid-1990’s, advancements in technology such as radio electronic identification (RFID) of animals, have led to a large increase in the measurement of FI for group housed animals (Cruz et al., 2011; Hill, 2012, Arthur et al., 2014). 2.2.1 Equipment and Guidelines for Measuring Feed Intake Traditional methods for measuring individual FI involved to individually housed cattle. Specifically, cattle were allocated to a pen where each animal’s feed was weighed before being placed into the bunk. Feed that was not consumed throughout the day, was subsequently weighed and subtracted from the initial feed weight. The difference in feed weight was the animal’s FI. This process was extremely time consuming and limited the number of animals that could be measured throughout the year. In addition, this method did not accurately reflect the behavior of group housed animals whose social behaviors may affect their FI (DeHaer and Mercks, 1992; Neilsen et al., 1995; Guiroy et al., 2001; Chapinal et al., 2007; Cruz et al., 2011) With increased need for the collection of feed intake data, research facilities and performance-testing centers have been equipped with the technology for the capability to measure individual feed intake on group housed animals (Hill, 2012). Technology to measure feed intake must be capable of identifying individual animals, weighing rations fed to the individual animal, associate the measured feed consumed to the appropriate animal and compile the data into a useable format (Dahlke et al., 2008). Prominent technologies used for measuring feed intake are the Calan Gate System (American Calan, Inc.; Northwood, NH), GrowSafe Systems (GrowSafe 10 Systems, Ltd., Airdire, Alberta, Canada), Insentec (Hokofarm; Marknesses, The Netherlands) and Smartfeed (C-Lock Inc.; Rapid City, SD). Calan Gate Systems (Figure 2.1) are a system of feed bunks that require a “key” for an animal to access the feed within their individual bunk. In this system the door of the bunk transmits an electrical signal which the animal’s key recognizes and the door is unlocked. The animal pushes the door open and is able to access the feed. While an animal is consuming feed in the bunk, the narrow door to the bunk prevents other animals in the pen from accessing the feed from that specific bunk. The restriction of animals to specific bunks allows researchers to dispense individual diets to specified animals in addition to measuring individual feed intake (American Calan, Inc.; http://americancalan.com). A disadvantage of the Calan Gate System is that animals must be trained to use the system and access the bunks (Stock and Klopfenstein, 1986; Cole, 1995). Therefore, it is imperative that animals have an extended adaptation period up to 3 weeks for Calan Gates (Stock, 1986). It should also be noted that a small percentage of cattle cannot be trained to this system which limits the number of cattle for data collection. Figure 2.1. Calan Gates are pictured on the left and animals equipped with electronic keys pictured on the bottom (http://www.animal.ufl.edu/facilities/bru/images/calang2.jpg). 11 In contrast, GrowSafe Systems (Figure 2.2) utilize electronic scales built into the feed bunk. Animals are equipped with an electronic ear tag that the GrowSafe system uses to identify each individual. When the ear tag enters into the GrowSafe feed bunk, the system registers the animal and weighs the feed in the bunk. When the animal removes its head from the bunk, the system weighs the feed again. The difference between the two weights is the animal’s measured feed intake. The presence of the electronic ear tag initiates the feeding event and intake record. The system also measures the amount of time an animal spends at the bunk. The data is then transmitted for processing and reporting of individual feed intake (GrowSafe Systems, Ltd.; http://growsafe.com; Dahlke et al., 2008). Unlike Calan Gates, as long as the cattle are accustomed to eating from a feed bunk, the time spent to acclimate animals to GrowSafe is reduced. Figure 2.2. Picture of GrowSafe System feed bunks at Colorado State University’s Feed Intake Unit. 12 The Insentec monitoring system (Figure 2.3) are a series of feed bunks with barriers that are lowered to allow access the feed within the bunk. Each individual animal is equipped with an electronic ear tag that Insentec uses for animal identification. As the animal approaches, an antenna detects the electronic ear tag for the individual animal and lowers the barrier, allowing the animal access to feed inside the bunk. When the animal leaves the bin, the barrier is raised until another animal approaches the feed bin. When the animal exits the feed bunk, Insentec records the initial and finial time and feed weight to determine feeding duration and intake (Chapinal et al., 2007). Figure 2.3. Picture of Insentec Monitoring System (http://www.hokofarmgroup.com/ric/feed-weigh.aspx). SmartFeed (Figure 2.4) measures feed intake similar to the GrowSafe system. SmartFeed utilizes an electronic ear tag that identifies an animal when their head enters the feed bunk. The 13 feed within the bunk is weighed and when the animal retracts their head from the bunk, the amount of feed is measured again. The difference in feed weight is the animals FI. The primary difference between SmartFeed and GrowSafe, is the mobility of SmartFeed. SmartFeed is designed to be portable, self-contained and can be purchased as transportable trailers with 2 to 4 feed bunks per trailer. These trailers have the potential for use in pastures for measurement of supplement intake. To date, there is limited literature evaluating the use of SmartFeed to measure FI. Most literature references for the use of SmartFeed has been for supplementation and trace mineral studies; however, the application for measuring feed intake using SmartFeed is increasing (McCarthy et al., 2018; Wyfells et al., 2018). Figure 2.4. SmartFeed feed monitoring system. On the left are the SmartFeed feed bunks in a feedlot and on the right is the SmartFeed trailer that can be transported to various locations (https://www.c-lockinc.com/shop/feed-intake-measurements/smartfeed/). The above section described 4 technologies that are prominently used for the collection of individual feed intake in cattle. Given the increasing interest in feed intake, new technologies and methods for measuring FI will continue to develop and evolve. 14 2.2.2 Feeding Trials for Feed Intake When incorporating feed intake or traits requiring feed intake measures into a breeding objective, the goal of the test is to produce the maximum number of responses for data collection and precision at the minimum cost (Archer et al., 1997). Measuring feed intake is expensive and time consuming (Wang et al., 2006; Nielsen et al., 2013), a problem which is exacerbated by limited capacity for testing facilities to measure individual feed intake (Nielsen et al., 2013). These limitations restrict the number of animals that can be measured within a year and therefore limit the amount of data generated for genetic evaluations. Optimizing testing periods for the measurement of feed intake and efficiency is crucial to increase the number of animals measured within facilities but still obtain reliable measures for intake and efficiency. In 1997, Archer et al. published the results from a study examining the optimum test duration to standardized measurement protocols for measuring feed intake and RFI. The authors compared the genetic and environmental variances, genetic and phenotypic correlations, and the predicted correlated response to selection (selection efficiency) of 119-d test with shortened tests. The shortened test lengths ranged from 7-d to 119-d. The resulting correlations were assessed for the test length with the same traits as the 119-d test. The authors concluded that the measurement of feed intake required a minimum of a 35-d test and a 70-d test would be required to obtain RFI measures. They also concluded that although phenotypic correlations would be useful indicators of the ability to shorten test lengths, if the ultimate goal was genetic selection comparison of genetic correlations between full and shortened tests would be more relevant. Following the work by Archer et al. (1997), Archer and Bergh (1999) examined different breeds of beef cattle and concluded that testing length for residual feed intake (RFI) could be shortened to 70-d regardless 15 of breed. More recently, it was reported that shortening testing periods to 56-d for the calculation of RFI would lead to limited loss in information compared to a 70-d testing period (Culbertson et al., 2015). In all research examining testing length, the driving factor for test length for feed efficiency was the ability to obtain a reliable measurement of average daily gain (ADG). Retallick et al. (2015) reported a strong genetic correlation between on-test ADG and post-weaning gain (PWG) from national cattle evaluations. Based on this genetic correlation, the authors concluded that the PWG could be used as a proxy for on-test ADG, allowing producers to reduce the length of feed intake testing periods. As a result of Archer et al. (1997), guidelines for measuring feed intake and efficiency were defined to be a 70-d test for standardize feeding trials for measuring FI. The Beef Improvement Federation (BIF) proposed a set of guidelines for the collection of feed intake and calculations of feed efficiency as well. The BIF guidelines recommend a 21-d adaptation period to allow cattle to acclimate to the testing facility. This was followed by either a 45-d or 70-d testing period depending on the phenotype of interest. A minimum of 70-d testing period was recommended to accurately measure average daily gain for the use of calculating feed efficiency and for feed intake a 45-d testing period are sufficient. An animal’s age during a testing period is related to their feed intake. Therefore, BIF recommends the age when an animal enters a feeding test be post weaning but no younger than 240-d, but the test should be completed prior to the animal reaching 390-d. Cattle should also be contemporary grouped within 60-d of age at the beginning of the testing period (BIF, 2016). 16 2.2.3 Measuring Grazing Intake Currently, individual feed intake measurements are collected in feedlot environments and have a direct application to feedlot performance. The translation of these feedlot-measured intakes to the cowherd grazing on rangeland is unknown. Approximately 50% of the varied feed costs in the beef industry are attributed to the mature cow herd (Whisnant, USDA-NIFA-CRIS; accessed April 2017). To select for a cowherd that is more efficient for forage utilization, individual grazing intake needs to be measured or an indicator trait for grazing intake needs to be established. Previous methods used for estimation of FI for grazing cattle lacked precision and were often tedious, expensive and time-consuming (Undi et al., 2008). Current techniques for measuring grazing FI typically involved digestive markers, group housed animals where herbage disappearances are measured, or equations predicting FI depending on net energy requirements (Meyer et al., 2008: Undi et al., 2008). Currently, there is no technology to efficiently measure individual feed intake on a large population of grazing cattle and the relationship between feed intake measured in a feedlot and intake from grazing cattle are relatively unknown. Studies involving group housed animals typically involve a number of animals confined to a pasture sections (referred to as paddocks) where herbage disappearance is measured and averaged for the group of animals. These studies usually utilize grazing cages (Figure 2.5), where a small section of the paddock is enclosed to keep animals from grazing and allow un-grazed forage growth. At the conclusion of the grazing trial, the difference in biomass within and outside of the cage are compared in order to calculate herbage disappearance (Burns et al., 1994; Undi et al., 2008). Grazing intake can be determined for the group of animals, but unless animals are individually housed within a paddock, determining individual grazing intake is not possible. 17 Figure 2.5. Picture of grazing cage (Nobel Research Institute, 2017). The most commonly used method of forage intake estimation is the use of digestive markers such as chromium oxide, titanium dioxide and n-alkanes (Gordon 1995; Titgemeyer et al., 2001; Undi et al., 2008). Long chain n-alkanes occur naturally in plants and have been used as digestive markers for the estimation of forage FI through the recovery of alkanes in feces (Dove and Mayes, 1991). Chemical digestive markers, such as chromium oxide and titanium dioxide, can be used to estimate the FI based on the concentration level of the marker in feces of individual cattle (Undi et al, 2008; Titgemeyer et al., 2001). The implementation of digestive markers for the collection of FI phenotypes in a production setting is not practical since it is labor intensive and tedious to obtain the actual measurement. Empirical methods of estimating FI for grazing cattle have also been tested. Prediction equations using BW and ADG have been developed to estimate FI of cattle (NRC 2000; Minson and McDonald, 1987; Undi et al., 2008). The National Research Council (2000) have published prediction equations which estimated FI as a function of dietary net energy for maintenance (NEm) and BW. These estimations were appropriate when estimating the required FI for a group of cattle; 18 however, the estimations fails to account for variability in FI between individual cattle of the same BW. 2.3 Measures of Feed Intake and Efficiency Efficiency is defined as a level of performance that uses the lowest amount of input to obtain the greatest level of output (www.investopia.com). Efficiency can be described at a production level as the saleable output per unit input, weighted according to their relative economic importance (Berry and Crowley, 2013). Feed intake and feed efficiency are important, contributing factors to the economics for production efficiency (Berry and Crowley, 2013; Hill 2012). Given that feed variable costs are the largest expense to producers, feed intake and efficiency has a direct economic relevance and is therefore considered an economically relevant trait (Neilsen et al., 2013). However, there is no definitive definition of feed efficiency in beef cattle and several definitions and calculations for feed efficiency exist. Feed efficiency in beef cattle is typically described as either a ratio or residual trait (Berry and Crowley, 2013). In the context of genetic improvement, there is often a debate as to what is the best measure for feed efficiency, how to incorporate feed efficiency into a breeding program and what the impact of selection would do to other performance traits (Berry and Pryce, 2013; Nielsen et al., 2013). 2.3.1 Feed Intake For the purpose of this review, feed intake (FI) is the amount of feed an individual animal ingests on a dry matter basis. Factors that influence individual FI in cattle are complex and not 19 fully understood (NRC, 2000). Physiological factors influencing FI are body composition, frame score, physiological state and age. Sex was reported by the NRC (2000) to have limited effect on FI. An animal’s body fat composition can affect FI. When predicting FI for beef cattle, percent body fat is often considered because the relationship between FI and body fat is a management tool for feedlots to determine the appropriate slaughter condition of beef cattle based on the animals’ FI (NRC, 2000). Fox et al. (1988) estimated a decrease in FI of 2.7 percent for each 1 percent increase in body fat within the range of 21.3 to 31.5 of percent body fat for growing cattle. The NRC (1987) theorized that adipose tissue may have a feedback roll that influences FI. Therefore, when assessing the FI of younger growing cattle or older mature cattle, the influence of percent body fat should be considered. The age of an animal when placed on feed can affect that animal’s FI. Yearling cattle have a higher FI when compared to weaned calves. However, this increase in FI may be attributed to the increase in body weight and size. The NRC (2000) reported that “the greater the ratio of age to body weight for yearling cattle prompts greater feed intake.” This ratio of age to body weight has been related to the increase in feed intake for cattle experiencing compensatory growth. Yearling cattle have been reported to have a 10 percent increase per unit body weight in estimated FI compared to cattle started on feed as calves (NRC, 1984; Fox et al., 1988). The frame score, or body size, of an animal can also influence their intake. The larger the animal, the higher the FI. Currently, there is a lack of designed studies to further the understanding of the biological effects of age and body weight or composition on FI (NRC, 2000). The physiological status of an animal, such as lactation or pregnancy, can significantly alter the animal’s energy requirements and therefore affect FI. For lactating cattle, net energy and 20 protein requirements are at their highest during peak lactation (Adams et al., 1996). According to the Agricultural Research Council (ARC, 1980), FI increases by 35 to 50 percent for lactating animals when compared to non-lactating animals of the same BW and diet. Therefore, cattle bred for higher levels of milk production would be expected to have an increase in FI due to the increase in energy requirements (NRC, 2000). A cow’s stage of pregnancy can also affect her FI; however, the overall physiological effect of pregnancy on individual feed intake is relatively unknown (Arthur et al., 2001). Nutritional studies have shown a decrease in FI for cows during their last stage of pregnancy. Research has shown a decrease of 1.5 to 2 percent per week of FI during the animals last month of pregnancy (Ingvartsent et al., 1992). 2.3.2 Feed Conversion Ratios Traditional measures of feed efficiency in the beef industry were ratios of intake and production traits. Feed conversion ratio (FCR) is the most commonly used measure for feed efficiency (Berry and Pryce, 2013) and widely used in production settings (Nielsen et al., 2013). However, FCR does not account for the differences in maintenance efficiency among individual animals (Berry and Crowley, 2013). Feed conversion ratio is routinely represented as follows: "#$ = &'()*+( -*./0 1*.2 "((3 425*6( 21 (Eq. 2.1) Feed conversion ratios are often referred to as gain to feed (G:F) or it’s reciprocal feed to gain (F:G). These measures are regularly used in feedlots using pen averages for ADG and feed intake. Animals with higher values for FCR are considered to be more efficient. Heritabilities for FCR range from 0.06 to 0.41 (Berry and Crowley, 2013). This suggests that genetic improvement in FCR is possible but direct selection on ratios makes the expected response to selection difficult to ascertain (Gunsett, 1986; Berry and Crowley, 2013). Gunsett (1986) argued “prediction of response to selection practiced to change a trait such as feed conversion assumes that the trait has a normal distribution with some mean and variance. The fact that feed conversion is a ratio of two traits has made the ability to predict the change of the trait in future generations difficult.” Placing selection pressure on the components that comprised the ratio would be more effective for improved feed efficiency (Gunsett, 1986). Although FCR is easy to calculate and accepted for use in the U. S. beef industry, it is not an ideal measure of feed efficiency for the purpose of genetic improvement given the inherit problems with selection on ratios as the phenotype. This has led to the proposal of other traits for genetic improvement on feed efficiency, such as residual feed intake. 2.3.3 Residual Feed Intake Koch et al. (1963) introduced the use of RFI as a measure of feed efficiency. The authors proposed that feed efficiency was not a directly measurable trait but must be calculated as a function of feed intake, increase in body weight, and time. They concluded that efficiency expressed as gain adjusted for differences in feed consumption, or the deviation from the regression of gain on feed intake, was considered the most accurate mathematical description for 22 phenotypic feed efficiency. Since 1963, the general definition of RFI has developed into the difference between actual feed intake and the estimated feed intake adjusted for the requirements of production (Kennedy et al., 1993). A typical RFI equation for beef cattle would be: $"4 = -74 − (:; &-1 + := "*5 + :> ?@ A.CD ) (Eq. 2.2) where -74 was the individual animal’s dry matter intake, &-1 was an animal’s average daily gain, "*5 is the animal’s ultrasound measurement for back fat, WT0.75 was the metabolic mid test weight for an animal, and :F is the regression coefficient for the corresponding predictor (i.e. ADG). Metabolic mid weight is estimated by taking the animal’s weight at the midpoint of the test and raising it to the ¾ power. Including WT0.75 in the model for RFI accounts for energy sinks associated with the energy requirements for body weight (Berry and Crowley, 2013; NRC, 2000). Cattle with positive RFI values would be considered inefficient as their feed intake was more than what was expected for their level of performance. Negative RFI values suggest cattle who are more efficient as their feed intakes were less than what was expected given their level of performance. An attraction of RFI is its independence from variables included in the multiple regression model (i.e. ADG). Given that RFI are residual terms of the model (Eq. 2.2), they are dependent on the variables included in the model. As the complexity of the model increases, the variation in RFI will reduce but the risk of over parameterizing the model increases as well (Koch et al., 1963; Kennedy et al., 1993; Berry and Pryce, 2014). An advantage to RFI is that it is a measure of feed efficiency (Berry and Pryce, 2014). This is compared to FI which only measures the amount of feed ingested by cattle and doesn’t account 23 for the animal’s performance. An animal’s intake will depend on their level of performance, stage in life and the actual size (NRC, 2000). Larger cattle will have a higher FI while FI for smaller cattle will be lower. Selecting for cattle with lower FI may inadvertently select for smaller cattle (Nielsen et al., 2013) and therefore, a single measure of feed efficiency would have to account for reduced FI without sacrificing gain in body weight. Residual feed intake is also heritable, which would mean that genetic selection for lower RFI would be possible. Numerous studies have estimated heritabilities for RFI in several populations of cattle. Estimates of RFI have been reported ranging from 0.07 to 0.62 (Berry and Pryce, 2014; Berry and Crowley, 2013). Berry and Pryce (2014) reported a pooled heritability for RFI at 0.33 from 36 previous studies which would be considered moderate. Selection on RFI compared to FI included in an index was shown to be mathematically equivalent by Kennedy et al. (1993). Selecting for RFI does have substantial benefits over selecting for FCR, since, as stated above, the selection of cattle for breeding based on ratios are problematic (Gunsett, 1986). There are several disadvantages to RFI for application in the beef industry. One disadvantage of RFI is that it can be conceptually difficult to explain to producers (Berry and Pryce, 2014). From a technical standpoint, calculations for RFI would seem complex and difficult for some producers to understand. Residual feed intake values dependent on the group in which they were calculated (i.e. their contemporary group) and are susceptible to genetic by environment interactions (Berry and Crowley, 2013) and a direct comparison of RFI values cannot be made across contemporary groups. Since RFI is a residual from within a regression model, the phenotypic value of the RFI can only be compared to other animals that were included within the model. Actual RFI values are dependent on effects included in the model as these would change the resulting residuals. Residual feed intake is essentially a selection index (Eisen, 1997) and RFI 24 values are dependent on contemporary groups (CG) since phenotypic indexes do not account for environmental differences (Bourdon, 1997). These disadvantages of RFI become problematic when trying to incorporate this variable into a genetic evaluation. Varying conditions such as different equipment between testing facilities or environmental conditions may be problematic. These varying conditions potentially affect the mean and the variance of the observations (Nielsen et al., 2013). Equations for estimating RFI would also have to be standardized. Differences in what is included in the models would change the RFI values and could result in a re-ranking of animals. 2.4 Biological Factors of Feed Efficiency The biological functions influencing feed efficiency are not fully understood and it is to be expected that many mechanisms are associated with phenotypic feed efficiency in livestock (Herd and Arthur, 2009; NRC 2000). Intuitively, variations in feed efficiency depend on differences in biological processes (Herd and Arthur, 2009) and this variation is likely associated with at least 5 major processes: FI, feed digestion, metabolism, activity and thermoregulation (Herd et al., 2004). Richardson and Herd (2004) described many physiological mechanisms that contribute to the variation observed in RFI for Angus steers divergently selected for low and high RFI. They concluded that metabolic heat production, body composition, and physical activity accounted for 73% of variation in RFI. Figure 2.5 illustrates the portions of variation of RFI explained by each physiological function. 25 Figure 2.6. Contributions of biological mechanisms to variation in residual feed intake as determined from experiments on divergently selected cattle (Richardson and Herd, 2004). The body composition of an animal affects the variation of feed efficiency of that animal. The deposition of fat versus lean tissue has different energy costs. There is less variation for the depositing of fat gain when compared to lean gain. Theoretical partial efficiencies of nutrient use for lean gain is estimated at 40 to 50% where the nutrient use for fat gain is estimated at 70 to 95%. The metabolism of protein has a greater amount of variation in efficiency when compared to fat metabolism. This variation in body composition and gain would influence the efficiency of nutrient utilization (Herd and Arthur, 2009). Richardson et al. (2001) reported a correlation between chemical composition and genetic variation for RFI for Angus steers divergently selected for RFI. The authors of that report stated that steers from low-RFI parents had less whole-body fat and more whole-body protein then the steers from high-RFI parents. Also, been reported and described in literature, that animals with high RFI tend to have more fat deposition then animals with lower RFI values (Carstens et al, 2002; Nkrumah et al., 2007; Hill, 2012). 26 2.4.1 Mitochondrial Function Feed efficiency is affected at many levels from the animal as a whole, from environmental effects, to differences at the cellular level (Bottje and Kong, 2013). Mitochondria are the energy production organelles of the cell, producing approximately 90% of the cell’s energy and the majority of ATP (Kolath et al., 2006; Herd and Arthur, 2009). The mitochondrion have a crucial role in growth and animal development and has been linked with production efficiency (Hill, 2012). Variation in the mitochondria’s ability to produce energy results in phenotypic difference in feed efficiency of an animal (Herd and Arthur, 2009). Kolath et al. (2006) found no difference in mitochondrial function between low or high RFI animals; however, the rate of mitochondrial respiration was increased in low RFI animals suggesting an efficiency of electron transfer. The authors concluded that mitochondrial function was not impaired for steers with high RFI but the flux of electrons through the electron transport chain was impaired in low RFI steers. Hill (2012) discussed potential areas of mitochondrial inefficiencies through electron transport defects and mitochondrial defects. The electron transport chain (ETC) is a source of reactive oxygen species (ROS) and endogenous oxidative stress. Reactive oxygen species forms superoxide (O2-) as a result of electron leakage from the electron transport chain. Low levels of ROS are needed for cellular function and are metabolized by antioxidants. However, ROS is capable of altering gene expression and has been linked to diabetes, Alzheimer’s and cancer in humans. The author suggested that elevated levels of ROS in animals that are less efficient in feed conversion could play a role in gene regulation and protein expression, and mitochondrial function with phenotypic expression of feed efficiency. 27 Nitric oxide (NO) is involved in the regulation of mitochondrial respiration when nitric oxide synthase produces NO near the ETC. Nitric oxide has been shown to competitively inhibit cytochrome c and regulate oxygen absorption. When NO reacts with ROS, several reactive nitrogen species are released which damages cellular structures such as complexes I and II of the ETC (Hill, 2012). The functional integrity of mitochondria is due to a balance of mitochondrial DNA (mtDNA) and nuclear DNA (nDNA). There is a lack of protective histones for mtDNA and it has a close proximity to the ETC. As a result, mtDNA has a tendency for ROS oxidation, which leads to mitochondrial dysfunction. The damaged mtDNA has a restricted ability to encode subunits or proteins, which leads to a diminished ability of the mitochondria to achieve its respiratory ability. Complexes I, II and IV were particularly affected by this and as a result the ETC would have decreased activity. From the standpoint of animal feed efficiency, there could be a relationship between inefficient animals and a decrease in the activity of respiratory chain complexes (Hill, 2012). Protons pumping across the inner mitochondrial membrane are used to drive ATP synthesis. Protons can also flow back into the mitochondria essentially short circuiting the coupling of ATP synthesis. This process is termed a proton leak and represents 30% and 50% of oxygen consumption in liver and muscle cells, respectively, and contributes up to 25% of total basal metabolic rate of an animal. It stands to reason that proton leak could contribute to feed efficiency in cattle. When ADP levels are high, the animal’s respiration rate will be dependent on oxidative phosphorylation and the reaction that produces ATP. When ADP levels are minimal, the proton leak across the inner membrane of the mitochondria controls oxygen consumption (Hill, 2012). 28 The final mitochondrial inefficiency examined by Hill (2012) was the uncoupling attenuation of oxidative stress. This uncoupling is a result of cellular inefficiency but alleviates oxidative stress by reducing ROS production. When examining broilers, Ojano-Dirain et al. (2007) found uncoupling lowered ROS production in those with inferior gain to feed ratios but was not found in mitochondria from individuals with superior gain to feed ratios. It was also found that ROS production was significantly higher in broilers who were less efficient for feed utilization and as a result uncoupling would be expected. These studies indicate that higher mitochondrial ROS associated with the phenotypic expression of less efficient FCR or RFI would indicate differences in membrane characteristics that affect the proton conductance of the mitochondria (Bottje et al., 2002; Hill, 2012). Mitochondria play a clear role in the efficiency of feed utilization in livestock animals. Proton leak and ROS production are inefficient mitochondrial activities and may be indicative of less-efficient animals. The development of genomic markers from nDNA or mtDNA to identify efficient or inefficient animals is not currently available given the complex nature of the interaction of n- and mt-encoded proteins (Hill, 2015). 2.4.2 Biological Markers of RFI Important factors influencing the variation of feed utilization may be explained by biological differences in the growth hormone/IGF-1 axis (Hill 2012). Glucose and amino acid metabolism, protein accretion, and linear growth are all affected by endocrine actions of IGF-1 (Jones and Clemmons, 1995) suggesting a role in feed utilization and efficiency. Australian research on IGF-1 in weaned pigs reported a moderate to high positive genetic correlation between 29 plasma IGF-1 concentrations and FCR (Luxford et al., 1998; Hermesch et al., 2001). Bunter et al. (2010) estimated genetic correlations between RFI and IGF-1 in pigs to be 0.63 ± 0.15. In Bos taurus cattle, genetic correlations between IGF-1 concentration and RFI were positive and ranged from 0.39 to 0.63 (Arthur et al., 2004; Brown et al., 2004; Moore et al., 2005; Hill, 2012). Herd and Arthur (2009) examined data from Australian Angus cattle prior to 2004 and found a genetic correlation of 0.57 between RFI and serum IGF-1 concentrations collected at or before weaning. The authors concluded that this would suggest that many of the genes responsible for greater concentrations of IGF-1 are also associated with high RFI measures. In contrast, researchers analyzed data available prior to 2007, and estimated the correlations between IGF-1 and RFI from yearling steers before harvest (feedlot) and RFI from younger cattle (postweaning). The genetic correlation between postweaning RFI and feedlot RFI with IGF-1 were 0.17± 0.11 and -0.22 ± 0.16, respectively. These lower correlations suggested that the effect of IGF-1 for RFI is lower than initially expected and the effect of many genes on RFI differ from postweaning and feedlot cattle (Hill, 2012). In addition, as cattle become more physiologically mature, the relationship between IGF-1 and RFI decreased or becames negative. Lancaster et al. (2008) suggested that body composition be considered when examining the relationship between serum IGF-1 concertation and RFI. Limited research involving RFI has been conducted in Bos indicus cattle. Wolcott et al. (2006) examined correlations between serum concentrations of IGF-1 and RFI in Bos indicus and Bos taurus crosses. Resulting genetic correlations were -0.12 for Brahman cattle and -0.80 for tropical composites. These results would suggest that genotype (i.e. species) would affect the relationship between IGF-1 and RFI. 30 The relationship between leptin and RFI have also been examined. Leptin is commonly associated with fatness in cattle. Nkrumah et al. (2007) reported a significant phenotypic correlation of 0.31 for serum leptin concentrations and RFI, whereas, Brown et al. (2004) did not results in a phenotypic correlation between leptin and RFI. 2.5. Genetic Parameters of Feed Efficiency and Intake 2.5.1 Heritability Heritability is defined as the measure of strength of the relationship between breeding values (genetics) and performance and is an indication of what we observe is due to inheritance (Bourdon, 1997). Heritability is expressed as a ratio of variances: = HIJ ℎ = = HK = (Eq. 2.3) = where HIJ was the variance of breeding values and HK= was the phenotypic variance. For selection and genetic improvement, heritability is crucial for polygenetic traits, such as feed efficiency. Increases in heritability leads to an increase in response to selection. The following section is a summarization of heritability estimates for FI and feed efficiency. 31 2.5.1.1 Heritabilities for Feed Efficiency and Intake There is a large range of heritabilities reported for feed efficiency (RFI and FCR) and FI which is not surprising considering the differences in analysis that estimated the heritabilities and the various methods used to collect phenotypic measures. Tables 2.1, 2.2 and 2.3 present the range of heritabilities for RFI, FI and FCR for growing and mature cattle, respectively (adapted from Berry and Crowley, 2013). Berry and Pryce (2013) presented an abbreviated version of table 2.1 and 2.2 with pooled heritabilities for all the traits (Table 2.4). Table 2.1. Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a range of studies prior to 2000 on growing animals across different breeds. Animals, FI RFI FCR Breeds1 Reference n 0.62 (0.12) 0.62 (0.14) 0.42 (0.13) AN, HE, Polled HE, SH 760 Archer et al. (1997) 0.59 (0.07) 0.44 (0.07) 0.31 (0.09) AN, HE, SH 966 Arthur et al. (1997) 0.37 (0.19) 0.19 (0.16) Bonsmara 298 Bergh et al. (1992) 0.06 (0.12) 0.46 (0.20) FR x HE 327 Bishop et al. (1992) 0.14 (0.07) AN 393 Brown et al. (1988) 0.13 (0.08) HE 340 Brown et al. (1988) 0.27 (0.15) 0.23 (0.12) 0.35 (0.22) AN 263 Fan et al. (1995) 0.18 (0.10) 0.07 (0.13) 0.08 (0.09) HE 271 Fan et al. (1995) 0.58 (na) 0.16 (na) BB 1,442 Gengler et al. (1995) 0.24 (na) 0.14 (na) HE 486 Glaze and Schalles (1995) 0.26 (na) 0.27 (na) HO, BS 630 Jensen et al. (1991) 0.28 (0.11) HO, BS 650 Jensen et al. (1992) 0.64 (0.12) 0.28 (0.11) AN, HE, SH 1,324 Koch et al. (1963) 0.56 (0.11) 0.22 (0.11) 0.18 (0.08) HO, HO x Dutch 417 Korver et al. (1991) 0.33 (0.10) HE 452 Mrode et al. (1990) 0.46 (0.14) 0.19 (0.12) 0.37 (0.14) HO 360 Van Arendonk et al. (1991) AN = Angus; BA = Brangus; BB = Belgium Blue; BS = Brown Swiss; CH = Charolais; CHX = Charolais crossbred; FR x HE = Freisian and Hereford crossbreds; HE = Hereford; HO = Holstein; LI = Limousin; SH = Shorthorn; SI = Simmental. 1 32 Table 2.2. Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a range of studies after 2000 on growing animals across different breeds. FI 0.39 (0.03) RFI 0.39 (0.03) FCR 0.29 (0.04) 0.48 (0.04) 0.39 (0.04) 0.46 (0.04) 0.48 (0.06) 0.43 (0.04) 0.31 (0.06) 0.49 (0.15) Breeds1 AN Animals, n 1,180 Reference Arthur et al. (2001a) CH 792 Arthur et al. (2001c) CH 397 Arthur et al. (2001c) 0.24 (0.11) Brahman 700 Barwick et al. (2009) 0.51 (0.14) 0.38 (0.12) Tropical Composite 787 Barwick et al. (2009) 0.30 (0.08) 0.26 (0.10) 0.30 (0.12) BA 678 Bouquet et al. (2010) 0.48 (0.14) 0.45 (0.18) 0.23 (0.15) LI 708 Bouquet et al. (2010) 0.30 (0.06) CH sired steers 281 Crews et al. (2003) 0.26 (0.07) CH sired steers 274 Crews et al. (2003) 0.49 (0.07) 0.45 (0.07) 0.30 (0.06) AH, CH, HE, SI, LI 2,605 Crowley et al. (2010) 0.30 (0.15) 0.19 (0.12) 0.07 (0.09) ANX, CHX 402 Durunna et al. (2011b) 0.43 (0.14) 0.36 (0.13) 0.26 (0.12) ANX, CHX 419 Durunna et al. (2011b) 0.21 (0.07) 0.14 (0.06) 0.18 (0.07) AN, BR, BA 1,129 Elzo et al. (2010) 0.31 (0.08) 0.16 (0.08) 0.17 (0.09) HE 540 Herd and Bishop (2000) 0.34 (0.11) 0.24 (0.11) 0.15 (0.04) Wagyu 740 Hoque et al. (2006) 0.36 (0.09) 0.49 (0.09) 0.38 (0.07) Wagyu 514 Hoque et al. (2009) 0.70 (0.11) 0.22 (0.07) 0.11 (0.05) Wagyu 863 Inoue et al. (2011) 0.48 (0.14) 0.47 (0.13) 0.29 (0.12) Brangus Lancaster et al. (2009) 0.18 (0.14) AN, CH, composite 468 4,215 to 18,169 387 0.41 (0.12) 0.29 (0.12) AN, CH, composite 721 Muijibi et al. (2011) 0.54 (0.15) 0.21 (0.12) 0.41 (0.15) AN, CH, composite 464 Nkumah et al. (2007b) 0.33 0.29 0.14 Wagyu 1,304 0.27 (0.06) 0.18 (0.06) 0.06 (0.04) Tropically adapted 1,481 0.14 0.14 AN 698 Okanishi et al. (2006) Robinson and Oddy (2004) Rolf et al. (2010) 0.40 (0.02) 0.52 (0.14) Multibreed 1,141 Rolf et al. (2011) AH, CH, HE, SI, LI 3,724 Savietto et al. (2014) AN, CH, LI, SI, HE, BA 2,284 0.36 (0.05) AN 0.27 (0.10) 0.5 0.44 (0.06) 0.38 (0.07) 0.37 (0.06) MacNeil et al. (2011) Muijibi et al. (2010) Schenkel et al. (2004) Van der Westhuizen et 0.31 0.34 Bonsmara 6,738 al. (2004) 0.17 (0.10) 0.27 (0.12) HO 903 Williams et al. (2011) 1 AN = Angus; BA = Brangus; BB = Belgium Blue; BS = Brown Swiss; CH = Charolais; CHX = Charolais crossbred; FR x HE = Freisian and hereford crossbreds; HE = Hereford; HO = Holstein; LI = Limousin; SH = Shorthorn; SI = Simmental. 33 Table 2.3. Heritability estimates (SE) for feed intake (FI), residual feed intake (RFI) and feed conversion ratio (FCR) for a lactating or dry mature animals across different breeds adapted from Berry and Crowley (2013). Animals, FI RFI FCR Breeds2 n Reference 0.28 0.02 (0.02) 0.11 (0.02) 0.03 (0.01) 0.16 (0.02) 0.23 0.23 (0.11) 0.03 (0.01) 0.03 (0.02) 0.22 (0.04) 0.05 to 0.38 0.16 0.18 to 0.63 0.16 (0.09) 1 2 0.26 0.18 (0.15) 0.11 (0.06) 0.11 (0.10) 0.05 (0.01) 0.32 (0.13) 0.04 (0.05) 0.38 0.01 (0.05) 0.14 (0.06) AN, HE, SH HE HE, multibreed HE HE, multibreed Holstein-Friesian HO HO Norwegian HO HO 751 295 1,174 206 729 463 247 402 353 204 970 Archer et al. (2002) Fan et al. (1996a) Fan et al. (1996a) Fan et al. (1996b) Fan et al. (1996b) Lopez-Vallalobos et al. (2008) Ngwerume and mao (1992) Spurlock et al. (2012) Svendsen et al. (1993) Veerkamp et al. (1995) Vallimont et al. (2011) na = not available AN = Angus; HE = Hereford; HO = Holstein; SH = Shorthorn. Table 2.4. Number of studies (N), pooled heritabilities (pooled), minimum (min) and maximum (max) heritability estimates for average daily gain (ADG), weight (WT), dry matter feed intake (FI), residual feed intake (RFI), feed conversion ratio (FCR) adapted from Berry and Pryce (2013). ADG WT FI RFI FCR N 35 25 37 36 34 Pooled (S.E.) 0.31 (0.01) 0.39 (0.01) 0.40 (0.01) 0.33 (0.01) 0.23 (0.01) Min 0.06 0.30 0.06 0.07 0.06 Max 0.65 0.88 0.70 0.62 0.46 Minimum heritability estimates for FI, RFI and FCR were 0.02, 0.01 and 0.05, respectively, with respective maximum estimates of 0.70, 0.62 and 0.46. Heritability estimates for mature cows were less than estimates for growing cattle, however, the number of studies was considerably less and indicative of the lack of knowledge for mature cattle (Berry and Crowley, 2013). When studies presented heritabilities for both FI and RFI, the heritabilities for FI were higher than RFI with the exception of two studies (Rolfe et al., 2011 and Williams et al., 2011). 34 2.5.2 Genetic Correlations Genetic correlation is defined as the relationship between breeding values of one trait and the breeding values of another trait (Bourdon, 1997). When traits are genetically correlated, selection on one trait can influence the expression of another trait. In addition, performance in one trait can be used to predict the performance of a genetically correlated trait. In the context of feed efficiency and intake, understanding the relationship between genetically correlated traits is crucial for two reasons. First, there is a lack of knowledge surrounding the effect of selection for feed efficiency on other performance traits, especially survival traits (i.e. health and reproduction). Second, measuring feed intake is expensive and time consuming in addition to a limitation to the availability of facilities to measure intake. The use of an indicator trait could help to mitigate the expense of measurement and enable the ability to measure a greater number of animals. The following section presents genetic correlation estimates reported in literature. 2.5.2.1 Genetic Correlations of Feed Efficiency and Intake The opportunity to improve production efficiency is dependent on the magnitude of genetic correlations between FI or feed efficiency and other production traits (Herd et al., 2003). In general, estimation of precise genetic correlations of feed efficiency or intake is generally not achievable due to relatively small datasets. In addition, genetic correlations with lowly heritable traits tend to reduce the ability to estimate precise genetic correlations (Berry and Crowley, 35 2013; Berry and Pryce, 2013). Tables 2.5, 2.6 and 2.7 present genetic correlations of feed efficiency and feed intake to performance, carcass, mature cow and reproductive traits. Table 2.5. Genetic correlations between feed efficiency traits 1 2 Traits FI FCR References FCR 0.31 (0.07) Arthur et al. (2001a) FCR -0.49 (0.22) Robinson and Oddy (2004) FCR 0.64 (0.07) Arthur et al. (2001b) FCR -0.60 (0.18) Rolfe et al. (2011) RFI 0.69 (0.03) 0.66 (0.05) Arthur et al. (2001a) RFI 0.64 (0.16) 0.70 (0.22) Herd and Bishop (2000) RFI 0.43 (0.15) 0.41 (0.32) Robinson and Oddy (2004) RFI 0.79 (0.04) 0.85 (0.05) Arthur et al. (2001b) RFI 0.66 (0.12) Rolfe et al. (2011) 1 FCR = Feed conversion ratio; RFI = Residual feed intake 2 FI = Feed intake 36 Table 2.6. Genetic correlations (S.E.) for feed efficiency and postweaning traits. 1 Trait ADG ADG ADG ADG ADG MMWT MMWT MMWT MMWT LWT 200d WT 200d WT 400d WT 400d WT 2 3 FI 0.54 (0.06) FCR -0.62 (0.06) 0.87 (0.05) 0.39 (0.08) 0.56 (0.16) 0.65 (0.03) -0.86 (0.10) -0.46 (0.08) -0.01 (0.07)* 0.76 (0.07) 0.71 (0.11) 0.83 (0.04) 0.28 (0.15) -0.62 (0.18) 0.56 (0.09) -0.09 (0.15) 0.24 (0.09) -0.21 (0.20) 4 RFI -0.04 (0.08) 0.09 (0.29)* 0.09 (0.20)* 0.32 (0.10) -0.06 (0.06)* 0.22 (0.29)* -0.20 (0.16) -0.10 (0.13)* -0.45 (0.17) 0.34 (0.34)* -0.26 (0.13) 0.15 (0.28)* 1 Reference Arthur et al. (2001a) Herd and Bishop (2000) Robinson and Oddy (2004) Arthur et al. (2001b) Rolfe et al. (2011) Arthur et al. (2001a) Herd and Bishop (2000) Robinson and Oddy (2004) Rolfe et al. (2011) Arthur et al. (2001b) Arthur et al. (2001a) Herd and Bishop (2000) Arthur et al. (2001a) Herd and Bishop (2000) WT = weight; ADG = Average daily gain; MMWT = metabolic mid-weight (WT0.75); LWT = Live weight; 2 FI = Feed intake 3 FCR = Feed conversion ratio of feed to gain 4 RFI = Residual feed intake * indicates that the estimate is not statistically different from zero as stated by the authors of the respective study. 37 Table 2.7. Genetic correlations between feed efficiency and carcass traits. 1 2 3 4 Trait FI FCR RFI Reference RIB 0.27 (0.05) 0.03 (0.06) 0.17 (0.05) Arthur et al. (2001a) RIB 0.61 (0.11) 0.38 (0.32) 0.48 (0.12) Robinson and Oddy (2004) P8 0.14 (0.05) -0.04 (0.07)* 0.06 (0.06)* Arthur et al. (2001a) P8 0.59 (0.10) 0.40 (0.33) 0.72 (0.17) Robinson and Oddy (2004) LMA 0.43 (0.07) -0.12 (0.11) 0.09 (0.09)* Arthur et al. (2001a) LMA 0.23 (0.16) 0.20 (0.42)* -0.24 (0.26)* Robinson and Oddy (2004) IMF% 0.39 (0.14) 0.08 (0.28)* 0.22 (0.17) Robinson and Oddy (2004) LCC -0.43 (0.23) Herd and Biship (2000) CC -0.07 (0.16)* 0.12 (0.19)* -0.06 (0.17) Crowley et al. (2011) CF 0.02 (0.21)* 0.15 (0.23)* 0.19 (0.21)* Crowley et al. (2011) CWT 0.16 (0.17)* 0.29 (0.19) -0.01 (0.17)* Crowley et al. (2011) 1 RIB = 12/13th rib fat depth; P8 = rump P8 fat depth; LMA = longissimus muscle area; LCC = lean carcass content; IMF% = intramuscular fat; CC = carcass conformation; CF = carcass confirmation; CWT = carcass weight. 2 FI = Feed intake 3 FCR = Feed conversion ratio 4 RFI = Residual feed intake * indicates that the estimate is not statistically different from zero as stated by the authors of the respective study. Genetic correlations between RFI and postweaning traits suggest that selection for lower RFI has the potential to reduce feed intake without a reduction in cattle size and therefore improving the efficiency of cattle (Herd et al., 2003). The association between RFI and reproduction traits are in general unfavorable but have large standard errors. Crowley et al. (2011a) found unfavorable genetic correlations for feed efficiency measures with age at first calving (-0.55 ± 0.14 for FCR and -0.29 ± 0.14 for RFI) but correlations for calving interval and calving to first service were not different from zero. Basarab et al. (2011) analyzed the significance of calving rates when ultrasound back fat is included or removed from the calculation of RFI. They showed when ultrasound back fat was excluded from the calculation of RFI, a significant difference in calving rates was found for low RFI heifers (72.63%) compared to high RFI heifers 38 (84.21%). However, when ultrasound back fat was included, there was no difference in the calving rates. When compared to other production traits, few studies have examined the impact of selection for feed efficiency on reproductive performance. Arthur et al. (2005) reported, from a divergent RFI selection experiment, a 5-d later calving date in cows with low RFI compared to high RFI cows. The effect of selection on feed efficiency and the correlated to response to fertility and survival traits merit further research (Berry and Crowley, 2013). However, the association of selection for reduced RFI and forage intake for mature, grazing cattle is unknown (Herd et al., 2003). Genetic correlations between RFI and carcass traits lacked consistency across studies and resulted in large standard errors. That said, cattle with higher RFI values had improved carcass conformation (Berry and Crowley, 2013). There was a tendency for RFI to be negatively correlated with carcass traits in beef cattle suggesting that as RFI decreased (improves), carcass merit also improved. There was a tendency for FI, FCR and RFI to be positively correlated with body fat in beef cattle, 0.28 ± 0.04, 0.08 ± 0.05 and 0.20 ± 0.04 respectively (pooled estimates; Berry and Crowley, 2013). There are few studies that have examined the genetic correlation between feed efficiency and meat quality. Genetic correlations between both RFI and FCR and meat fatty acid composition were examined in Japanese Black steers. The correlations with RFI were zero and with FCR was -0.38 (C18:0 and C18:1) to 0.43 (C14:1) with standard errors of approximately 0.20 (Inoue et al., 2011; Berry and Crowley, 2013). 39 2.5.3 Genetic Improvement of Feed Efficiency and Intake There is an ongoing debate on whether to include feed intake or RFI in a breeding objective (Berry and Pryce, 2013). However, reducing feed intake only should not be the goal of the breeding objective. Selection pressure should also be placed on production or output traits while attempting to reduce feed intake (Nielsen et al., 2013). From the perspective of genetic improvement for feed efficiency, selection for feed efficiency can be accomplished through selection using an index for output (i.e. body weight) and input traits (i.e. FI). Appropriately weighting the index traits for output as positive and input traits as negative, feed efficiency would not have to be explicitly be calculated (MacNeil et al, 2013; Neilsen et al., 2013). Berry and Crowley (2013) stated “achieving improved efficiency of production through genetic selection can be best achieved through a balanced breeding goal, selecting on all traits influencing profitability simultaneously rather than selection on individual traits.” Kennedy et al. (1993) showed the equivalence of RFI to the selection index when economic weights were calculated correctly. Efficiency measures, such as RFI, that are calculated from feed intake and performance traits, provide no additional information beyond the traits used to calculate the efficiency measures (Kennedy et al., 1993). Van der Werf (2004) stated that in growing animals, including all component traits of RFI in a breeding objective or selection index is mathematically equivalent to including RFI assuming no fixed effects were included in the genetic evaluation model. Therefore, there was no additional benefit of including RFI (or any feed efficiency measure) in a breeding goal or selection index that already included the individual feed and production traits. In the context of national cattle evaluation (NCE), it was recommended to analyze feed intake. In order to increase accuracy of feed intake, known genetically correlated traits that were more easily or 40 cheaply measured (i.e. post weaning weight) were suggested to be included in NCE for feed intake (Neilsen et al., 2013). Selection decision for genetic improvement of feed efficiency should be based on genetic prediction from multi-trait genetic evaluations of feed intake (MacNeil et al., 2013; Neilsen et al., 2013). Estimating higher accuracies for selection of feed efficiency and intake has been a substantial obstacle for the implementation of feed efficiency traits in breeding objectives (Berry and Pryce, 2014). Given the expense of measuring feed intake on cattle, producers tend to test their more elite animals. As a result, databases of recorded FI may not be truly representative of the cattle population which has led to use of densely recorded traits, such as weaning weight, in multitrait analyses for the publication of EPD. 2.6 Conclusion There is a large body of research on the subject of feed intake and feed efficiency; however there are gaps in knowledge pertaining to feed intake and efficiency. There are few studies examining feed efficiency and the correlation to cow performance or health traits. The robustness of feed reduction and how it affects feed efficient cattle is largely unknown. In addition, the relationship of feed intake and grazing intake is unknown. In order to select for a cowherd that is more efficient for forage utilization, grazing intake needs to be measured. 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Sci. 2:S89-S92. 55 Chapter III ESTIMATION OF VARIANCE COMPONENTS DUE TO DIRECT AND MATERNAL EFFECTS FOR FEED INTAKE FOR RED ANGUS AND GELBVIEH CATTLE 3.1 Introduction Feed costs are the largest variable expense in the beef industry, accounting for 50 to 70% of total production costs (Anderson et al., 2005). Genetic improvement of feed utilization has the potential to decrease production costs and increase profitability. As a result, interest in selecting for cattle that are more feed efficient has increased, and several beef cattle breed associations are currently publishing expected progeny differences (EPD) for feed intake or for a feed efficiency trait, such as residual feed intake (RFI) and residual average daily gain (RADG). The accurate calculations of these EPD are dependent on reliable estimation of variance components for the traits of interest. Through the environment provided by the dam, maternal effects are known to influence performance of some traits, such as weaning weight. The phenotype of progeny is influenced by the dam’s contribution of half of direct, additive genes for that trait, in addition to her genetic potential for the environment she provides for her off-spring. As a result of the environmental influence of the dam, the maternal effect can be an important source of variation. For traits that are influenced by maternal effects, the exclusion of these effects when estimating variance components can substantially inflate direct heritability estimates (Meyer, 1992). Studies have shown that maternal effects have an important influence on traits before and after weaning for up 56 to a year (Mavrogenis et al., 1978; Meyer, 1992; Lee et al., 2000), but the magnitude of the influences tends to dissipate for traits measured after weaning (Meyer, 1992). Beef Improvement Federation (BIF) guidelines for the measurement of DMI proposed that feed intake be measured on cattle postweaning and no older than 390 d at the conclusion of data collection (BIF, 2010). To date, few studies have examined maternal effects on DMI and the significance of its inclusion for the estimation of variance components should be explored as maternal effects are not currently included in genetic evaluations for feed intake. In addition, some beef cattle breed associations are incorporating weaning weight in a multivariate estimation for DMI EPD as a method to account for selection bias for animals with DMI records, but little is known for the relationship between DMI and weaning weight maternal. If a substantial correlation between DMI and weaning weight maternal exists, the genetic correlation between DMI and weaning weight direct could be inflated if maternal effects are not included. Therefore, the objectives of this study were to 1) estimate the variance components for direct and maternal effects on feed intake and 2) to estimate the genetic correlation between DMI and weaning weight maternal on two populations of cattle, Red Angus and Gelbvieh. 3.2 Materials and Methods Data. The data used was provided from preexisting databases used for genetic evaluations. Therefore, animal care and use committee approval was not needed for this study. To address the first objective, estimates of variance components were obtained from a single trait animal model for dry matter feed intake (DMI) where direct and maternal effects were included. The second objective was met using a multivariate model with DMI as the first 57 trait and weaning weight included as the second with maternal genetic and permanent environmental effects included for weaning weight only. Two data sets containing records for dry matter feed intake (DMI), weaning weight (WWT), and pedigree information were provided by the American Gelbvieh Association (AGA) and the Red Angus Association of American (RAAA). The weaning weight data provided were not pre-adjusted for age and DMI records were available for both males and females. The contemporary group (CG) for DMI established by both AGA and RAAA were formed using sex, pen, feed trial designation, trial length and year. Age at the start of test (AGE) was calculated by subtracting the animal’s birth date from the start date of the test. At the beginning of a test, animals younger than 240 d (BIF, 2016) and older than 365 d were removed from the analysis to restrict the data to postweaning cattle less than a year of age. Considering maternal effects have been shown to influence postweaning traits up to a year of age, the data was truncated to only include postweaning cattle up to a year of age to focus on the age category where maternal effects are most likely to be found. For traits measured on animals older than a year of age, the maternal effects are often considered to be negligible (Meyer, 1992) and were therefore removed. For the purpose of this study, embryo transfer calves were also removed since pedigree and breed information for surrogate dams were unknown and therefore the ability to account for the maternal environment provided by the surrogate dams was not possible (Shaeffer and Kennedy, 1989). For the single trait analysis of DMI, Gelbvieh had a final data set which consisted of 3,021 animals with DMI records in 95 unique CG with an average size of 32 and Red Angus data consisted of 3,213 animals in 104 unique CG with the average size of 31. Starting with animals with records, a 3-generation pedigree was formed. The pedigree for Gelbvieh included 15,418 animals with 3,027 unique sires and 9,494 unique dams. For Red 58 Angus, the pedigree was comprised of 13,747 animals with 2,476 and 8,117 unique sire and dams, respectively. A multi-trait analysis was also conducted to examine the potential genetic correlation of DMI to maternal weaning weight. Due to limited capacity of testing facilities to measure DMI and the relative expense of collecting intake data, only select animals were measured. To account for this selection bias, multi-trait models including DMI and correlated traits, such as weaning weight, are often used. This was accomplished by including all the animals recorded in the correlated trait’s CG from which animals with DMI records were also recorded (Neilsen et al., 2013). Weaning weight CG was defined as weaning date, breeder, herd, and sex. To ensure complete CG for both DMI and WWT, all animals within the WWT CG for animals with DMI records were included. As a result, animals were included with no DMI records, but their WWT records were included due to being in their weaning weight contemporary group of animals with DMI observations. As with the DMI records, embryo transfer calves were removed. Following Beef Improvement Federation Guidelines (BIF, 2016), age of dam (AOD) were assigned for animals with observations from dams aged 2, 3, 4, 10, 11 and 12 years old as their respective age in years. Dams 5 to 9 years of age received an AOD classification of 5 years of age and dams greater than or equal to 13 years of age were classified as 13. Age at weaning was determined by subtracting the animal’s birth date from the weaning date. The final data set for the multi-trait analysis consisted of 7,792 and 4,342 records for Gelbvieh and Red Angus, respectively. A 3generation pedigree was built for Gelbvieh with 26,412 animals and 16,676 animals for Red Angus. For weaning weight, Gelbvieh had 525 unique contemporary groups for weaning weight with an average size of 15 animals and Red Angus had 284 unique contemporary groups, also averaging in size of 15 animals. 59 Statistical Analysis. Data for Gelbvieh and Red Angus were analyzed separately. Genetic and residual (co)variance parameters were estimated using ASREML 3.0 software package (Gilmour et al., 2009). For the single trait analysis, a linear animal mixed model including both genetic and environmental effects was performed using the following model: L = MN + OP QP + OR QR + OST QST + T (Eq. 3.1) where y was the vector of observations for DMI, b was a vector of unknown fixed effect solutions, QP was a vector of additive genetic effects, QR was a vector of maternal genetic effects, QST was a vector of permanent environmental effects of the dam, e was a vector of residual effects, and X, OP , OR , OST were known incidence matrices relating effects in b, QP , QR , and QST to observations in y, respectively. Fixed effects for both Gelbvieh and Red Angus were AGE as a covariate and DMI CG. Variances and means included in the model were assumed to be the following: U(L) = MN U(T) = U(Q) = 0 \H = QP ⎡ ] Q ⎢\H '*) WQ R X = ⎢ ]^ 0 ST ⎢ T ⎣ 0 \H]^ = \H^ 0 0 0 0 = _ST H`a 0 0 ⎤ 0 ⎥ 0 ⎥ ⎥ _T Ha= ⎦ (Eq. 3.2) where A was the numerator relationship matrix, Ipe was an identity matrix with an order of the number dams, Ie was an identity matrix with an order of the number of animals with 60 observations, efP was the direct additive genetic variance, ePR was the direct-maternal genetic covariance, efR was the maternal additive genetic variance, efST was the maternal permanent environmental variance, and efT was the residual variance. For the multi-trait model, the following animal model was used: Lh M gL i = j h 0 f O 0 Nh k j k + j Ph Mf Nf 0 0 0 0 Th 0 QPh 0 0 0 k gQ i + j kj k + j0 O k jQ k + gT i OPf 0 ORf QRf Pf f STf STf (Eq. 3.3) Where yi was the vector of observations for the ith trait (1=DMI, 2= weaning weight), bi was the vector of fixed effects, udi was the vector of random direct additive genetic effects and umi was also a vector for maternal additive genetic effects, upei was a vector of maternal permanent environment effects, ex was a vector of residual effects and Xi, Zdi, Zmi, Zpei were the incidence matrices corresponding to bi, udi, umi, and upei, respectively. The fixed effects for DMI remained the same as the single trait analysis. For weaning weight, age, AOD and weaning CG were included as fixed effects. The weaning CG for both Gelbvieh and Red Angus included sex, breeder, breed percentage, weaning working group and weaning date. Breed percentages were partitioned into four groups: 25% to 43.75%, 43.76% to 62.5%, 62.3% to 87.5%, and 87.6% to 100%. The variances and means of the model are as follows: U(Ll ) = Ml Nl U(Tl ) = U(Ql ) = 0 61 = \H]; QPh ⎡ ⎡ QPf ⎤ \H ⎢ QRf ⎥ ⎢ ];,]= '*) ⎢Q ⎥ = ⎢\H];,^= ⎢ STf ⎥ ⎢ 0 ⎢ Th ⎥ ⎢ 0 ⎣ Tf ⎦ ⎣ 0 \H];,]= = \H]= \H]=,^= 0 0 0 \H];,^= 0 \H]=,^= 0 0 = \H^= = 0 4H`a= 0 0 0 0 0 0 0 0 = _Ha; _Ha;,a= 0 0 0 0 ⎤ ⎥ ⎥ ⎥ _Ha;,a= ⎥ = _Ha= ⎦ (Eq. 3.4) where A was the numerator relationship matrix, Ipei was an identity matrix with an order of the number dams for trait i, Iei was an identity matrix with an order of the number of animals with observations of the ith trait, efPl was the direct additive genetic variance for trait i, ePl,Pln was the direct genetic covariance for between the traits, ePl,Rl was the direct-maternal genetic covariance for the ith trait, efR was the maternal additive genetic variance for WWT, efST was the maternal permanent environmental variance for WWT, efTl was the residual variance for trait i, and eTl,Tln was the residual covariance between traits. The convergence criteria for the model was a REML log-likelihood change of less than 0.002 and the parameter estimates changed by less than 1% (Gilmour et al., 2009). 3.3 Results and Discussion Summary statistics for DMI observations are presented in Table 3.1 On average, Gelbvieh cattle had trait values higher compared to Red Angus. The variation for DMI observations for Gelbvieh cattle was approximately half of the variation for Red Angus cattle. As for age, Gelbvieh cattle were on average 6 days younger than Red Angus cattle but the standard deviations for both data sets in regard to AGE were similar. 62 Table 3.1. Summary statistics for cattle with feed intake records for Gelbvieh and Red Angus cattle. 1 n mean SD minimum maximum DMI 11.08 1.71 4.60 24.10 Gelbvieh 2 Age 3038 289.14 34.71 240.00 365.00 3 Test 71.84 9.44 51.00 133.00 1 DMI 10.58 2.14 2.07 20.07 Red Angus 2 Age 3213 295.77 33.95 240.00 365.00 3 Test 52.17 12.20 35.00 90.00 1 DMI = Dry matter feed intake in kg Age = Age of cattle in days at the start of feed test 3 Test = Test length in days for the collection DMI. 2 Table 3.2 presents the summary statistics for WWT and age at weaning for Gelbvieh and Red Angus cattle. On average, the age at weaning and distribution for age were similar among breeds. For WWT, Gelbvieh cattle were on average heavier at weaning compared to Red Angus cattle but the standard deviation for both breeds were similar. Table 3.2. Weaning weight summary statistics for cattle with feed intake records for Gelbvieh and Red Angus cattle. n mean SD minimum maximum Gelbvieh 1 2 WWT Age 7,792 270.86 200.05 44.62 21.70 129.27 160.00 464.93 249.00 1 WWT = weaning weight in kg 2 Age = Age of cattle in days at weaning 63 Red Angus 1 2 WWT Age 4,342 253.56 202.42 41.32 21.33 106.59 160.00 423.66 249.00 Direct and maternal heritabilities from the single trait analysis are shown in table 3.3. The heritabilities for DMI direct for Red Angus and Gelbvieh cattle were moderate to high (0.24 ± 0.06 and 0.45 ± 0.06, respectively) and were both within the range of previously reported heritabilities for DMI (0.14 to 0.70; Berry and Crowley 2013). The DMI maternal heritability for Gelbvieh was zero and Red Angus DMI maternal heritability was very low at 0.05 ± 0.04. The correlation between DMI direct and maternal was 0.70 x 10-3 ± 0.10 x 10-3 and -0.77 ± 0.20 for Gelbvieh and Red Angus cattle, respectively. The difference in genetic variances estimated for Gelbvieh and Red Angus would be expected given the different population structures, both genetic and non-genetic, between the two breeds. There are few studies that have examined maternal effects of DMI in cattle. Hoque et al. (2007) examined the maternal effects for 740 Japanese Black cattle. In that study, no important influence of maternal effects on feed intake or feed efficiency was identified and Hoque et al. (2007) concluded the inclusion of maternal effects for feed intake in a genetic evaluation was not warranted. However, in a study conducted by Crowley et al. (2010), non-zero maternal heritability of 0.10 for DMI was estimated for 2,605 Irish beef bulls with an average age of 309 days. Crowley et al. (2010) found the inclusion of maternal genetic effects accounted for variability in DMI that was previously attributed to the direct genetic effect and that the inclusion of maternal effects decreased heritabilities for DMI from 0.49 to 0.38. The results obtained for Gelbvieh in the current study would support the findings of Hoque et al. (2007). Unlike Gelbvieh, the DMI maternal heritability for Red Angus was not zero, but it was lower than the estimates obtained by Crowley et al. (2010). The genetic variance for DMI maternal for Red Angus was 0.10 which only accounted for 6% of the phenotypic variance for DMI; therefore, the effect of the inclusion of a maternal effect for DMI in a genetic evaluation would be minimal. 64 Table 3.3. Direct and maternal variance components of dry matter feed intake for Gelbvieh and Red Angus cattle. H2d H2m H H2pe 2 e h2d Gelbvieh Red Angus 0.52 ± 0.07 0.46 ± 0.13 0.16 x 10-7 ± 0.15 x 10-8 0.10 ± 0.08 0.64 ± 0.06 1.26 ± 0.09 0.75 x 10-7 ± 0.69 x 10-8 0.09 ± 0.06 0.45 ± 0.06 0.26 ± 0.07 h2m 0.00 ± 0.00 0.06 ± 0.05 H2d = direct additive genetic variance; H2m = maternal additive genetic variance; H2e = residual variance; H2pe = permanent environment variance The heritabilities and genetic correlations from the multi-trait analysis of DMI and WWT for Gelbvieh and Red Angus cattle are presented in table 3.4. Given the physiological relationship between DMI and body size (NRC, 2000), a moderate to high genetic correlation for DMI and WWT direct was anticipated. For Red Angus cattle, the estimated genetic correlation between DMI and WWT direct was moderate (0.54 ± 0.17) but the same genetic correlation for Gelbvieh was lower than expected (0.11 ± 0.13). There is a large body of literature describing genetic correlations between DMI and performance traits such as ADG or post weaning traits. However, only three studies (Arthur et al. 2001; Bouquet et al. 2010; Crowley et al., 2011) examined DMI and weaning weight. Arthur et al. (2001) reported a genetic correlation between DMI and weaning weight direct of 0.28 ± 0.15 for Angus cattle with an average age of 268 days. Bouquet et al. (2010) used records from Blonde d’Aquitaine and Limousin bulls 7 to 9 months in age and reported higher correlations of 0.91 ± 0.09 and 0.62 ± 0.12. The current study’s estimated genetic correlation for Red Angus 65 cattle would fall within the correlations reported by Arthur et al. (2001) and Bouquet et al. (2010) but the DMI heritability estimated for Red Angus cattle (0.27 ± 0.05) was lower than the heritabilities reported by Arthur et al. (2001) and Bouquet et al. (2010) of 0.39 and 0.30, respectively. These previously reported heritabilities were similar to our heritability estimated for Gelbvieh cattle; however, the genetic correlation for DMI and WWT direct estimated for Gelbvieh cattle (0.11 ± 0.13) was below the same correlation reported by Arthur et al. (2001) and Bouquet et al. (2010). Crowley et al. (2011) did not report a genetic correlation with DMI and WWT direct. Of the above-mentioned studies, only Arthur et al. (2001) and Crowley et al. (2011) included weaning weight maternal in their analysis. The Bouquet et al. (2010) study did not include maternal genetic effect to overcome calculation limitations. Arthur et al. (2001) and Crowley et al. (2011) estimated genetic correlations between DMI and WWT maternal of 0.45 ± 0.16 and 0.32 ± 0.22, respectively. Both reported correlations were larger than the genetic correlations found in the current analysis. In this current study, low genetic correlations of weaning weight maternal to DMI of 0.12 ± 0.24 resulted for Red Angus cattle and 0.12 ± 0.13 for Gelbvieh cattle with large standard errors for both analyses. 66 Table 3.4. Estimated heritabilities (± S.E.) on the diagonal, above the diagonal is the residual correlation, and genetic correlations (± S.E.) below the diagonal for dry matter intake (DMI), weaning weight direct (WWTD) and weaning weight maternal (WWTM) for Gelbvieh and Red Angus cattle. Breed 1 Gelbvieh DMI 0.45 ± 0.05 WWTD 0.37 ±0.06 WWTD 0.11 ± 0.13 0.36 ± 0.06 - 0.54 ± 0.17 0.21 ± 0.06 WWTM 0.12 ± 0.13 -0.68 ± 0.12 0.15 ± 0.05 0.12 ± 0.24 -0.21 ± 0.32 1 Trait DMI Red Angus WWTM DMI WWTM 0.27 ± 0.05 WWTD 0.37 ± 0.05 - - 0.16 ± 0.07 Traits are measured in kilograms 3.4 Conclusion The accurate estimation of EPD for feed intake traits are dependent on the reliable estimation of variance components. The exclusion of maternal effects when maternal effects can influence the phenotype of a trait, can significantly inflate heritability estimates for traits. This is significant given the increasing interest on selecting cattle for improved feed utilization and the increasing number of breed associations publishing EPD for feed intake and efficiency. The inclusion of maternal effects for the estimation of variance components for feed intake is zero for Gelbveih cattle and only 6% percent of the variability observed in Red Angus cattle. The estimates from this study indicate that the inclusion of maternal effects in genetic evaluations for feed intake would not be warranted. 67 LITERATURE CITED Anderson, R. V., R. J. Rasby, T. J. Klopfenstein, and R. T. Clark. 2005. An evaluation of production and economic efficiency of two beef systems from calving to slaughter. J. Anim. Sci. 83: 694-704. Arthur, P. F., J. A. Archer, D. J. Johnson, R. M. Herd, E. C. Richardson, and P. F. Parnell. 2001a. Genetic and phenotypic variance and covariance components for feed intake, feed efficiency and other postweaning traits in Angus cattle. J. Anim. Sci. 79:2805–2811. Berry, D. P. and J. J. Crowley. 2013. Cell Biology Symposium: Genetics of feed efficiency in dairy and beef cattle. J. Anim. Sci. 91: 1594-1613. BIF. 2016. Guidelines for uniform beef improvement programs. 9th ed. Beef Improvement Federation. p. 25-28. Bouquet, A., M.-N. Fouilloux, G. Renand, and F. Phocas. 2010. Genetic parameters for growth, muscularity, feed efficiency and carcass traits of young beef bulls. Livest. Sci. 129:38– 48. Crowley, J. J., M. McGee, D. A. Kenny, D. H. Crews Jr., R. D. Evans, and D. P. Berry. 2010. Phenotypic and genetic parameters for different measures of feed efficiency in different breeds of Irish performance-tested beef bulls. J. Anim. Sci. 88:885-894. Crowley, J. J., R. D. Evans, N. Mc Hugh, D. A. Kenny, M. McGee, D. H. Crews Jr., and D. P. Berry. 2011. Genetic relationships between feed efficiency in growing males and beef cow performance. J. Anim. Sci. 89:3372–3381. 68 Gilmour, A. R., B. Goegel, B. Cullis, R. Thompson, and D. Butler. 2009. ASReml user guide release 3.0. BSN International Ltd, Hemel Hepstead, UK. Hoque, M. A., P. F. Arthur, K. Hiramoto, A. R. Gilmour, and T. Oikawa. 2007. Variance components due to direct genetic, maternal genetic and permanent environmental effect for growth and feed-efficiency traits in young male Japanese Black cattle. J. Anim. Breed. Genet. 124: 102-107. Lee, J. W., S. B. Choi, Y. H. Jung, J. F. Keown, and L. D. Van Vleck. 2000. Parameter estimates for direct and maternal genetic effects on yearling, eighteen-month, and slaughter weights of Korean native cattle. J. Anim. Sci. 78:1414-1421. Mavrogenis, A. P., E. U. Dillard, and O. W. Robinson. 1978. Genetic analysis of postweaning performance of Hereford bulls. J. Anim. Sci. 47:1004-1013. Meyer, K. 1992. Variance components due to direct and maternal effects for growth traits of Australian Beef Cattle. Livest. Prod. Sci. 31:179-204 Nielsen, M. K., M. D. MacNeil, J. C. M. Dekkers, D. H. Crews Jr., T. A. Rathje, R. M. Enns, and R. L. Weaber. 2013. Review: Lifecycle, total-industry genetic improvement of feed efficiency in beef cattle: Blueprint for the Beef Improvement Federation. Prof. Anim. Sci. 29:559-565. NRC. 2000. Nutrient requirements of beef cattle. 7th rev. ed. Natl. Acad. Press, Washington, DC. Schaeffer, L. R. and B. W. Kennedy. 1989. Effects of embryo transfer in beef cattle on genetic evaluation methodology. J. Anim. Sci. 67:2536-2543. 69 Chapter IV A SIMULATION STUDY EXAMINING GENETIC SELECTION FOR FEED INTAKE AND RESIDUAL FEED INTAKE ON CORRELATED PERFORMANCE TRAITS IN BEEF CATTLE 4.1 Introduction Feed costs are reported as the largest variable expense to producers in the beef industry, accounting for 50 to 70% of total production costs (Anderson et. al, 2005). Due to the large impact of feed cost on profitability, beef cattle producers have become increasingly aware of the need to improve feed utilization. However, there is a debate as to what is the best phenotype for feed efficiency in cattle, how to incorporate it into a breeding program or genetic evaluation, and how the selection for feed efficiency impacts other performance traits (Berry and Pryce, 2013). With advancements in technology, dry matter feed intake (DMI) has become a trait of interest and is readily accepted and understood by beef cattle producers since it is a direct measure of feed consumption. Given that DMI is only a measure of the amount of feed consumed by an animal, it gives no indication of an animal’s performance for other production traits. As such, DMI is not a measure of feed efficiency but is a significant component for the determination of that measure (Berry and Pryce, 2013). Feed efficiency is not a directly measurable trait but must be calculated as a function both inputs and outputs, which in this case are feed intake and production (Koch et al., 1963). Residual feed intake (RFI) has become a prominent, yet contested, trait of interest of feed 70 efficiency (Lu et al., 2015) and is defined as the difference between the actual feed intake and the estimated feed intake adjusted for the requirements of production (Kennedy et al., 1993). The attraction of RFI is that on a phenotypic level, it is independent from the production traits included in its calculation, such as ADG. However, on a genetic level, RFI has been found to be negatively correlated with other productions traits, such as yearling weight. In addition, RFI is conceptually difficult to explain to producers as the calculations for RFI seems complex and difficult to understand (Berry and Pryce, 2013). In the context of genetic improvement of feed efficiency, reducing feed intake should not be the sole goal of a breeding program. Selection pressure should be placed on increasing production traits relevant to a producer’s marketing scheme while simultaneously reducing feed intake (Nielsen et al., 2013). Currently, the effects of selection for RFI or DMI on correlated performance traits, such as weaning or yearling weight, is generally unknown. The objective of this study is to use simulated data to examine the effects of single trait selection on either RFI or DMI on genetically correlated traits of weaning and yearling weight. A third simulation also examines the same traits when a selection is based on the highest-ranking animals from an economic selection index weighted for intake and weight traits. After generating 10 years of simulated data for single trait selection of DMI or RFI, or selecting animals from an index, the effects of the genetically correlated traits of weaning weight and yearling weight were compared. 4.2 Materials and Methods For this study, the performance traits of interest were weaning weight (WWT) and yearling weight (YWT). Three scenarios were simulated using R program (R Core Team, 2018). 71 The first scenario examined single trait selection for average daily dry matter intake (DDMI), the second examined single trait selection for RFI and the final scenario selected animals based on an economic selection index (ESI). In order to generate simulated populations of cattle, phenotypic means were required in addition to genetic and residual (co)variance matrices which were obtained from previously published genetic parameters. Once simulated populations were established, the top 5% of bulls and 20% of heifers for the specific scenario’s trait of interest were chosen as replacements. A 90% conception rate was assumed with cows older than 16 years of age removed and bulls were replaced after 2 years. 4.2.1 Estimation of Weighted Means of Phenotypic Averages and Genetic (Co)variances Given that the objective of this study was the effect of single trait selection for DDMI or RFI on genetically correlated traits, the estimation of the (co)variance components for DDMI, RFI, WWT and YWT are crucial. The estimation of breeding values (EBV) using best linear unbiased prediction (BLUP) requires that variance components were known and as such, the estimation of variance components are important for genetic evaluations. These (co)variances were the dispersion parameters that described the random blocks (i.e. genetic and residual effects) for Henderson’s mixed model equations. The genetic (co)variances described the genetic variation within a trait through direct genetic variance and covariances between. Residual (co)variance describes the within and between trait environmental influences. Within a typical multi-trait BLUP model, each trait included in the model lends information to other traits in the model when genetic and residual covariances exist. The general matrix form of these equations were as follows: 72 0; o g0 i = j ; 0 = 0 :; p kj k + j ; o= :; 0 (; 0 q; k gq i + g( i p= = = (Eq. 4.1) where 0F was a vector of observations for the trait, :F was a vector of fixed effects, qF was a vector of additive genetic effects, (F was a vector for residual effects, and oF and pF were incidence matrices corresponding to :F , and qF , respectively. Variances included in the model were as follows: 1;,; 1;,= q; ⎡ 1=,; 1=,= q '*) W (= X = ⎢ ; ⎢ 0 0 (= ⎣ 0 0 Hr=s & Hrs rt & 0 0 ⎡ ⎤ = 0 0 ⎥ ⎢Hrs rt & Hrt & =⎢ $;,; $;,= ⎥ 0 0 ⎢ $=,; $=,= ⎦ ⎣ 0 0 0 0 0 0 4; Ha=s 4Has at ⎤ ⎥ 4Has at ⎥ ⎥ 4= Ha=t ⎦ (Eq. 4.2) where A was the numerator relationship matrix, I was the identity matrix with an order of the number of animals with observations, Hr=u was the direct additive genetic variance, Hru ruv was the genetic covariance between traits, Ha=u was the residual variance, and Hau auv was the residual covariance. To accurately model the response of genetically correlated traits from selection on DDMI or RFI, both genetic and residual (co)variances needed to be estimated which were the elements of two respective matrices G and R. In order to simulate data that mimic real herd situations, weighted averages of (co)variances components were compiled from phenotypic, genetic and residual estimates previously published in literature using procedures outlined by Koots et al. (1994a). Weighted phenotypic averages were estimated using equation 4.3: 73 ∑{F|; 2F w̅F w̅ y = { ∑F|; 2F (Eq. 4.3) where w̅y was the weighted phenotypic mean of the trait of interest, w̅F was the trait mean from the ith study, 2F was the number of records in the ith study, and k was the number of studies. The weighted phenotypic averages for DDMI, RFI, WWT and YWT were presented in table 4.1. 74 Table 4.1. Weighted averages calculated from literature for residual feed intake (RFI), daily dry matter intake (DDMI), weaning weight (WWT), and yearling weight (YWT). Trait Est. a n Source b RFI -0.01 15 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 17, 18, 19, 22, 24 DDMI (kg) 10.01 15 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 16, 17, 19, 22, 24 WWT (kg) 258.91 8 2, 5, 7, 11, 14, 15, 20, 23 YWT (kg) 479.99 7 2, 5, 7, 10, 11, 14, 23 a Est. = Weighted averages calculated from literature. 1 = Archer et al. (1997), 2 = Arthur et al. (2001a), 3 = Arthur et al. (2001c), 4 = Barwick et al. (2009), 5 = Bouquet et al., 2010, 6 = Ceacero et al. (2016), 7 = Costa et al. (2011), 8 = Crowley et al. (2010), 9 = Durunna et al. (2011b), 10 = Fan et al. (1995), 11 = Herd and Bishop (2000), 12 = Hoque et al. (2006), 13 = Hoque et al. (2009), 14 = Iwaisaki et al. (2005a), 15 = Iwaisaki et al. (2005b), 16 = Korver et al. (1991), 17 = Lancaster et al. (2009), 18 = Mujibi et al. (2011), 19 = Nkrumah et al. (2007b), 20 = Phocas et al. (2004), 19 = Robinson and Oddy (2004), 22 = Rolf et al. (2011), 23 = Roughsedge et al. (2005), 24 = Schenkel et al. (2004), 25 = Williams et al. (2011). b Heritability estimates obtained from a literature review were averaged (Eq. 4.4: Koots et al., 1994a) using a weighting factor of the inverse of the sampling variance for each estimate (Eq. 4.5; Koots et al., 1994a). = ℎy = ℎ= ∑ÇF|; FÅ = }~Uut Ä ∑ÇF|; 1Ñ = }~Uut Ä 75 (Eq. 4.4) = where ℎy is the weighed mean for heritability, ℎF= is the heritability estimated from the ith published study, and ~Ut is the standard error estimate corresponding to the heritability. u Ö(.+ℎ5 Üá ℎF= = 1 = }~Uut Ä (Eq. 4.5) The standard errors for heritability weighted means (~Uy ) were calculated by taking the square root of the summation of weighted factors (Eq. 4.6; Koots et al., 1994a). ~Uy = 1 à Ç 1 ∑F|; â Ñ~U t ä u (Eq. 4.6) All phenotypic and genetic correlations (r) were transformed to approximate a normal scale using a Fisher’s Z transformation (Eq. 4.7; Steele and Torrie, 1980; Koots et al., 1994b). p = 0.5/Ü+ 76 (1 + )) (1 − )) (Eq. 4.7) With standard errors: ~Uå = ç1è(2 − 3) (Eq. 4.8) where r was the correlation (phenotypic and genetic) from literature and n was the number of animals for a phenotypic correlation and number sires for a genetic correlation. Over all studies, the value of Z was pooled with weighting by the inverse of the sampling variance (Eq. 4.9; Koots et al., 1994b): p`êêëa] ∑ÇF|; pFÑ = í~Uåu ì = Ç ∑F|; 1Ñ = í~Uåu ì (Eq. 4.9) The pooled Z values was transformed back to a correlation (Eq. 4.10; Koots et al., 1994b): )= (( =å − 1) (( =å + 1) (Eq. 4.10) Table 4.2 are the weighted genetic variances, correlations (genetic and residual) and heritabilities for DDMI, RFI, WWT, and YWT. 77 Table 4.2. Number of estimates (Est.) from literature (n) and weighted estimates with standard error in parenthesis for genetic variance (diagonal), genetic correlation (above diagonal), residual correlation (below diagonal), and heritability (h2) for residual feed intake (RFI), average daily dry matter intake (DDMI), weaning weight (WWT) and yearling weight (YWT) with sources cited. Trait RFI Est. n RFI 0.18 (0.01) 16 DDMI 0.57 (0.05) WWT 0.02 (0.14) YWT 0.03 (0.14) a Source 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 17, 18, 19, 22, 24, 25 Est. 0.73 (0.08) DDMI n Source a Est. Est. YWT n Source a 12 2, 3, 4, 6, 8, 9, 12, 17, 18, 19, 21, 22 -0.21 (0.23) 2 2, 5 -0.21 (0.23) 2 2, 5 16 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 17, 18, 19, 22, 24, 25 0.79 (0.20) 2 2, 5 0.93 (0.13) 2 2, 5 8 2, 5, 7, 11, 14, 15, 20, 23 0.88 (0.08) 4 2, 7, 15, 23 2 7, 15 598.33 (0.003) 7 2, 5, 7, 10, 11, 15, 23 2, 3, 4, 6, 8, 9, 12, 17, 18, 19, 21, 22 0.69 (0.02) 2 2, 5 0.02 (0.14) 1 5 230.77 (0.20) 2 2, 5 0.53 (0.14) 1 5 0.59 (0.08) 12 WWT n Source a 1, 2, 3, 4, 5, 8, 1, 2, 3, 4, 5, 2, 5, 7, 11, 0.41 0.29 0.35 2, 5, 7, 10, 11, 10, 11, 12, 13, 8, 10, 11, 12, h 16 16 8 14, 15, 20, 7 (0.06) (0.04) (0.11) 15, 23 17, 18, 19, 22, 13, 17, 18, 23 24, 25 19, 22, 24, 25 a 1 = Archer et al. (1997), 2 = Arthur et al. (2001a), 3 = Arthur et al. (2001b), 4 = Barwick et al. (2009), 5 = Bouquet et al., 2010, 6 = Ceacero et al. (2016), 7 = Costa et al. (2011), 8 = Crowley et al. (2010), 9 = Durunna et al. (2011), 10 = Fan et al. (1995), 11 = Herd and Bishop (2000), 12 = Hoque et al. (2006), 13 = Hoque et al. (2009), 14 = Iwaisaki et al. (2005a), 15 = Iwaisaki et al. (2005b), 16 = Korver et al. (1991), 17 = Lancaster et al. (2009), 18 = Mujibi et al. (2011), 19 = Nkrumah et al. (2007b), 20 = Phocas et al. (2004), 19 = Robinson and Oddy (2004), 22 = Rolf et al. (2011), 23 = Roughsedge et al. (2005), 24 = Schenkel et al. (2004), 25 = Williams et al. (2011). 2 0.37 (0.07) 78 4.2.2 Simulated Data In order to simulate a population of beef cattle that would represent industry herds, a base population of 10,000 cows was established to obtain an age distribution that was similar to what occurs in industry. No selection pressure was placed on the base population. From this base population, true breeding values (TBV) were estimated using the weighted heritabilities and (co)variances presented in table 4.1. Selection for decreased DMI, RFI or using an economic selection index (ESI) began using the progeny from the base population as replacements. Replacements were selected dependent on their true breeding values (TBV) for the trait of interest depending on the selection scenario. The simulation continued until 10 years of progeny was generated. The method used to develop the base population and the subsequent selection for decreased DMI and RFI are detailed in the following sections. Female Base Population. A base population of females was established using the R statistical software package (R Core Team, 2018) and the R code written by Larry Schaeffer (http://www.aps.uoguelph.ca/~lrs/Summer2012Full/MTiter.R), this simulated base population began with 10,000 females randomly assigned to 50 herds. A 20% replacement rate was assigned for the establishment of this female base population. In addition, no selection pressure was placed on the population, and 20% of the females were randomly removed for 16 years. Once 16 years of a population was established, females from the initial year were removed (females greater than 16 years of age). With the removal of females greater than 16 years of age, the population of 10,000 females reached an equilibrium for the distribution of age. 79 Table 4.3 was the number and percentage of females expected for each age group within the base population. The generation interval for the age distribution of the female base population was determined (Eq. 4.11). != ∑$%&' ∗ )*+, )./.*0 (Eq. 4.11) Where age is the age of the females (i.e. 2 to 16) from the base population, nage is the number of females for the specific age, and ntotal was the total number of females within the population, in this case 10,000. The distribution of female age resulted in a generation interval of 5.52 years. This population of simulated females was used as the base population of females for the following selection scenarios for DDMI, RFI or ESI. Table 4.3. Number of females for each age group used as a base population for a simulation study (n=10,000). 1 1 Females 0 137 118 148 170 207 287 377 417 530 701 824 1048 1372 1664 2000 Age 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 Percentage 0% 1% 1% 1% 2% 2% 3% 4% 4% 5% 7% 8% 10% 14% 17% 20% Females are the number of females for each age. 80 Simulation of Data. Four hundred fifty bulls were simulated to establish a 1:22 bull to cow ratio and were randomly assigned to the 50 herds established during the development of the female base population. The females from the established base population were randomly mated to the bulls with an assumed 90% conception rate for females, resulting in 9,000 progeny born year 1 of the simulation (P1). Progeny were classified by the year they are born as Pn, where n represents the year of birth. For example, progeny born during year 1, 2 and 3 are designated as P1, P2, and P3, respectively. Cows that did not produce offspring (open) were removed from the simulation resulting in 9,000 females from the base population that were retained to year 2. Open cows were designated by the simulation randomly, regardless of their TBV. Selection for the trait of interest only occurred on replacement heifers and bulls based on their TBV for that specific trait. Since cattle are 2 years of age when their first offspring are born, there is a delay before replacement heifers and bulls are contributing progeny to the population. As a result, selection for the traits of interest did not occur until progeny from the base population were old enough to be used as replacements. The progeny born year 1 of the simulation (P1) contributed offspring to the population year 3, and progeny born year 2 (P2) contributed offspring to year 4, and so forth until year 10 (Figure 1). 81 Year 1 Base Population (BP) 90% Conception Rate Progeny from year 1 (P1) n =9,000 Cows = 10,000 Bulls = 450 Cull open cows Replacements: 2,000 heifers, 225 bulls Year 2 Base Population (BP) Progeny from year 2 (P2) n = 8,100 Cows = 9,000 Bulls = 450 Retained 8,000 cows & 225 bulls Replacements: 2,000 heifers, 225 bulls Year 3 BP + P1 Progeny from year 3 (P3) n = 9,000 Cows & Heifers = 10,000 Bulls = 450 Retained 8,000 cows & 225 bulls Replacements: 2,000 heifers, 225 bulls Year 4 BP + P1 + P2 Progeny from year 4 (P4) n = 9,000 Cows = 10,000 Bulls = 450 Replacements: 2,000 heifers, 225 bulls Repeat until year 10 Year 5 Year 6 Year 10 BP + P1 + P2 + … + P8 Progeny from year 10 (P10) Final calf crop Cows = 10,000 Figure 4.1. Schematic representation of simulated data used to generate populations of cattle for single trait selection for either daily dry matter intake, residual feed intake, or an economic selection index. 82 For year 2, only animals from the base population were used for the simulation of P2 since replacement heifers and bulls would be too young to produce offspring until year 3. At a conception rate of 90%, the number of females from the base population, as well as the number of progeny, would reduce from 9,000 to 8,100 for year 3. Year 2 is the only year were the calf crop is below 9,000, each subsequent year, the calf crop would remain at 9,000. Beginning during year 2 and subsequent years, females greater than 16 years of age were removed. From year 3 to year 10, only 8,000 cows would be retained for the next year. Once cows were culled due to reproductive failure or age, the simulation randomly selected 8,000 retained cows to produce progeny for the next year. Progeny from replacement heifers and bulls born year 1 (P1) were introduced into the breeding population during year 3. Progeny from each year were ranked by their TBV with the top 2,000 heifers and 225 bulls chosen as replacements each year. For progeny from year 3 to year 10, yearling and 2-year-old bulls were used resulting in a generation interval of 2.5 years for males. Animals that failed to gain more than 40 kg from weaning to yearling weight, were removed as potential replacements regardless of their TBV. Selection for the trait of interest began with the replacement heifers and bulls producing calves during year 3. From year 3 to year 10, all 3-year-old bulls were replaced each year and 20% of the cows were culled and replaced with 2,000 heifers reestablishing a female population of 10,000 each year. Based on the R code written by Larry Schaeffer (http://www.aps.uoguelph.ca/~lrs/Summer2012Full/MTiter.R), true breeding values (TBV) and observations were created using the R program (R Core Team, 2018). Genetic (G) and residual (R) covariance matrices were constructed using the weighted heritabilities, genetic variances and correlations mentioned previously (Table 4.1). No observations were simulated for the base 83 population, but true breeding values were estimated for the initial base population using a Cholesky decomposition as a function of the G and R matrices. The Cholesky decomposition factors a positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose (Meyer, 1996; Mrode, 2005). For the Cholesky decomposition of matrix A (Eq. 4.12): A = LL3 (Eq. 4.12) where L was the lower triangular matrix (Cholesky factor) with elements 456 $456 = 0 for < > >- and L3 was the inverse of L. The elements of L can be derived by the following (Eq. 4.13 and 4.14) 6FG E L6,6 = @A6,6 − C L6,D DHG (Eq. 4.13) L5,6 6FG 1 = JA5,6 − C L5,D L6,D K L6,6 DHG LMN > > < (Eq. 4.14) True breeding values for progeny were simulated using the average of the parents’ TBV and a mendelian sampling effect. The mendelian sampling effect was estimated by multiplying a vector of randomly generated numbers with an average of zero and a standard deviation of 1 by the Cholesky factor of the G matrix. For each year’s progeny, observations were estimated as the trait average, fixed effects (sex and herd), and TBV (Eq. 4.15): 84 O56 = P6 + ℎ5 + STU56 (Eq. 4.15) Where O56 was the simulated observation for the ith animal for the jth trait, P6 was the average of the jth trait, ℎ5 was the fixed effects of sex and herd, and STU56 was the true breeding value. The fixed effect for herd was estimated by using randomly generated, normally distributed vector of numbers with a mean of zero and a non-specified standard deviation. Previously published sex effects for weaning and yearling weight (Van Vleck and Cundiff, 1998) were used. Initial observations for progeny born year 1 used weighted phenotypic averages calculated using equation 4.1 (Table 4.1; Koots et al., 1994a). For each year, new population phenotypic averages would be recalculated using the simulated observations. It was anticipated that the phenotypic observations for each trait would change as genetic selection occurred. Selection Scenarios. Three selection scenarios were used for this study. The first scenario (SDDMI) was the single trait selection for DDMI, the second scenario (SRFI) was the single trait selection for RFI, and the last scenario (SESI) was selection using an economic selection index (ESI). Selection on DDMI and RFI followed the same procedures. Selection on the index followed a similar procedure except for the calculation of the ESI and selection which was based on the index values (Table 4.5) instead of DDMI or RFI. All three scenarios used simulated data from the female base population. For selection scenarios SDDMI and SRFI, true breeding values for DDMI and RFI were used for the selection of replacement bulls and heifers. For the third selection scenario (SESI), TBV were weighted for DDMI, average daily gain, weaning and yearling weight to estimate 85 economic selection index values. Animals were ranked based on those index values and chosen from the top 5% for bulls and top 20% for heifers to be used as replacements. Economic Selection Index. An economic selection index is a method of multi-trait selection by applying economic weights to the breeding values for relevant traits to predict an aggregate breeding value for an individual and is represented as follows (Eq. 4.16; Bourdon, 1997): V = UG WXG + UE WXE + ⋯ + U. WX. (Eq. 4.16) Where H was the index value, U5 was the economic weight for the trait, WX5 was the breeding values for the trait, and t is the total number of traits incorporated in the index. The economic selection index for this study was developed to account for yearling cattle prices as a revenue source and feed prices as an expense for the profitability of the simulated cattle populations. Other factors such as cow costs, labor and herd health were not considered for this index. Cattle prices were estimated using monthly futures market prices for United States fed cattle (www.investing.com/commodities/live-cattle-historical-data), averaged over 10 years resulting in a fed cattle price of $2.64/kg. A finishing ration of 80% corn, 10% hay, 5% distillers’ grain and 5% supplement were assumed for the calculation of feed costs. The cost of each feedstuff within the ration were calculated using a 10-year average of commodity prices with the exception of the supplement which was considered as a constant. Table 4.3 is the average price for fed cattle, the cost of each feed ingredient per kilogram and the total ration cost per kilogram. 86 Table 4.4. Ten-year average for cattle and commodity prices. 1 Cattle Corn 3 DDGS Average per kg $2.64 $0.18 $0.18 Hay $0.17 Supplement Total Ration Cost $0.29 2 Source www.investing.com/commodities/live-cattle-historical-data www.nass.usda.gov/Charts_and_Maps/graphics/data/pricecn.txt www.marketnews.usda.gov/mnp/ls-report-config www.asi.k-state.edu/about/newsletters/focus-on-feedlots/monthlyreports.html www.iowabeefcenter.org/calculators.html $0.18 1 Ten year average per kilogram Reference for cattle and commodity prices 3 Distillers' grain 2 To estimate total feed consumed for finished yearling cattle in a feedlot, a 10-year average for days on feed was calculated (Focus on Feedlots Monthly Reports, https://www.asi.kstate.edu/about/newsletters/focus-on-feedlots/monthly-reports.html) resulting in 157 d as the average days to finish. Using the methods previously described, phenotypes for DDMI, ADG, WWT and YWT as well as TBV for a population of cattle was simulated using the G and R matrices from the DDMI simulation. Using this population of cattle, the profit for each animal was calculated as follows (Eq. 4.17): ZNML>S = $2.64 ∗ `ab + 157 ∗ $0.18 ∗ ffgh (Eq. 4.17) where YWT and DDMI are the phenotypes for yearling weight and average daily dry matter intake, respectively, and 157 was the average days on feed. 87 To estimate an economic index, profit was regressed on the TBV of the simulated population of cattle (Eq. 4.18): ZNML>S = bWXiijk UG + bWXlim UE + bWXnno Up + bWXqno Ur + ' (Eq. 4.18) Regression coefficients and corresponding p-values are presented in table 4.4. Average daily gain and weaning weight were not important (p > 0.05) in the model. Average daily dry matter intake had the largest, negative coefficient which was expected given its significant cost to producers. With the establishment of the index (Eq. 4.19), data was simulated using the same genetic parameters as the DDMI simulation with the selection of replacement bulls and heifers dependent on their index value instead of the TBV. Table 4.5. Regression coefficients for the selection index for dry matter intake. Trait Coefficient P-value 1 DDMI -29.669 <0.0001 2 ADG 21.994 0.555 3 WWT 0.097 0.554 4 YWT 2.551 <0.0001 Average daily dry matter Intake breeding value 2 Average daily gain breeding value 3 Weaning weight breeding value 4 Yearling weight breeding value 1 V = −29.669WXiijk + 21.994WXlim + 0.097WXnno + 2.551WXqno 88 (Eq. 4.19) 4.3 Results and Discussion Figure 4.2 illustrated the change in DDMI and YWT over the ten years of simulated data and the averages for DDMI, WWT and YWT for all 3 simulations are presented in table 4.5. In the first simulation, for the selection on DDMI demonstrated the largest decline in all traits included in the simulation. There was a yearly average decrease of 0.85 kg/year in DDMI and a decrease of 7.09 kg for progeny averages of P1 compared to P10. This simulation also demonstrated a drastic decline for both genetically correlated traits, weaning and yearling weights. There was an annual average loss of 14.03 kg/year and 27.83 kg/year for weaning and yearling weight, respectively, resulting in decreased progeny averages of 119.14 kg for weaning weight and 240.18 kg for yearling weights over the specified time frame. In addition to the loss in growth traits, there was also a decrease in the number of progeny. Since the simulation assigned observations (phenotypes) based on a distribution and accounted for environmental effects such as herd and sex, the rapid decrease in DDMI resulted in some progeny having a negative DDMI. Since this was not biologically plausible, simulated cattle with DDMI less than 1 were removed resulting in a reduction in population size for this simulation (table 4.6). 89 14.00 600.00 12.00 500.00 10.00 400.00 8.00 300.00 6.00 200.00 4.00 100.00 2.00 0.00 0.00 1 2 3 4 5 6 7 8 9 Dry Mater Intake (kg) Cattle Weight (kg) 700.00 10 Year SDDMI Yearling Weight SRFI Yearling Weight SESI Yearling Weight SDDMI Dry Matter Intake SRFI Dry Matter Intake SESI Dry Matter Intake Figure 4.2. The simulated changes in phenotypic dry matter intake and yearling weight for three selection scenarios. SDDMI was the single trait selection of dry matter intake and the response to the genetically correlated trait yearling weight. SRFI was the selection of residual feed intake and the response of genetically correlated traits of dry matter intake and yearling weight. SESI was a simulation of selection using economic index values with genetically correlated traits of dry matter intake and yearling weight. 90 Table 4.6. The phenotypic average for each year's progeny from 3 simulation scenarios with selection on average daily dry matter intake (DDMI), residual feed intake (RFI) and an economic selection index. Included are the progeny averages of DDMI and genetically correlated traits included in each simulation (weaning weight and yearling weight). Year DDMI (kg) Weaning Weight (kg) Yearling Weight (kg) SDDMI1 SRFI2 SESI3 SDDMI1 SRFI2 SESI3 SDDMI1 SRFI2 SESI3 1 9.51 9.91 9.52 248.10 248.50 248.10 480.50 481.00 480.50 2 9.52 9.91 9.52 248.20 248.30 248.20 480.50 480.60 480.50 3 6.94 9.42 10.69 203.30 239.90 264.30 398.90 467.50 509.80 4 6.88 9.47 9.66 211.67 237.20 250.40 409.20 455.30 503.20 5 5.31 9.14 10.89 179.55 236.10 269.00 348.20 453.90 525.70 6 4.57 9.05 11.00 170.46 235.00 271.40 329.40 447.70 536.10 7 3.78 8.81 11.59 158.60 234.00 280.80 309.50 444.70 552.60 8 2.97 8.62 12.14 141.44 234.20 290.90 272.76 441.50 572.50 9 2.88 8.54 12.64 139.00 234.60 300.00 268.90 441.60 591.00 10 2.42 8.21 13.33 128.96 233.40 313.00 240.32 434.50 614.30 1 SDDMI was the simulation of single trait selection for DDMI and correlated traits of weaning weight and yearling weight. SRFI2 was the simulation of single trait selection for RFI and correlated traits of weaning weight and yearling weight. SESI3 was the simulated data from selection based on economic selection index values. 91 Table 4.7. Number of simulated progenies produced each year for three simulations scenarios. Year SDDMI1 SRFI2 SESI3 1 8964 8965 8964 2 8067 8069 8067 3 8960 8963 8935 4 8980 8960 8952 5 8903 8960 8917 6 8760 8958 8936 7 7190 8937 8824 8 6802 8957 8895 9 6527 8961 8862 10 4536 8959 8829 1 SDDMI was the simulation of single trait selection for DDMI and the response of correlated traits weaning weight and yearling weight. SRFI2 was the simulation of single trait selection for residual feed intake and correlated traits of weaning weight and yearling weight. SESI3 was the simulated data from selection based on selection index values. The number of progeny per year for SDDMI began to decline after the fifth year. This was compared to the other simulation scenarios that had minimal loss in number of progeny. A decline in progeny number of this extent would significantly affect the profitability and sustainability of production operations. The first simulation scenario performed as expected with regards to the decline in DDMI, WWT and YWT. Increasing output traits, such as yearling weight, will cause input traits, such as DDMI, to also increase (Meyer et al., 2008). It is reasonable to expect that the inverse is also true, decreased input would simultaneously decrease output as evident in SDDMI. Published genetic correlations between feed intake and performance traits of weaning and yearling weight are limited; however, these few published correlations (Arthur et al., 2001a; Bouquet et al., 92 2001) indicate a strong correlation between DDMI to weaning and yearling weights. This strong correlation coupled with a weighted heritability of 0.41 was evident in the rapid decline in DDMI, WWT and YWT for SDDMI. The simulation protocol for the selection for decreased RFI TBV demonstrated a less severe decrease in DDMI and YWT compared to SDDMI. The decrease in DDMI for SRFI was an average annual decrease of 0.19kg/year which was less of a decline than what was seen with SDDMI. A decrease in weaning and yearling weights were also seen with an average annual decline of 1.64 kg/year and 5.13 kg/year, respectively. From year 1 to year 10, there was a decrease of 45.60 kg for average progeny yearling weight. This loss in progeny yearling weight was not as drastic as SDDMI and as a result, there was minimal change in progeny numbers from year to year. When comparing SDDMI and SRFI, SRFI suggests a better selection scenario for a production operation; however, for operations selling cattle based on yearling weight, there would still be a potential loss in profit given the decrease in YWT with only slight decreases in DDMI. The popularity of RFI as a measure of feed efficiency has increased since it was proposed by Koch et al. (1963). The increased interest in RFI has been due to the zero phenotypic correlation of RFI to performance traits included in the calculation of RFI (Berry and Crowley, 2013). Typically, these performance traits include average daily gain, metabolic weight and back fat thickness but has no consideration of performance traits that most cattle are valued at, such as actual live or carcass weights. Herd et al. (2003) argued that an opportunity existed for the improvement of whole-herd production for efficiency through exploiting genetic variation in RFI in addition to genetic correlations with other performance traits. However, the computation of RFI give no direct consideration for underlying genetic regressions (Kennedy et al., 1993) and 93 there are genetic correlations to performance traits which would over time, affect the performance of those traits. Simulation 2 demonstrated the effect of genetic correlations between RFI and performance traits WWT and YWT leading to a decrease in performance for both weight traits. For beef cattle production systems whose end product is dependent on cattle weight, selection for RFI may not be optimal for these operations. The final simulation (SESI) used economic index values for selection. Economic weights were placed on the TBV of DDMI, ADG, WWT and YWT with selection of replacement animals dependent on the animal’s ranking of index values. An increase for DDMI, ADG, WWT and YWT was observed. An average annual increase of 0.42 kg/year occurred for DDMI with an increase of 3.81 kg from the progeny average from year 10 compared to year 1. Both weaning and yearling weight also increased by 7.11 kg/year and 14.84 kg/year, respectively. In contrast to SDDMI and SRFI, SESI was the only simulation that resulted in a gain in output traits such as WWT and YWT, but it consequently resulted in an elevation of DDMI. When defining feed efficiency as a gain in output traits, such as WWT and YWT, while simultaneously reducing input traits (DDMI), SESI appears to not have met this requirement since there was an increase in DDMI. Simulations SDDMI and SRFI also failed to meet this requirement given that WWT and YWT both decreased. The implementation of a restricted selection index (Gibson and Kennedy, 1990) could be utilized to meet the requirements for the definition of feed efficiency by maintaining a genetic gain for DDMI to zero. A restricted selection index was constructed to maximize improvement in output traits (i.e. WWT and YWT) while limiting genetic change on an input trait (i.e. DMI; Eisen, 1997). Gibson and Kennedy (1990) concluded that constrained indexes would not be ideal economically as they would cause severe economic losses. The response to selection for an economic index was determined by the economic merit 94 of the traits included in the index. Within a restricted index, the economic merit was also restricted resulting in a loss of potential economic gain (Gibson and Kennedy, 1990). To explore the economic merit for all 3 simulations, the average yearling price was estimated using the 10-year average cattle price and feed cost in presented in table 4.3. In addition, a 10-year average for days to finish was also estimated at 157 d (Focus on Feedlots Monthly Reports, https://www.asi.k-state.edu/about/newsletters/focus-on-feedlots/monthlyreports.html). Total feed intake cost for a finishing phase was estimated by multiplying the average DDMI to 157 days to finish to the total ration cost of $0.18/kg. An estimated selling price of cattle was calculated by using the yearling weight multiplied to the estimated 10-year average cattle price of $2.64/kg. The feed cost was subtracted from the estimated cattle price. The differences in profits were presented in figures 4.2 and 4.3. Figure 4.2 illustrates the profit or loss on a per head basis using the annual progeny average for each year. Figure 4.3 uses the same profit or loss as presented in figure 4.2 but also included the number of progenies for each year. 95 $1,400.00 $1,200.00 $1,000.00 $800.00 SDDMI Profit SRFI Profit $600.00 SESI Profit $400.00 $200.00 $1 2 3 4 5 6 7 8 9 10 Year Figure 4.3. The average per head progeny profit or loss for three simulation scenarios. SDDMI was a simulation for the single trait selection on average daily dry matter intake, SRFI was the simulation for selection on residual feed intake, and SESI is the simulation for use of an economic index for yearling weight and feed intake. 96 $12,000,000.00 $10,000,000.00 $8,000,000.00 SDDMI Profit $6,000,000.00 SRFI Profit SESI Profit $4,000,000.00 $2,000,000.00 $1 2 3 4 5 6 7 8 9 10 Year Figure 4.4 The profit or loss for the progeny from three simulation scenarios. SDDMI was a simulation for the single trait selection on average daily dry matter intake, SRFI was the simulation for selection on residual feed intake, and SESI is the simulation for use of an economic index for yearling weight and feed intake. The comparison of the profitability on a per head basis of all three simulations was presented in table 4.7. The economic index simulation (SESI) was the only simulation that resulted in an increase of output (yearling weight) resulting in an increase in the average income from cattle prices. Simulation 3 also resulted in an increase in input costs (DDMI), the increase in yearling weight, and subsequent increase in average income from cattle prices, was significant enough to increase the profitability even with an increase in input costs. The results from SESI would support the recommendation of Nielsen et al. (2013) to incorporate feed intake into national cattle evaluations as an economically relevant trait within a selection index. Simulation 1 resulted in the largest decrease in DDMI, but it simultaneously resulted in a decrease in YWT. On a per head basis, the economic loss of SDDMI was the largest compared to the other 97 simulations. When considering the entire population of simulated cattle, the economic loss of SDDMI was even more drastic given the significant loss of progeny after year 5. The simulation for the single trait selection of RFI also showed a negative profitability after 10 years of selection but the degree of the loss was not as drastic as SDDMI. Although SRFI did decrease DDMI there was also a decrease in WWT and YWT through the genetic correlation of RFI to these traits, resulting in an overall economic loss for this simulation. Table 4.8. Changes in estimated costs and incomes from the simulation of selection on average daily dry matter intake (SDDMI), residual feed intake (SRFI) or an economic index (SESI) on the average per head basis from year 1 to year 10. SDDMI DDMI a Cattle b Year 1 c Year 10 Profit e d SRFI SESI $ (200.48) $ (47.96) $ 107.78 $ (634.08) $ (120.38) $ 353.23 $ 999.60 $ 989.90 $ 999.60 $ 566.00 $ 917.47 $ 1,245.05 $ (433.60) $ (72.43) $ 245.45 DDMI a change in cost of feed from year 1 to year 10 for simulated data. Cattle b was the change income from averaged per head cattle prices from year 1 to year 10 for simulated data. Year 1 c was the difference from average cattle per head sale price and feed cost for year 1 of simulated data. Year 10 d was the difference from average cattle per head sale price and feed cost for year 10 of simulated data. Profit e was the change in profit from year 1 to year 10. Values within parenthesis are negative dollar amounts. 98 4.4 Conclusion Simulated data were used to illustrate the effects of selection for decreased feed intake and the response to this selection on correlated weight traits. Single trait selection for decreased DDMI or RFI resulted in decreased performance in output traits of WWT and YWT. As a consequence of decreased WWT and YWT, the overall production of these scenarios decreased. Although DDMI was reduced and therefore reduced production cost, this savings in cost was not important enough to account for the loss in revenue from decreased cattle weight. The third selection scenario used economic weights to account for the cost of production and revenue from cattle. Although simulation 3 resulted in an increase in DDMI, there were also increases in WWT and YWT resulting in higher revenues. Residual feed intake has increased in popularity as a feed efficiency trait that accounts for production traits, such as ADG. Although RFI has a zero phenotypic correlation to production traits, this study illustrated how selection for lowering RFI breeding values could affect production traits such as WWT and YWT and ultimately affect profitability of the herd. The results of this study also illustrated the application of an economic index as a method of multi-trait selection to increase revenue by increasing YWT but account for the cost of DDMI therefore increasing the profitability of an operation. A weakness of this study was its dependence of published genetic and phenotypic estimates for RFI and DDMI and their correlations to production traits. The majority of published correlations with DDMI and RFI are to traits measured during feeding trails for measuring intake (i.e. metabolic mid-weight, average daily gain). Overall, there was a general lack of published genetic parameters of feed efficiency and its correlation to production traits, such as yearling weight. 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Dairy Sci. 94:4715–4726. 106 Chapter V ESTIMATION OF FORAGE INTAKE FOR GRAZING BEEF CATTLE USING EAR TAG ACCELEROMETER TECHNOLOGY 5.1 Introduction Producing efficient beef cattle is a goal for animal breeders to meet the increasing demands of the world’s growing population (9.7 billion by 2050; FAO, 2009) that relies on limited resources for food production. In addition, feed intake has been shown to be positively correlated to greenhouse gas emission from beef cattle (0.65 ± 0.02; Herd et al., 2014) and reducing the overall feed intake of the cow herd while maintaining production through genetic selection would reduce greenhouse gas emissions. Given that cattle finished in a feedlot spend 50 to 70% of their lifespan grazing forage prior to feedlot entry (Capper, 2011), a reduction of forage intake would likely contribute to the reduction of greenhouse gases. Furthermore, decreasing forage intake on rangeland has the potential of improving pasture quality. When cattle require less feed for production, stress placed on pastures due to drought, overgrazing or climate change could be mitigated. Currently, individual feed intake measurements are collected in feedlot environments. The application of feedlot-measured intakes has a direct application to fed cattle, but the translation of these intakes to a cowherd grazing on rangeland is unknown. Feed costs are the largest variable expense to producers in the beef industry (Anderson et al., 2005) and 107 approximately 50% of which are attributed to the mature cow herd (Whisnet, USDA-NIFACRIS) with 70 to 75% of the total annual energy for maintenance (Ferrell and Jenkins, 1985). Selection for beef cattle with decreased feed costs without sacrificing production, would increase profitability for producers. However, to select for decreased feed intake, individual feed intake must be measured. To date, there is no technology to easily measure feed intake on a population of grazing cattle and the relationship between feed intake measured in a feedlot and intake from grazing cattle are unknown. Therefore, the objectives of this study were 1) to examine the use of an ear tag accelerometer (CowManger; Agis Automatisering BV, Harmelen, Netherlands) and corresponding data to develop a proxy for grazing intakes 2) to validate the data collected by the ear tag accelerometer, 3) to explore potential interference from other technologies, such as GrowSafe, with the ear tag accleerometer, 4) to examine the phenotypic correlation between grazing and feedlot intake and 5) to validate the use of a biomarker for the estimation of DMI. 5.2 Materials and Methods Animals and Procedures. Institutional Animal Care and Use Committee at Colorado State University approved all animal procedures (approval number 17-7179A). Yearling Angus steers (n = 98) from the Colorado State University Beef Improvement Center (BIC) were placed in the Feed Intake Unit (FIU) at Colorado State University’s Agriculture Research, Development and Education Center (ARDEC) located north of Fort Collins, CO mid-April 2017. The Feed Intake Unit was equipped with GrowSafe Feed Intake monitoring system (GrowSafe Systems, Ltd., Airdire, AB, Canada) that contains 6 pens capable of housing up to 35 animals per pen with 4 GrowSafe nodes per pen. Upon arrival, steers were equipped with an electronic ear tag (EID; 108 Allflex USA Inc., Dallas TX) for individual identification of animals by GrowSafe. In addition, cattle were also equipped with a CowManager ear tag accelerometer (CME) to monitor eating, rumination and activity behavior (Agis Automatisering BV, Harmelen, The Netherlands). The CowManager ear tag is a 3-deminsional accelerometer that attaches to an EID and was placed in the center of the animal’s ear. Based on the ear and jaw movement of cattle, the CME has developed a proprietary algorithm to calculate time spent eating, ruminating, resting and activity within each hour. These data were collected by CME and transmitted to a router with a 1,524 m radius. From the router, the information is sent to a coordinator connected to a laptop with an internet connection located at the research center. The raw data is transmitted to Agis Automatisering BV, Netherlands, where their algorithms transform the data for each behavior. Final behavioral data was downloaded to researchers each day in addition to the CowManager online application. Five behaviors were recorded by CME: eating (EAT), rumination (RUM), not active (NACT), active (ACT) and high active (HACT). The behavior of EAT measured the amount of time the animal spent consuming feed and RUM measured the amount of time when regurgitation occurred. Three levels of activity were observed by CME: NACT, ACT and HACT. The activity level of NACT was measured as the time the animal was inactive and not eating or ruminating. Active was measured as a low level of activity such as walking short distances, scratching or licking and HACT was measured as a higher level of activity such as mounting. Since each minute within an hour was allocated to each behavior, the summation of the reported behaviors within each hour was 60 minutes with no overlapping of behavioral times. The behavior times were summed to account for a 24-hour period. Times that did not sum to 1440 minutes (24 hours) were removed from the study. 109 Steers were weighed before entry into the FIU for a 21-d adaptation period, followed by a shortened 54-d performance test to measure feed intake in accordance with findings from Culbertson et al., (2015). Cattle were weighed on d 0, 14, 28, 42 and 54 with individual feed intakes collected by the GrowSafe Feed Intake monitoring system. Cattle were fed ration ad libitum. The ration (Table 5.1) consisted of NEg of 51.50 mcal/cwt and a CP of 14.87%. Based on DMI, the 15 lowest intake and 15 highest intake animals were identified. These low/high intake (LHI) animals were used to quantify grazing intake using the biomarker titanium dioxide (TiO2). It should be noted that DMI was not adjusted in any way for weight or body size since the objective of this study was to identify an indicator for intake in a grazing setting. Table 5.1 Composition of rations fed to cattle in Colorado State University Feed Intake Unit on an as fed basis. Percentage 9.77% 38.00% 8.00% 25.00% 14.48% 0.89% 0.10% 3.75% Ingredient Alfalfa Hay Corn Silage Wheat Straw Corn Dry Grain Distillers Grain Limestone Salt 30% Hay Treat Immediately following the performance test in the FIU, cattle were transported on July 1, 2017 to Colorado State University Eastern Colorado Research Center (ECRC) in Akron, CO where the cattle were placed on a 180 acre pasture comprised of western wheatgrass (Pascopyrum smithii), sand bluestem (Andropogon hallii), blue gamma (Bouteloua gracilis), and prairie sand reed (Calamovilfa longifolia). Cattle had a 1-week adaptation period when placed on 110 pasture before data was collected using CME beginning on July 8, 2017. Cattle were maintained on pasture for a total of 43 days and were removed on August 13, 2017. The first router for CME was placed at the pasture’s water source and the second router placed 957 m from the water source and 852 m from ECRC’s main office where the coordinator and laptop were located in ECRC’s main office (Figure 1; Google Earth, 2019). 111 Figure 5.1. Picture of Colorado State University’s Eastern Colorado Research Center diagraming the positioning of CowManager routers (Google Earth, 2019). 112 In order to quantify grazing intake, a TiO2 biomarker was used (Meyer et al., 2004; Titgemeyer et al., 2001). For the final 20 d of maintaining cattle on pasture, the subset of LHI cattle (n = 30) were administer a 10 g of TiO2 bolus each morning. It was required to bolus individual steers daily to ensure the adequate daily dose of TiO2 was received. Each bolus contained 10 g of powdered TiO2 within a gelatin capsule 7 cm in length and 1 cm radius (Torpac; Fairfeild, NJ). Steers were adapted to the TiO2 for 14 d prior to fecal collections. Following the adaptation period, rectal fecal collections were conducted twice daily for 6 consecutive days with collections occurring 12 h apart. Every 24 h, time of collection was advanced 2 hours to minimize effects of diurnal variation (Meyer et al., 2004; Titgemeyer et al., 2001). As a result, each of the 30 steers sampled had 12 samples per steer. Once fecal collections were completed, each fecal sample was placed in an aluminum pan and dried at 60°C in forced-air ovens for 48 h to 72 h. Once dry, samples were ground into fine particles using coffee bean grinders. For the 12 samples per animal, 10% of the dried weight of each sample per animal was combined into one final composite sample for each individual animal (12 samples were combined into 1 composite sample per animal). The final composite samples were analyzed for TiO2 dioxide concentrations. Using the method proposed by Theurer (1996), grazing intake (GI) was estimated on a dry matter basis using equation 5.1: !" = %&'*()(+ ∗ 100 (Eq. 5.1) In the above equation, GI was the dry matter grazing intake in kg/d, FO was fecal output in kg/d, and DMD was the in vitro dry matter disappearance of feed samples expressed as a percentage. The fecal output was determined using equation 5.2: 113 &' = ('/0*&) (Eq. 5.2) Where DOSE was the TiO2 administered in g/d and FM was the fecal marker (mg/g). Validation Study. On January 16, 2018, 128 steers from BIC were placed in the FIU. The processing and testing procedures for the FIU, as stated previously, were repeated. During processing, animals were randomly allocated to 4 pens within the FIU resulting in 32 steers per pen. Individual DMI was measured using the GrowSafe system and data was collected via CowManager. On day 30, the variance of DMI within each pen was estimated. The pen with the most variance in DMI was identified and used for the validation of TiO2. The validation of TiO2 was conducted by the addition of 320 g of TiO2 (10g per head per day) into the steers’ daily ration. The TiO2 was mixed into the steers’ ration daily when feedstuffs were mixed by the feed truck each day. The cattle were fed TiO2 for 14 days as an adaptation period followed by 6 days of fecal sample collection. Fecal samples were collected following the same procedures performed in the previous year. The estimated intakes from the TiO2 concentrations were compared to the intakes measured using the GrowSafe system. The validation of the CME for the measurement of feeding behaviors was also conducted. Over the course of 3 days, 4 to 7 steers were chosen each day at random for a total of 18 steers. The number of steers per day varied due to the number of observers present. These steers were marked with chalk for ease of recognition. Observers were assigned 1 to 2 steers per observer. All observers were trained to record observations of rumination and eating by watching videos of steers expressing said behaviors. Some animals were assigned to more than 1 observer to 114 validate the observers’ ability to record observations. The observers recorded the animal’s eating, rumination and activity level for 4 hours. Observations made by 2 observers watching the same steer were compared to insure consistency between observers. Correlations over all behaviors observed for 1 animal between 2 observers less than 0.95 resulted in the removal of the observations from those observers from the analysis. As a result, 5 steers with observations remained for validation. These observations were then compared to the measurements recorded by CME. To explore potential interference of GrowSafe with CME, the latter was placed in 5 finishing steers located at ARDEC not housed in the FIU. These steers were located in a 10 head pen with a concrete feed bunk. Unlike the GrowSafe system, the concrete bunk required the animals to completely lower their head down to the ground to access feed. When the GrowSafe feed bunks were filled with feed, cattle feeding from the GrowSafe bunks were not required to lower their heads in order to reach feed and could have caused a potential interference with how CME recorded eating or rumination (Figure 1). The observation of these 5 finishing steers allowed for a comparison of observations collected from steers within the GrowSafe system and outside of GrowSafe to examine any possible electronic interference of GrowSafe with CME. These 5 steers were equipped with CME 7 days prior to observations. Steers were observed for 2 hours by two observers. Each observer was assigned 3 steers each with 1 steer being observed by both observers. As with the previous observations of steers in the FIU, correlations of behaviors for the single steer observed by both observers was used to validate the consistency of the observations made between observers. A correlation of 0.98 was achieved and therefore the observations of both observers for all steers were included. Observations and CME measurements were compared for those 2 hours. 115 Figure 5.2 Picture of GrowSafe System feed bunks (right side of picture) and concrete feed bunk (left side of picture) at Colorado State University’s Feed Intake Unit. Given that the CME were initially developed for use in dairy cattle and differences with monitoring systems have been observed between dairy and beef cattle (Goldhawk et al., 2013), to further investigate potential differences between dairy and beef cattle, 4 dairy cows located at a dairy utilizing CME, were also observed for 2 hours. Two observers selected 4 dairy cows and observed eating, rumination and activity levels for 2 hours. The observational period began shortly after the cows returned from the milking parlor. Observation and CME measurements were compared. Statistical Analysis. A regression analysis was used to examine the association between DMI and CME measurements. Each variable was the observation averaged over the time period of measurement. For example, DMI was the total dry matter intake consumed divided by the 116 number of days intake was measured. Variables measured by CME were the total minutes measured divided by the days of measurement for each behavior (EAT, RUM, NACT, ACT and HACT). Using the step function in R program (R Core Team, 2018), a stepwise model selection procedure was performed using Akaike information criteria (AIC) as the criteria for variable selection. The stepwise procedure uses an iterative process of adding and removing explanatory variables to find the subset of variables that optimized the predetermined model criteria, which in this case was AIC. Three stepwise model procedures were executed. For all three procedures, DMI was the dependent variable. For the first procedure, EAT, RUM, NACT, ACT and HACT were all included as the explanatory variables in the full model and a stepwise model selection reduced the model from the full model (equation 5.3). 1234 = 56 + 589: ;89: + 5<=3 ;<=3 + 5>9?: ;>9?: + 59?: ;9?: + 5@9?: ;@9?: + A (Eq. 5.3) where YDMI was the dependent variable of DMI, 56 was the intercept, Xi was the explanatory variable for EAT, RUM, NACT, ACT or HACT, 5B was the regression coefficient for each explanatory variable and e is the model error term. The second stepwise model selection procedure explored protentional higher order variables by including a quadratic term for each explanatory variable from the previous full model. For the final stepwise procedures, interactions for each explanatory variable were included in the full model. The method used by CME for allocating time for each behavior creates a dependency for each behavior since the summation of combined behavioral time would have to equal 1440 117 minutes of a 24-hour period. As such, a principle component analysis (PCA) in addition to a principle component regression (PCR) was also performed. A principle component analysis was performed including EAT, RUM, NACT, ACT and HACT. The resulting principle components were used as regressors on DMI for the PCR. 5.3 Results and Discussion Tables 5.2 and 5.3 present the summary statistics of the steers at the conclusion of the 2017 performance test. The summary statistics for subset of LHI animals were presented in table 5.4. Table 5.2. Summary statistics for cattle (n=98) at the conclusion of the 2017 feed intake performance test. ADG (kg/d) Age (d) Weight (kg) DMI (kg) Mean 479 428.95 3.35 10.95 SD 21 58.27 0.52 1.72 Min 419 285.76 1.86 6.65 Max 523 555.65 4.27 14.72 118 Table 5.3. Summary statistics for CowManager ear tag accelerometer measurements of time (in minutes) for eating (EAT), rumination (RUM), not active (NACT), active (ACT) and high active (HACT) on Angus cattle (n=98) during the 2017 feed intake performance test. Mean SD Min Max EAT 112.81 39.78 32.43 246.67 RUM 348.40 54.02 140.68 514.80 NACT 471.80 62.98 314.11 641.52 ACT 170.36 38.77 111.65 322.86 HACT 326.37 49.45 230.49 437.67 Table 5.4. Summary statistics for the 15 lowest and highest intake animals, based on GrowSafe measures from the 2017 feed intake performance test. Mean SD Min Max Low Intake Steers (n=15) Age (d) Weight (kg) DMI (kg) 465.67 377.09 8.54 20.83 58.58 0.82 419 285.76 5.95 493 489.88 9.19 High Intake Steers (n=15) Age (d) Weight (kg) DMI (kg) 481.07 483.23 12.83 13.77 64.23 0.41 452 349.27 12.18 497 553.38 13.48 For the initial 2017 performance test, dry matter intake and measurements from CME were averaged over the 54-d feeding trial. Pearson’s correlations for averaged DMI and CME measurements are presented in table 5.5. The correlations of CME measurements to DMI ranged from -0.11 to 0.12. The correlation between DMI to EAT was 0.09 (P = 0.36). Correlations for feeding time and DMI have been previously reported as moderate. Robinson and Oddy (2004) and Nkrumah et al. (2007) reported correlations of DMI to feeding time of 0.30 and 0.27, respectively. For both of these studies, eating time was measured with the same monitoring system that measured DMI. In this study, feeding time was measured by two different systems (CME and GrowSafe) which resulted in a low correlation. This low correlation is also in contradiction to Wolfger et al. (2015) which concluded that ear tag accelerometers were highly sensitive for measuring feeding time. In the study conducted by Wolfger et al. (2015), 119 investigators visually observed 18 yearling Hereford x Angus feedlot steers to validate the use of CME in beef cattle for the measurement of time spent eating and ruminating. Their conclusion of the sensitivity of CME for measuring feeding time resulted from 0.79 concordance correlation between observed time spent eating and CME measured time for eating. Cattle for the Wolfger et al. (2015) were slick bunk fed compared to the current study where steers were fed ad libitum from GrowSafe feed bunks. This difference in how cattle were fed was explored further the second year of the study. To the author’s knowledge, there are no reported studies examining the relationship between DMI and time spent ruminating in beef cattle; however, a few studies have been conducted in dairy cattle correlating DMI to rumination time. In studies by Krause et al. (2002), Schirmann et al. (2010) and Byskov et al. (2017), correlations between rumination time and DMI ranged from -0.28 to 0.61. Schirmann et al. (2010) and Byskov et al. (2017) both concluded that no relation between rumination time and DMI was evident with their study and the use of rumination time as an indicator of DMI was limited. Our study would support Schirmann et al. (2010) and Byskov et al. (2017) conclusions with a Pearson’s correlation of -0.09 (P = 0.39) suggesting minimal relation between rumination time and DMI. Krause et al. (2002) estimated correlations between rumination time and DMI that ranged from -0.26 to 0.61. The variation of correlations was found to be dependent on the forage particle size. As particle size increased so did the correlation of rumination time to DMI indicating the use of rumination time as an indicator of DMI would be highly dependent on the ration and amount of forage included in the ration. This dependency of ration would be problematic for the use of rumination time for an indicator of DMI when comparing animals in a feedlot to those grazing rangeland. 120 The correlation between DMI with ACT and HACT were of the highest magnitude at -0.11 and 0.12, respectively; however, neither of these correlations were significant with pvalues greater than 0.05. Although there were no significant (P > 0.05) correlations between DMI and CME measurements, correlations within the CME measurements were significant. The highest correlation estimate was that between RUM and NACT (-0.66, P < 0.05). The significant correlations between CME measurements were anticipated given how the accelerometer allocates each minute to a specific behavior. Table 5.5. Pearson's correlations for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT) and dry matter intake (DMI) measured by a GrowSafe system. DMI EAT RUM NACT ACT HACT DMI 1.00 EAT 0.09 1.00 RUM -0.09 0.14 1.00 NACT 0.03 -0.32 -0.66 1.00 ACT -0.11 -0.38 -0.56 0.39 1.00 HACT 0.12 -0.21 0.08 -0.55 -0.32 1.00 The results from the stepwise regression procedure for the full model found no significant CME variables as explanatory variables for feedlot DMI for any reduced models. This would be expected given the low correlations of CME measurements and DMI. The model with the lowest AIC was the “null” model which consisted of DMI and the intercept only (the average of DMI). The stepwise procedure performed for models including quadratic and interaction terms for explanatory variables found no significant variables and both resulted in the “null” model with the lowest AIC. A principle component analysis (PCA) in addition to a principle component regression was also performed. Both analyses resulted in no significant variables for the estimation of DMI 121 using CME measurements (Figure 1). The principle component regression resulted in an adjusted R2 of 0.01 in addition to none of the principle components being found to be significant explanatory variables for DMI with p-values above 0.05. Figure 5.3. Plot from the principle component analysis for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT). To further investigate the potential relationship between DMI and CME measures, similar correlation analyses were performed on the LHI steers for the data collected while the steers were in the FIU. Table 5.6 presents the correlations for the LHI steers. The correlation between DMI and RUM was -0.39 (P = 0.04) for LHI steers which was larger than the same correlation from the entire cohort of steers measured in the FIU. However, the interpretation of these 122 correlations should be done with caution as they result from a subset of steers who represented the extremes of the distribution for DMI. Table 5.6. Pearson's correlations for CowManager ear tag accelerometer measurements of eating (EAT), rumination (RUM), not active (NACT), active (ACT), high active (HACT) and dry matter intake (DMI) measured by a GrowSafe system for a subset of cattle with the highest and lowest intake values. DMI EAT RUM NACT ACT HACT DMI EAT RUM NACT ACT HACT 1.00 0.00 1.00 -0.39 -0.25 1.00 0.25 0.13 -0.44 1.00 0.09 -0.86 -0.03 -0.34 1.00 0.00 -0.12 -0.26 0.02 -0.02 1.00 Once the feeding trial was completed in the FIU, animals were transported to ECRC and placed on pasture where rectal fecal samples were taken to estimate grazing intake. The average estimated grazing DMI from theTiO2 analysis (GDMI) for the LHI steers was 12.03 ± 2.36 kg. This was compared to the average DMI measured in the feedlot on the same steers was 10.69 ± 2.27. The Pearson’s correlation between GDMI and DMI measured in the feedlot was 0.84 ± 0.10 (P < 0.05) with a Spearman rank correlation of 0.99 ± 0.03 (P < 0.05). The Spearman’s rank correlation would suggest minimal change in ranking of animals based on their DMI. The high Pearson’s correlation suggest an important relationship between grazing and feedlot DMI; however, it was less than perfect (i.e. not equal to 1) suggesting some change between DMI and GDMI. A contributing factor to the less than perfect correlation may be attributed to the estimated GDMI was on average higher than DMI measured in a feedlot. This would be expected given that animals were moved from a diet of 25% concentrate to a straight forage diet. Dry matter intake was dependent on the energy content of the diet provided (NRC, 1996). In order to 123 meet their nutritional requirements while maintained on pasture, their intakes would have to increase. There is little research exploring the differences in the effect of diet on DMI (Shike et al., 2016) and to our knowledge, there was no direct comparison of grazing intake to feedlot intake. Shike et al. (2016) estimated a 0.58 phenotypic correlation for DMI for steers fed grain diets to forage diets. This correlation was lower than the observations in our study. The diet fed in the FIU to the steers for this study was a 73% roughage diet which may account for the higher correlations estimated in this study since cattle were fed a higher roughage diet with a lower percentage of concentrate then was used for Shike et al. (2016). The estimated GDMI were compared to measurements gathered from CME presented in table 5.7. Since the estimated GDMI was a measurement of intake for a 10 day period, the CME measurements used for comparison were averaged for the same 10 day period. The correlation between GDMI and EAT was the largest correlation of -0.22 (P = 0.23). This correlation suggested that intake would decrease as more time was spent eating. These results are in contrast to what was estimated by Robinson and Oddy (2004) who estimated a phenotypic estimate of 0.30 ± 0.03 in a feedlot environment. Estimated correlation between GDMI and RUM was -0.11 (P=0.58), which would indicate that as intake increased time spent for rumination would decrease. As forage in a diet increased, the rate of passage decreased, thus increasing the time spent for rumination (Krause et al., 2002). None of these correlation estimates were statistically significant (P > 0.05). 124 Table 5.7 Phenotypic correlations for grazing intake estimated using TiO2 (GDMI, kg) and measurements using CowManager ear accelerometers. GDMI RUM EAT NACT ACT HACT GDMI 1.00 RUM1 -0.11 1.00 EAT2 -0.22 -0.25 1.00 NACT3 0.02 -0.44 0.13 1.00 ACT4 0.21 -0.03 -0.86 -0.34 1.00 HACT5 0.19 -0.26 -0.12 0.02 -0.02 1.00 RUM1 is rumination measured by CowManager in minutes. EAT2 is time spent eating measured by CowManager in minutes. NACT3 is the amount of time an animal was not active measured by CowManager in minutes ACT4 was the time the animal spent being active as measured by CowManager in minutes. HACT5 was high activity measured by CowManager in minutes. Validation Study: For the animals selected for TiO2 supplementation (n = 32) during the second year’s performance test, summary statistics for DMI and estimated DMI using TiO2 are presented in table 5.8. The resulting Pearson’s correlation of DMI and TiO2 estimated DMI was 0.98 ± 0.03 (P < 0.05), indicating a strong association. A Spearman’s rank correlation was also estimated to be 0.97 ± 0.04 (P < 0.05), which suggested minimal change in ranking of animals. Due to the high correlations of DMI and TiO2 estimated DMI, these results would indicate that TiO2 was a reliable method for estimating intake. As such, these results also validate that estimated GDMI from the previous year as a reliable measure of grazing intake. 125 Table 5.8. Summary statistics for dry matter intake measured by a GrowSafe system and estimated dry matter intake with the use of a biomarker titanium dioxide on beef steers (n=32). 1 Average SD Min Max 1 GrowSafe 9.29 1.83 5.63 12.67 2 TiO2 9.61 2.26 4.96 14.60 Dry matter intake (kg) measured by GrowSafe 2 Dry matter intake (kg) estimated with the use of titanium dioxide The estimation of low correlations and lack of association between CME measurements and DMI were not expected. In particular, the correlation of EAT and DMI for cattle in the FIU was 0.09 and 0.00 for LHI steers. The correlation to EAT and GDMI was -0.22 which suggested an increase of intake while less time was spent eating which would be counterintuitive for cattle maintained on pasture. Correlations between EAT and DMI were anticipated to be positive and moderate. As previously mentioned, reported correlations to time spent eating and DMI was reported to be moderate and positive ranging from 0.27 to 0.30 (Nkrumah et al., 2007; Robinson and Oddy, 2004). To investigate these low correlations and lack of association between DMI and CME measurements, measurements recorded by CME were validated by observers recording the same measurements. A concordance correlation was used to evaluate the measurements between CME and the observers for EAT, RUM, NACT, ACT and HACT. The decision to use a concordance correlation was due to the parameter’s ability to quantify the agreement between two variables and the repeatability of the measurement observations (Lin, 1989). In this case, the first of the two variables of interest were the measurements recorded by CME and the second 126 were the visual observations made by the observers. Our interest lies in how much the recorded observed behavior was in agreement with what CME measured. If these correlations were low, the reliability of CME as a measure of cattle behavior would be suspect. The CowManager ear tag accelerometer measured HACT in all the steers but none of the observers noted any activity that would be categorized as HACT. One of the primary uses of CME is heat detection in dairy cattle. High activity measured by CME is designed to identify cows demonstrating standing estrus. This is achieved by the fact that cows in standing estrus are mounted or mounting in addition to increased walking. The steers in the FIU expressed little activity with minimal walking and no mounting. After communicating with CowManager, ACT and HACT were combined as one variable (AH). The concordance correlations were 0.39 ± 0.53, 0.58 ± 0.47, 0.65 ± 0.44, and 0.19 ± 0.57 for EAT, RUM, NACT and AH, respectively. Large standard errors for these correlations were a result of the small sample size (n = 5). The correlations were lower than those reported by Bikker et al. (2014; dairy cattle) and Wolfger et al. (2015; beef cattle). In both studies, the CowManager Sensors were evaluated for the accuracy of measuring feeding behavior and activity. Bikker et al. (2014) used CME in dairy cattle while Wolfger et al. (2015) used CME in beef cattle in a feedlot. Both studies found a 0.75 concordance correlation for eating but Bikker et al., (2014) found a 0.93 concordance correlation for rumination whereas Wolfger et al. (2015) found a lower correlation of 0.41. In the current study, the concordance correlation for eating was 0.39 which was lower than those reported by either Bikker et al. (2014) and Wolfger et al. (2015). However, for rumination, the concordance correlation was 0.58 ± 0.47 which was lower than the 0.93 reported by Bikker et al. (2014) and higher than 0.41 which Wolfger et al. (2015) reported. 127 Visual assessment of steers eating brought to attention a potential interference of the GrowSafe system with CME. The feed within the feed bunks were higher than if placed in an average concrete feed bunk, resulting in a steer not having to lower their heads in order to eat. In addition, animals have to pass their heads through an opening to access the feed bunk. In some cases, the ear would rest on the opening and movement of the ear would be restricted. Since the allocation of time to a behavior is dependent on the ear and jaw movement of the steer, this potential restricted ear movement might have affected CME’s ability to measure EAT. For the observations of finished beef steers fed from concrete feed bunks and CME measurements, the estimated concordance correlations between observers and steers were 0.01 ± 0.58, -0.14 ± 0.57, 0.23 ± 0.56, and -0.37 ± 0.54 for EAT, RUM, NACT and HA, respectively. As with the previous observations, the large standard errors were a result of the small samples size (n = 5). These steers were fed in concrete bunks with none of the previously mentioned interference from GrowSafe. For the observation of rumination, only 1 of the 5 steers was observed to ruminate during the observational period. The CME measurement during the hour when the animal was observed to be ruminating recorded no time spent ruminating. In addition, the 4 remaining animals that had no rumination observed had CME measurements for RUM. These measurements and observations resulted in a -0.14 ± 0.57 concordance correlation. Wolfger et al. (2015) concluded that CME measurement of RUM was low for sensitivity but highly specific. The authors for the Wolfger et al. (2015) study argued that CME was not as accurate for measuring every minute of rumination but didn’t inappropriately allocate minutes to rumination. However, results from the current study showed that this was not the case and minutes for RUM were allocated to steers when those steers did not in fact ruminate. These 128 results indicate a lack of accuracy for the measurement of eating and rumination time measured by CME. Since CME was initially developed for use in dairy cattle, 4 dairy cows equipped with CME was observed for the comparison of how CME measures behaviors and how it compared to what was measured in beef cattle. Concordance correlations for the observations of dairy cattle and CME measurements of EAT, RUM, NACT and HA were 0.90 ± 0.31, 0.89 ± 0.32, 0.68 ± 0.52 and 0.24 ± 0.69, respectively. The results for EAT and RUM were much higher than those measured in the beef cattle. Goldhawk et al. (2013) noted that technology that has high accuracy in dairy cattle may not have the same accuracy in beef cattle. This was attributed to a difference in dietary and physical differences of dewlaps, musculature and skin thickness between dairy and beef cattle (Goldhawk et al., 2013). As previously noted in the beef cattle, HACT was measured by CME but observers did not record any activity that would be considered high activity while observing the dairy cows. Because CME compiled the raw data and their algorithms are proprietary, further investigation into the disagreement of CME and observed behaviors was not possible. These results would indicate a difference in accuracy between beef cattle compared to dairy cattle for the use of CME. 5.4 Conclusion There have been numerous technological advancements in the application of remote sensors for monitoring cattle. To date, the largest application of this technology for cattle has been within the dairy industry with limited application of these technologies in the beef industry. This study was able to show the application of remote sensor technology for monitoring cattle 129 maintained on rangeland; however, the accuracy of measurements from CME failed to provide an indicator for DMI. A strong relationship between feedlot measured DMI and DMI for grazing cattle was established in this study. In order to truly understand the relationship between grazing and feedlot measured intake, grazing behavior must also be explored in addition to the relationship of these behaviors and their effects on grazing intake. There is great potential for the application of these technologies in the beef industry, however further exploration of the efficacy of these technologies in beef cattle needs to continue. 130 LITERATURE CITED Anderson, R. V., R. J. Rasby, T. J. Klopfenstein, and R. T. Clark. 2005. An evaluation of production and economic efficiency Bikker, J. P., H. van Laar, P. Rump, J. Doorenbos, K. van Meurs, G. M. Griffioen and J. Dijkstra. Technical note: Evaluation of an ear-attached movement sensor to record cow feeding behavior and activity. J. Dairy Sci. 97:2974-2979. Byskov, M. V., A. Fogh and P. Lovendahl. 2017. Genetic parameters of rumination time and feed efficiency traits in primiparous Holstein cows under research and commercial conditions. Capper, J. L. 2011. The environmental impact of beef production in the United States: 1977 compared with 2007. J. Anim. Sci. 89: 4249-4261. Culbertson, M. M., S. E. Speidel, R. K. Peel, R. R. Cockrum, M. G. Thomas, and R. M. Enns. 2015. Optimum measurement period for evaluating feed intake traits in beef cattle. J. Anim. Sci. 93: 2482-2487. FAO. 2009. How to feed the world in 2050. Food and Agriculture Organization of the United Nations, Rome, Italy. Ferrell, C. L. and T. G. Jenkins. 1985. Cow type and the nutritional environment: Nutritional aspects. J. Anim. Sci. 3: 725-741. Goldhawk, C., K. Schwartzkopf-Genswein and K. A. Beauchemin. 2013. Technical note: Validation of rumination collars for beef cattle. J. Anim. Sci. 91:2858-2862. 131 Google Earth. https://earth.google.com/web/@40.392738,103.1980838,1297.2116285a,781.68900289d,35y,0h,45t,0r/data=ChUaEwoLL2cvMXR meDVjeTkYAiABKAIoAg (Accessed February 15, 2019). Herd, R. M., P. F. Arthur, K. A. Donoghue, S. H. Bird, T. Bird-Gardiner and R. S. Hegarty. 2014. Measures of methane production and their phenotypic relationships with dry matter intake, growth, and body composition traits in beef cattle. J. Anim. Sci. 92: 5267-5274. Krause, K. M., D. K. Combs and K. A. Beauchemin. 2002. Effects of forage particle size on grain fermentation in midlactating cows. II. Ruminal pH and chewing activity. J. Dairy Sci. 85:1947-1957. Lin, L. I., 1989. A concordance correlation to evaluate reproducibility. Biometrics. 45:255-268 Myers, W. D., P. A. Ludden, V. Nayigihugu and B. W. Hess. 2004. Technical Note: A procedure for the preparation and quantitative analysis of samples for titanium dioxide. J. Anim. Sci. 82:179-183. Nkrumah, J. D., J. A. Basarab, Z. Wang, C. Li, M. A. Price, E. K. Okine, D. H. Crews, Jr., and S. S. Moore. 2007. Genetic and phenotypic relationships of feed intake and measures of efficiency with growth and carcass merit of beef cattle. J. Anim. Sci. 85:2711-2720. R Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. Robinson, D. L. and V. H. Oddy. 2004. Genetic parameters for feed efficiency, fatness, muscle area and feeding behavior of feedlot beef cattle. Livest. Prod. Sci. 255-270. Schirmann, K., N. Chapinal, D. M. Weary, W. Heuwieser and M. A. G. von Keyserlingk. 2010. Rumination and its relationship to feeding and lying behavior in Holstein dairy cows. J. Dairy Sci. 95:3212-3217. 132 Shike, D. W., C. J. Cassady, T. L. Felix and J. E. Beever. 2016. Effects of timing and duration of test period and diet type on intake and feed efficiency in Charolais-sired cattle. BIF Proc. 57-64. Theurer 1996 Titgemeyer, E. C., C. K. Armendariz, D. J. Bindel, R. H. Greenwood and C. A. Loest. 2001. Evaluation of titanium dioxide as a digestibility marker for cattle. J. Anim. Sci. 79: 10591063. Whisnant, C. USDA-NIFA-CRIS Research. http://cris.csrees.usda.gov/cgibin/starfinder/6244/crisassist.txt (Accessed April 30, 2017). Wolfger, B., E. Timsti. E. A. Pajor, N. Cook, H. W. Barkema, and K. Orel. 2015. Technical note: Accuracy of an ear tag-attached accelerometer to monitor rumination and feeding behavior in feedlot cattle. J. Anim. Sci. 93: 3164-3168. 133 APPENDIX A: R CODE USED TO CREATE SIMULTED DATA FOR FEMALE BASE POPULATION 134 ####Create a distribution of age for females ##R code to create base population of females with age distribution at equilibrium ##No selection for female base population ##20% Replacement ## ID for year 00 females (n=10000) fid00 = c(1:10000) yr00 <- data.frame(id = fid00, year = 00) nam = 10000 ## ID for year 01 replacement females fid01 = c(10001:12000) yr01 <- data.frame(id = fid01, year = 01) nam1 = nam + length(fid01) ## Creating progeny from yr00 females in year 2 n_progeny = nam set.seed(1234) isex=(rbinom(nam, 1, 0.5))+1 prg_of_yr00 = data.frame(year = 02, sex = isex) hfr = subset(prg_of_yr00, sex == 2) hfr1<- hfr[sample(1:nrow(hfr), 2000, replace=FALSE),] fid02 = c(12001:14000) yr02 <- data.frame(id = fid02, year = hfr1$year) ##Random loss of 20% from yr00 females n <- round(nrow(yr00)*0.8) females00 <- yr00[sample(1:nrow(yr00), n, replace=FALSE),] females = rbind(females00, yr01) ##Creating progeny for year 3 fid03 = c(14001:16000) yr03 <- data.frame(id = fid03, year = 03) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr01) ##Creating progeny for year 4 fid04 = c(16001:18000) yr04 <- data.frame(id = fid04, year = 04) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] 135 females = rbind(females00, yr02) ##Creating progeny for year 5 fid05 = c(18001:20000) yr05 <- data.frame(id = fid05, year = 05) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr03) ##Creating progeny for year 6 fid06 = c(20001:22000) yr06 <- data.frame(id = fid06, year = 06) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr04) ##Creating progeny for year 7 fid07 = c(22001:24000) yr07 <- data.frame(id = fid07, year = 07) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr05) ##Creating progeny for year 8 fid08 = c(24001:26000) yr08 <- data.frame(id = fid08, year = 08) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr06) ##Creating progeny for year 9 fid09 = c(26001:28000) yr09 <- data.frame(id = fid09, year = 09) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr07) 136 ##Creating progeny for year 10 fid10 = c(28001:30000) yr10 <- data.frame(id = fid10, year = 10) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr08) ##Creating progeny for year 11 fid11 = c(30001:32000) yr11 <- data.frame(id = fid11, year = 11) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr09) ##Creating progeny for year 12 fid12 = c(32001:34000) yr12 <- data.frame(id = fid12, year = 12) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr10) ##Creating progeny for year 13 fid13 = c(34001:36000) yr13 <- data.frame(id = fid13, year = 13) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr11) ##Creating progeny for year 14 fid14 = c(36001:38000) yr14 <- data.frame(id = fid14, year = 14) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr12) 137 ##Creating progeny for year 15 fid15 = c(38001:40000) yr15 <- data.frame(id = fid15, year = 15) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr13) ##Creating progeny for year 16 fid16 = c(40001:42000) yr16 <- data.frame(id = fid16, year = 16) ##Random loss of 20% from females n <- round(nrow(females)*0.8) females00 <- females[sample(1:nrow(females), n, replace=FALSE),] females = rbind(females00, yr14) ##Creating progeny for year 17 fid17 = c(42001:44000) yr17 <- data.frame(id = fid17, year = 17) ##Remove animals from year 00 (these females are 16 years old) young.fem = subset(females, year > 0) ##Random loss of 20% from females females01 <- young.fem[sample(1:nrow(young.fem), 8000, replace=FALSE),] fem = rbind(females01, yr15) ############################################################################# ############################################################################# ####Equilibrium reached once year 00 was removed. ####Using year 17 for base pop for females ####Remove females 16 years of age table(unlist(fem$year)) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #135 114 152 167 206 268 376 426 529 692 837 1064 1381 1653 2000 ##Recode file for simulation fem1 <- fem[ order(fem$id), ] fem.id <- c(1:10000) base.females <- data.frame(id = fem.id, year = fem1$year, sex = 2) ############################################################################## #### 138 APPENDIX B: R CODE USED TO CREATE SIMULTED DATA FOR SINGLE TRAIT SELECTION ON DRY MATTER INTAKE 139 ###Final analysis with updated G and R matrices #R code based on Dr. Larry Schaeffer’s R code for multiple trait models && Hamad Saad's disertation #Creating a simulated data (Selection on decreasing feed intake) ## Traits were: Feed intake (FI), 200 d weight (WWT), 400 d weight (YWT), and average daily gain (ADG) # First creating the base population (No selection) setwd("/Users/Randie/Documents/PhD Research/Simulation/SimRcode") ## To clear environment #FISimData_v2 rm(list = ls()) ##Run DistFem_USE.R first source("DistFem_USE.R") library(MASS) #Herd effects (50 herds) on FI, ADG, WWT and YWT set.seed(1234) herdFI=(rnorm(50,0)) set.seed(1234) herdWW=(rnorm(50,0))*2 set.seed(1234) herdYW=(rnorm(50,0))*10 set.seed(1234) herdADG=(rnorm(50,0))*0.25 ##Crews et al 2006 (SD for ADG) herd=matrix(data = c(herdFI,herdADG,herdWW,herdYW),byrow = TRUE, nrow = 4) # sex effects (50 herds) on FI, ADG, WWT, and YWT ##Sex effects for wwt and ywwt from Van Vleck & Cundiff 1998 ##ADG sex effects used Hamad's sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages ##Matrices are positive definite #G eigen values: 7.913849e+02 3.866650e+01 1.583454e-01 1.237949e-03 #R eigen values: 1390.9704349 294.3559224 0.9810670 0.0165757 140 #ID for animals (founders (10000 dams, 450 sires)) aid = c(1:10400) ##creating fields in the data file for sire (20 progeny each), dams (1 progeny each), herds (size of 200 each), sex (50% females and 50% males) sid = c(numeric(10400),rep(1:400, by=1, each=20)) base.sire <- data.frame(id = c(10001:10400), year = 15, sex = 1) did <- c(numeric(10400),1:10000) bi=c(rep(1,10400),rep(0.5,10000)) set.seed(1234) iherd=c(sample(rep(1:52, by=1, each=200),10400,replace=F)) # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) nam = 10400 # Simulate true breeding values for all animals (founders and their F1 progeny) # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} tbv = jd(nam,4)*0 for(i in 1:nam){ x = LG %*% (sqrt(bi[i])*rnorm(4,0,1)) if(sid[i]>0){ ks=sid[i] kd=did[i] x = x + 0.5*(tbv[ks, ]+tbv[kd, ]) } 141 tbv[i,]=x } nrec=10400 ################################################################## ################################################################### ##Creating base popuation with tbv but no observations ####Use base.females from DistFem_USE.R base.pop <- rbind(base.females, base.sire) simulateddata <- data.frame (id = base.pop$id, sire = c(rep(NA,10400)), dam = c(rep(NA,10400)), sex = base.pop$sex, year = base.pop$year, herd = iherd, FI = c(rep(NA,10400)), ADG = c(rep(NA,10400)), WWT = c(rep(NA,10400)), YWT = c(rep(NA,10400)), FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simulateddata) animlist = c(simulateddata[ ,1]) detach(simulateddata) uniqueanimlist = c(sort(unique(animlist))) pedigree = data.frame(id = uniqueanimlist, sire = c(rep(NA,10400)), dam = c(rep(NA,10400))) length(uniqueanimlist) #10400 length(pedigree[,1]) #10400 #Header: id sire dam sex year herd FI ADG WWT YWT FItbv ADGtbv WWTtbv YWTtbv basepopdata <- simulateddata attach(basepopdata) ############################################################# ## creating P1 (progeny 1) ## Assuming 100% conception ???? ## No selection of FI. Must use whole population for first 2 generations ############################################################# ## redefine the total number of all animals and number of base population in previous simulation ############################## #total number of all animals (base pop + P1) nam = 20400 #number of sires and dams(founders) (400+10000) in base population nbase = 10400 ############################## ## selecting top 5% sires and 80% dams (TBV for FI is the selection criteria) ## selection of sires ## average FI TBV for sires and dams averages=by( basepopdata$FItbv, basepopdata$sex, mean) ave1males=averages[1] ave1females=averages[2] ## standard deviation of FI TBV for sires and dams 142 SDs=by( basepopdata$FItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## For first selection of cows from P1 only selected 100% of females to be mated to sires females.base <- subset(basepopdata, sex == 2) ##90% Conception Rate selectedallfemales <- females.base[sample(1:nrow(females.base), 9000, replace = FALSE),] nrow(females.base) nrow(selectedallfemales) nrow(selectedallfemales)/nrow(females.base) #0.9 ######################### #### 400 selected males and 10000 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales) n_progeny = n_sel_females # number of females per sire = 22.5 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire # because number of dams per sire is 22.5, then sires will have different numbers of progeny (some will have 22.5 and others will have 23 progeny) rounded_n_females_per_sire = round(n_females_per_sire) rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 22 progeny (200 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 23 progeny (200 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 22 times 143 selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 200 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 9000 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp1 = randomlymatedsires[ ,1] damlistp1 = selectedallfemales[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #9400 length(uniqueanimlist) #9400 ## creating P1 pedigree which include(selected parents and their pedigree + new P1 ID with their selected parents) pedP1 = rbind(subdata[,1:3],cbind(c((nam+1):(nam+n_progeny)),sirelistp1[1:n_progeny],damlistp1[1:n_ progeny])) ################## ############## ## P1 observations library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) 144 sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages anwr=c((nam+1):(nam+n_progeny)) aid = c(pedP1[ ,1]) sid = c(pedP1[ ,2]) did = c(pedP1[ ,3]) #number of herds length(unique(selectedallfemales[ ,6])) iherd=c(selectedallfemales[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} 145 nam1=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree1 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree1) dataped <- pedigree1[pedigree1$id>nam,] simdataP1 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2000, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP1) nrow(simdataP1) #9000 ## combine the data file of (base) with P1 data file p1andbasepopdata <- rbind(basepopdata,simdataP1) ## Data file for basepop and P1 (has both observations and TBV) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1=mean(p1andbasepopdata$WWT) WWTave_base_p1 #248.40 WWTsd_base_p1=sd(p1andbasepopdata$WWT) WWTsd_base_p1 #37.81 146 WWTave_base_p1-(3*WWTsd_base_p1) #134.98 WWTave_base_p1+(3*WWTsd_base_p1) #361.83 p1andbasepopdata <- subset(p1andbasepopdata, WWT > (WWTave_base_p1(3*WWTsd_base_p1))) p1andbasepopdata <- subset(p1andbasepopdata, WWT < (WWTave_base_p1+(3*WWTsd_base_p1))) summary(p1andbasepopdata$WWT) nrow(p1andbasepopdata) #8965 # keeping YWT observations within 3 SD YWTave_base_p1=mean(p1andbasepopdata$YWT) YWTave_base_p1 YWTsd_base_p1=sd(p1andbasepopdata$YWT) YWTsd_base_p1 YWTave_base_p1-(3*YWTsd_base_p1) YWTave_base_p1+(3*YWTsd_base_p1) p1andbasepop <- subset(p1andbasepopdata, YWT > (YWTave_base_p1-(3*YWTsd_base_p1))) p1andbasepopdata <- subset(p1andbasepopdata, YWT < (YWTave_base_p1+(3*YWTsd_base_p1))) summary(p1andbasepopdata$YWT) nrow(p1andbasepopdata) #8964 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,10] - p1andbasepopdata[ ,9] > 40) nrow(p1andbasepopdata) #8964 simdataP1 <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nam) summary(simdataP1$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #136.0 222.5 247.5 248.1 272.9 361.4 summary(simdataP1$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #279.3 433.4 480.8 480.5 526.9 662.2 nrow(simdataP1) #8938 N_sires = length(c(sort(unique(simdataP1$sire)))) N_sires #400 basepop_p1_data <- rbind(basepopdata,simdataP1) pedigreep1 <- data.frame (id = simdataP1$id, sire = simdataP1$sire, dam = simdataP1$dam) pedigreep1andbase <- rbind(pedigree,pedigreep1) ############################################################################## ############################################################################## ## Creating P2 (Year 2) 147 #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ####Still no selection. No replacements. ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now) nam2 = nam+nam1 ############################## ## selection of sires ## average FI TBV for sires and dams averages=by( basepopdata$FItbv, basepopdata$sex, mean) ave1males=averages[1] ave1females=averages[2] ## standard deviation of FI TBV for sires and dams SDs=by( basepopdata$FItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## Remove females from year 1 (older than 16 years) females <- subset(selectedallfemales, year > 1) selectedallfemales1 <- females[sample(1:nrow(females), 8100, replace = FALSE),] nrow(selectedallfemales1) nrow(selectedallfemales) nrow(selectedallfemales1)/nrow(selectedallfemales) #0.90 ######################### #### 400 selected males and 8100 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales1) n_progeny = n_sel_females # number of females per sire = 20.25 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire # because number of dams per sire is 20.25, then sires will have different numbers of progeny (some will have 20 and others will have 21 progeny) rounded_n_females_per_sire = round(n_females_per_sire) 148 rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 20 progeny (300 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 21 progeny (100 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 25 times selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 263 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 8100 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp2 = randomlymatedsires[ ,1] damlistp2 = selectedallfemales1[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales1) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) #uniqueanimlist = uniqueanimlist[-1] subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #8500 length(uniqueanimlist) #8500 ## creating P2 pedigree which include(selected parents and their pedigree + new P2 ID with their selected parents) 149 pedP2 = rbind(subdata[,1:3],cbind(c((nam2+1):(nam2+n_progeny)),sirelistp2[1:n_progeny],damlistp2[1: n_progeny])) ############## ## For P2, repeating the same code used to create P1. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages anwr=c((nam2+1):(nam2+n_progeny)) aid = c(pedP2[ ,1]) sid = c(pedP2[ ,2]) did <- c(pedP2[ ,3]) #number of herds length(unique(selectedallfemales1[ ,6])) iherd=c(selectedallfemales1[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 150 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam3=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam3){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales1[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## 151 pedigree2 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree2) dataped <- pedigree2[pedigree2$id>nam,] simdataP2 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2001, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP2) nrow(simdataP2) #8100 ## combine the data file of (base and P1) with P2 data file p2_p1_basepopdata <- rbind(p1andbasepopdata,simdataP2) ## Data file for basepop and P1 (has both observations and TBV) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2=mean(p2_p1_basepopdata$WWT) WWTave_base_p1_p2 WWTsd_base_p1_p2=sd(p2_p1_basepopdata$WWT) WWTsd_base_p1_p2 WWTave_base_p1_p2-(3*WWTsd_base_p1_p2) WWTave_base_p1_p2+(3*WWTsd_base_p1_p2) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT > (WWTave_base_p1_p2(3*WWTsd_base_p1_p2))) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT < (WWTave_base_p1_p2+(3*WWTsd_base_p1_p2))) summary(p2_p1_basepopdata$WWT) nrow(p2_p1_basepopdata) #17023 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,10] p2_p1_basepopdata[ ,9] > 40) nrow(p2_p1_basepopdata) #17023 simdataP2 <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nam2) summary(simdataP2$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #138.5 223.2 247.2 248.2 272.6 358.0 summary(simdataP2$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 259.0 433.9 481.8 480.5 526.6 682.0 nrow(simdataP2) #8024 N_sires = length(c(sort(unique(simdataP2$sire)))) N_sires #400 basepop_p2_p1_data <- rbind(basepop_p1_data,simdataP2) 152 pedigreep2 <- data.frame (id = simdataP2$id, sire = simdataP2$sire, dam = simdataP2$dam) pedigreep2p1andbase<- rbind(pedigreep1andbase,pedigreep2) ############################################################################## ############################################################################## ## Creating P3 (Year 3) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv # Begin selection for FI and use replacments from year 2000 ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam4 = nam2+nam3 ############################## ## selecting top 10% sirs and 80% dams ## selection of sires ## sires selection changed to 10% otherwise there were not enough sires averages=by( basepop_p1_data$FItbv, basepop_p1_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_data$FItbv, basepop_p1_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males3 <- subset(basepop_p1_data, sex == 1) bulls3 <- males3[order(males3$FItbv), ] selectedmales3 <- bulls3[1:450, ] summary(selectedmales3[ ,7], na.rm=TRUE) nrow(males3) #426 nrow(selectedmales3) #450 nrow(selectedmales3)/nrow(males3) #0.09 ######################### ## selection of dams ## FIRST: Remove females from year 2 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss and 90% conception rate females3 <- subset(basepop_p1_data, sex == 2 & year > 2 & year < 2000) femalesp3 <- females3[sample(1:nrow(females3), 8000, replace=FALSE),] hfs <- subset(basepop_p1_data, sex == 2 & year == 2000) 153 nrow(hfs) #4420 if(nrow(hfs) > 2000) { n = 2000 } else { n = nrow(hfs) } hfrs <- hfs[order(hfs$FItbv), ] selectedhfrs <- hfrs[1:n, ] fem3 <- rbind(femalesp3, selectedhfrs) selectedallfemales3 <- fem3[sample(1:nrow(fem3), 9000, replace = FALSE),] summary(selectedallfemales3[ ,7], na.rm=TRUE) nrow(femalesp3) #8000 nrow(selectedallfemales3) #9000 damlistp3 = c(selectedallfemales3[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales3) allselectedmales=selectedmales3[rep(seq_len(nrow(selectedmales3)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp3 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales3, selectedallfemales3) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_data[basepop_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #10446 length(uniqueanimlist) #10446 pedp3 = rbind(subdata[ ,1:3],cbind(c((nam4+1):(nam4+n_progeny)),sirelistp3[1:n_progeny],damlistp3[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) 154 ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P3 progeny, repeating the same code used to create P2. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam4+1):(nam4+n_progeny)) aid = c(pedp3[ ,1]) sid = c(pedp3[ ,2]) did <- c(pedp3[ ,3]) #number of herds length(unique(selectedallfemales3[ ,6])) iherd=c(selectedallfemales3[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) 155 h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam5=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam5){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales3[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) 156 obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree3 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree3) dataped <- pedigree3[pedigree3$id>nam4,] simdataP3 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2002, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP3) nrow(simdataP3) #9000 ## combine the data file of (base, P1 and P2) with P3 data file p3_p2_p1_basepopdata <- rbind(p2_p1_basepopdata,simdataP3) ## Data file for basepop and P1 (has both observations and TBV) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3 WWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3 WWTave_base_p1_p2_p3-(3*WWTsd_base_p1_p2_p3) WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3(3*WWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3))) summary(p3_p2_p1_basepopdata$WWT) nrow(p3_p2_p1_basepopdata) #25994 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3 YWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3 YWTave_base_p1_p2_p3-(3*YWTsd_base_p1_p2_p3) YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3(3*YWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3))) summary(p3_p2_p1_basepopdata$YWT) nrow(p3_p2_p1_basepopdata) #25984 157 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,10] p3_p2_p1_basepopdata[ ,9] > 40) nrow(p3_p2_p1_basepopdata) #25984 #Remove animals with FI less than 0 p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,7] > 1) nrow(p3_p2_p1_basepopdata) #25968 simdataP3 <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nam4) summary(simdataP3$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #104.3 177.8 202.4 203.3 227.6 350.2 summary(simdataP3$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #232.1 350.7 398.9 399.0 445.7 618.6 nrow(simdataP3) #8960 N_sires = length(c(sort(unique(simdataP3$sire)))) N_sires #450 basepop_p1_p2_p3_data <- rbind(basepop_p2_p1_data,simdataP3) pedigreep3 <- data.frame (id = simdataP3$id, sire = simdataP3$sire, dam = simdataP3$dam) pedigreep3p2p1andbase <- rbind(pedigreep2p1andbase,pedigreep3) ############################################################################## ############################################################################## ## Creating P4 (Year 4) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1 and P2) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam6 = nam4+nam5 ############################## ## selecting top 5% sires (2000 & 2001) and top heifers for replacements ## selection of sires averages=by( basepop_p2_p1_data$FItbv, basepop_p2_p1_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p2_p1_data$FItbv, basepop_p2_p1_data$sex, sd) sd1males=SDs[1] 158 sd1females=SDs[2] males4 <- subset(basepop_p2_p1_data, sex == 1 & year >= 2000) bulls4 <- males4[order(males4$FItbv), ] selectedmales4 <- bulls4[1:450, ] summary(selectedmales4[ ,7], na.rm=TRUE) nrow(males4) #8583 nrow(selectedmales4) #450 nrow(selectedmales4)/nrow(males4) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 3 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss ## Assume 90% Conception Rate females4 <- subset(selectedallfemales3, year > 3) femalesp4 <- females4[sample(1:nrow(females4), 8000, replace=FALSE),] heifers <- subset(basepop_p2_p1_data, sex == 2 & year == 2001) nrow(heifers) #3959 if(nrow(hfs) > 2000) { n = 2000 } else { n = nrow(hfs) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] fem4 <- rbind(femalesp4, selectedhfrs) selectedallfemales4 <- fem4[sample(1:nrow(fem4), 9000, replace = FALSE),] summary(selectedallfemales4[ ,7], na.rm=TRUE) nrow(femalesp4) #8000 nrow(selectedallfemales4) #9000 damlistp4 = c(selectedallfemales4[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales4) allselectedmales=selectedmales4[rep(seq_len(nrow(selectedmales4)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp4 = randomlymatedsires[ ,1] 159 #################### selectedparents=rbind(selectedmales4, selectedallfemales4) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p2_p1_data[basepop_p2_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #11179 length(uniqueanimlist) #11179 pedp4 = rbind(subdata[ ,1:3],cbind(c((nam6+1):(nam6+n_progeny)),sirelistp4[1:n_progeny],damlistp4[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P4 progeny, repeating the same code used to create P3. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) 160 # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam6+1):(nam6+n_progeny)) aid = c(pedp4[ ,1]) sid = c(pedp4[ ,2]) did <- c(pedp4[ ,3]) #number of herds length(unique(selectedallfemales4[ ,6])) iherd=c(selectedallfemales4[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam7=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam7){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } 161 damtbv= selectedallfemales4[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree4 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree4) dataped <- pedigree4[pedigree4$id>nam6,] simdataP4 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2003, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP4) nrow(simdataP4) #9000 ## combine the data file of (base, P1, P2 and P3) with P4 data file p4_p3_p2_p1_basepopdata <- rbind(p3_p2_p1_basepopdata,simdataP4) ## Data file for basepop, P1, P2, P3 and P4 (has both observations and TBV) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4 WWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4 WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4) WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4) 162 p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4))) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$WWT) nrow(p4_p3_p2_p1_basepopdata) #34928 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$YWT) nrow(p4_p3_p2_p1_basepopdata) #34923 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,10] - p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p4_p3_p2_p1_basepopdata) #34921 #Remove animals with FI less than 0 p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p4_p3_p2_p1_basepopdata) #34901 simdataP4 <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nam6) summary(simdataP4$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #99.65 185.76 210.58 211.78 235.95 352.71 summary(simdataP4$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #221.4 360.9 410.0 409.5 456.5 626.7 nrow(simdataP4) #8961 N_sires = length(c(sort(unique(simdataP4$sire)))) N_sires #450 basepop_p1_p2_p3_p4_data <- rbind(basepop_p1_p2_p3_data,simdataP4) pedigreep4 <- data.frame (id = simdataP4$id, sire = simdataP4$sire, dam = simdataP4$dam) pedigreep4p3p2p1andbase <- rbind(pedigreep3p2p1andbase,pedigreep4) 163 ############################################################################## ############################################################################## ## Creating P5 (Year 5) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2 and P3) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam8 = nam6+nam7 ############################## ## selecting top 5% sires and 80% dams ## selection of sires averages=by( basepop_p1_p2_p3_data$FItbv, basepop_p1_p2_p3_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_data$FItbv, basepop_p1_p2_p3_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males5 <- subset(basepop_p1_p2_p3_data, sex == 1 & year >= 2001) bulls5 <- males5[order(males5$FItbv), ] selectedmales5 <- bulls5[1:450, ] summary(selectedmales5[ ,7], na.rm=TRUE) nrow(males5) #8610 nrow(selectedmales5) #450 nrow(selectedmales5)/nrow(males5) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 4 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females5 <- subset(selectedallfemales4, year > 4) femalesp5 <- females5[sample(1:nrow(females5), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_data, sex == 2 & year == 2002) nrow(heifers) #4411 if(nrow(heifers) > 2000) { n = 2000 164 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] fem5 <- rbind(femalesp5, selectedhfrs) selectedallfemales5 <- fem5[sample(1:nrow(fem5), 9000, replace = FALSE),] summary(selectedallfemales5[ ,7], na.rm=TRUE) nrow(femalesp5) #8000 nrow(selectedallfemales5) #9000 damlistp5 = c(selectedallfemales5[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales5) allselectedmales=selectedmales5[rep(seq_len(nrow(selectedmales5)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp5 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales5, selectedallfemales5) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_data[basepop_p1_p2_p3_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #12194 length(uniqueanimlist) #12194 pedp5 = rbind(subdata[ ,1:3],cbind(c((nam8+1):(nam8+n_progeny)),sirelistp5[1:n_progeny],damlistp5[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave 165 ############## ############## ## P5 progeny, repeating the same code used to create P4. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam8+1):(nam8+n_progeny)) aid = c(pedp5[ ,1]) sid = c(pedp5[ ,2]) did <- c(pedp5[ ,3]) #number of herds length(unique(selectedallfemales5[ ,6])) iherd=c(selectedallfemales5[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix 166 CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam9=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam9){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales5[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree5 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree5) 167 dataped <- pedigree5[pedigree5$id>nam8,] simdataP5 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2004, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP5) nrow(simdataP5) #9000 ## combine the data file of (base, P1, P2, P3 and P4) with P5 data file p5_p4_p3_p2_p1_basepopdata <- rbind(p4_p3_p2_p1_basepopdata,simdataP5) ## Data file for basepop and P's (has both observations and TBV) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5 WWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5 WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5) WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43854 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5 YWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5 YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5) YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43837 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,10] - p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p5_p4_p3_p2_p1_basepopdata) #43817 168 #Remove animals with FI less than 0 p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p5_p4_p3_p2_p1_basepopdata) # 43499 simdataP5 <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nam8) summary(simdataP5$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #79.7 154.9 179.8 180.8 205.4 322.3 summary(simdataP5$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #180.2 302.8 350.5 350.9 396.8 582.1 nrow(simdataP5) #8598 N_sires = length(c(sort(unique(simdataP5$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_data <- rbind(basepop_p1_p2_p3_p4_data,simdataP5) pedigreep5 <- data.frame (id = simdataP5$id, sire = simdataP5$sire, dam = simdataP5$dam) pedigreep5p4p3p2p1andbase <- rbind(pedigreep4p3p2p1andbase,pedigreep5) ############################################################################## ############################################################################## ## Creating P6 (Year 6) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3 and P4) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5 and P5 nam10 = nam8+nam9 ############################## ## selecting top 5% sirs and 80% dams ## selection of sires males6 <- subset(basepop_p1_p2_p3_p4_data, sex == 1 & year >= 2002) bulls6 <- males6[order(males6$FItbv), ] selectedmales6 <- bulls6[1:450, ] summary(selectedmales6[ ,7], na.rm=TRUE) nrow(males6) #9071 nrow(selectedmales6) #450 169 nrow(selectedmales6)/nrow(males6) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 5 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females6 <- subset(selectedallfemales5, sex == 2 & year > 5) femalesp6 <- females6[sample(1:nrow(females6), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_data, sex == 2 & year == 2003) nrow(heifers) #4425 if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem6 <- rbind(femalesp6, selectedhfrs) selectedallfemales6 <- fem6[sample(1:nrow(fem6), 9000, replace = FALSE),] summary(selectedallfemales6[ ,7], na.rm=TRUE) nrow(femalesp6) #8000 nrow(selectedallfemales6) #9000 damlistp6 = c(selectedallfemales6[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales6) allselectedmales=selectedmales6[rep(seq_len(nrow(selectedmales6)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp6 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales6, selectedallfemales6) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] 170 subdata <- basepop_p1_p2_p3_p4_data[basepop_p1_p2_p3_p4_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #12964 length(uniqueanimlist) #12964 pedp6 = rbind(subdata[ ,1:3],cbind(c((nam10+1):(nam10+n_progeny)),sirelistp6[1:n_progeny],damlistp6[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P6 progeny, repeating the same code used to create P5. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam10+1):(nam10+n_progeny)) 171 aid = c(pedp6[ ,1]) sid = c(pedp6[ ,2]) did <- c(pedp6[ ,3]) #number of herds length(unique(selectedallfemales6[ ,6])) iherd=c(selectedallfemales6[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam11=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam11){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales6[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals 172 obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree6 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree6) dataped <- pedigree6[pedigree6$id>nam10,] simdataP6 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2005, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP6) nrow(simdataP6) #9000 ## combine the data file of (base, P1, P2, P3, P4 and P5) with P6 data file p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p5_p4_p3_p2_p1_basepopdata,simdataP6) ## Data file for basepop and P's (has both observations and TBV) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6 WWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6 WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6) WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52468 # keeping YWT observations within 3 SD 173 YWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6 YWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6 YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6) YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52460 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52414 #Remove animals with FI less than 0 p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #51445 simdataP6 <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam10) summary(simdataP6$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #67.07 148.03 171.83 173.50 197.87 311.98 summary(simdataP6$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #155.1 287.2 334.7 334.9 381.0 552.4 nrow(simdataP6) #7955 N_sires = length(c(sort(unique(simdataP6$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_data <- rbind(basepop_p1_p2_p3_p4_p5_data,simdataP6) pedigreep6 <- data.frame (id = simdataP6$id, sire = simdataP6$sire, dam = simdataP6$dam) pedigreep6p5p4p3p2p1andbase <- rbind(pedigreep5p4p3p2p1andbase,pedigreep6) ############################################################################## ############################################################################## ## Creating P7 (Year 7) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# 174 ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4 and P5) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6 and P7 nam12 = nam10+nam11 ############################## ## selecting top 5% sirs and 80% dams ## selection of sires averages=by( basepop_p1_p2_p3_p4_p5_data$FItbv, basepop_p1_p2_p3_p4_p5_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_p4_p5_data$FItbv, basepop_p1_p2_p3_p4_p5_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males7 <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 1 & year >= 2003) bulls7 <- males7[order(males7$FItbv), ] selectedmales7 <- bulls7[1:450, ] summary(selectedmales7[ ,7], na.rm=TRUE) nrow(males7) #8911 nrow(selectedmales7) #450 nrow(selectedmales7)/nrow(males7) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 6 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females7 <- subset(selectedallfemales6, sex == 2 & year > 6) femalesp7 <- females7[sample(1:nrow(females7), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 2 & year == 2004) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } 175 hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem7 <- rbind(femalesp7, selectedhfrs) selectedallfemales7 <- fem7[sample(1:nrow(fem7), 9000, replace = FALSE),] summary(selectedallfemales7[ ,7], na.rm=TRUE) nrow(femalesp7) #8000 nrow(selectedallfemales7) #9000 damlistp7 = c(selectedallfemales7[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales7) allselectedmales=selectedmales7[rep(seq_len(nrow(selectedmales7)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp7= randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales7, selectedallfemales7) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_data[basepop_p1_p2_p3_p4_p5_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #13831 length(uniqueanimlist) #13831 pedp7 = rbind(subdata[ ,1:3],cbind(c((nam12+1):(nam12+n_progeny)),sirelistp7[1:n_progeny],damlistp7[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## 176 ############## ## P7 progeny, repeating the same code used to create P6. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam12+1):(nam12+n_progeny)) aid = c(pedp7[ ,1]) sid = c(pedp7[ ,2]) did <- c(pedp7[ ,3]) #number of herds length(unique(selectedallfemales7[ ,6])) iherd=c(selectedallfemales7[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) 177 D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam13=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam13){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales7[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree7 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree7) dataped <- pedigree7[pedigree7$id>nam12,] 178 simdataP7 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2006, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP7) nrow(simdataP7) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5 and P6) with P7 data file p7_p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p6_p5_p4_p3_p2_p1_basepopdata,simdataP7) ## Data file for basepop, P1, P2, P3, P4, P5, P6 and P7 (has both observations and TBV) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7 WWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7 WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #60414 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #58898 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #57183 179 #Remove animals with FI less than 0 p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #57147 simdataP7 <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam12) summary(simdataP7$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #54.03 139.43 162.99 164.54 187.24 311.78 summary(simdataP7$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #219.8 273.2 315.3 317.6 357.5 518.8 nrow(simdataP7) #5958 N_sires = length(c(sort(unique(simdataP7$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_data <- rbind(basepop_p1_p2_p3_p4_p5_p6_data,simdataP7) pedigreep7 <- data.frame (id = simdataP7$id, sire = simdataP7$sire, dam = simdataP7$dam) pedigreep7p6p5p4p3p2p1andbase <- rbind(pedigreep6p5p4p3p2p1andbase,pedigreep7) ############################################################################## ############################################################################## ## Creating P8 (Year 8) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5 and P6) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7 and P8 nam14 = nam12+nam13 ############################## ## selecting top 5% sires ## selection of sires males8 <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 1 & year >= 2004) bulls8 <- males8[order(males8$FItbv), ] selectedmales8 <- bulls8[1:450, ] summary(selectedmales8[ ,7], na.rm=TRUE) nrow(males8) #8413 nrow(selectedmales8) #450 180 nrow(selectedmales8)/nrow(males8) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 7 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females8 <- subset(selectedallfemales7, sex == 2 & year > 7) femalesp8 <- females8[sample(1:nrow(females8), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 2 & year == 2005) nrow(heifers) #3917 if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem8 <- rbind(femalesp8, selectedhfrs) selectedallfemales8 <- fem8[sample(1:nrow(fem8), 9000, replace = FALSE),] summary(selectedallfemales8[ ,7], na.rm=TRUE) nrow(femalesp8) #8000 nrow(selectedallfemales8) #9000 damlistp8 = c(selectedallfemales8[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales8) allselectedmales=selectedmales8[rep(seq_len(nrow(selectedmales8)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp8 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales8, selectedallfemales8) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] 181 subdata <- basepop_p1_p2_p3_p4_p5_p6_data[basepop_p1_p2_p3_p4_p5_p6_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #14482 length(uniqueanimlist) #14482 pedp8 = rbind(subdata[ ,1:3],cbind(c((nam14+1):(nam14+n_progeny)),sirelistp8[1:n_progeny],damlistp8[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P8 progeny, repeating the same code used to create P7. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam14+1):(nam14+n_progeny)) 182 aid = c(pedp8[ ,1]) sid = c(pedp8[ ,2]) did <- c(pedp8[ ,3]) #number of herds length(unique(selectedallfemales8[ ,6])) iherd=c(selectedallfemales8[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam15=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam15){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales8[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals 183 obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree8 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree8) dataped <- pedigree8[pedigree8$id>nam14,] simdataP8 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2007, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP8) nrow(simdataP8) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6 and P7) with P8 data file p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP8) ## Data file for basepop and P's (has both observations and TBV) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WW T) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < 184 (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8)) ) summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #66112 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT ) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #66102 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #65787 #Remove animals with FI less than 0 p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #61787 simdataP8 <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam14) summary(simdataP8$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #42.85 128.13 151.16 152.80 176.31 312.48 summary(simdataP8$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #127.7 246.3 293.4 292.4 336.2 485.6 nrow(simdataP8) #4640 Loss of animal due to FI < 1 N_sires = length(c(sort(unique(simdataP8$sire)))) 185 N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_data,simdataP8) pedigreep8 <- data.frame (id = simdataP8$id, sire = simdataP8$sire, dam = simdataP8$dam) pedigreep8p7p6p5p4p3p2p1andbase <- rbind(pedigreep7p6p5p4p3p2p1andbase,pedigreep8) ############################################################################## ############################################################################## ## Creating P9 (Year 9) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam16 = nam14+nam15 ############################## ## selecting top 5% sires ## selection of sires males9 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 1 & year >= 2005) bulls9 <- males9[order(males9$FItbv), ] selectedmales9 <- bulls9[1:450, ] summary(selectedmales9[ ,7], na.rm=TRUE) nrow(males9) #7324 nrow(selectedmales9) #450 nrow(selectedmales9)/nrow(males9) #0.06 ######################### ## selection of dams ## FIRST: Remove females from year 8 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females9 <- subset(selectedallfemales8, sex == 2 & year > 8) femalesp9 <- females9[sample(1:nrow(females9), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 2 & year == 2006) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 186 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem9 <- rbind(femalesp8, selectedhfrs) selectedallfemales9 <- fem8[sample(1:nrow(fem9), 9000, replace = FALSE),] summary(selectedallfemales9[ ,7], na.rm=TRUE) nrow(femalesp9) #8000 nrow(selectedallfemales9) #10000 damlistp9 = c(selectedallfemales9[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales9) allselectedmales=selectedmales9[rep(seq_len(nrow(selectedmales9)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp9 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales9, selectedallfemales9) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_p6_p7_data[basepop_p1_p2_p3_p4_p5_p6_p7_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #14565 length(uniqueanimlist) #14565 pedp9 = rbind(subdata[ ,1:3],cbind(c((nam16+1):(nam16+n_progeny)),sirelistp9[1:n_progeny],damlistp9[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave 187 YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P9 progeny, repeating the same code used to create P8. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam16+1):(nam16+n_progeny)) aid = c(pedp9[ ,1]) sid = c(pedp9[ ,2]) did <- c(pedp9[ ,3]) #number of herds length(unique(selectedallfemales9[ ,6])) iherd=c(selectedallfemales9[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 188 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam17=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales9[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## 189 pedigree9 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree9) dataped <- pedigree9[pedigree9$id>nam16,] simdataP9 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2008, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP9) nrow(simdataP9) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7 and P8) with P9 data file p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP9) ## Data file for basepop and P's (has both observations and TBV) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basep opdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_ p8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70753 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepo pdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 190 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 _p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70746 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70408 #Remove animals with FI less than 0 p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #66280 simdataP9 <- subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam16) summary(simdataP9$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #37.79 127.37 150.44 152.12 175.37 313.02 summary(simdataP9$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #133.1 244.6 291.9 290.8 334.7 500.6 nrow(simdataP9) #4504 N_sires = length(c(sort(unique(simdataP9$sire)))) N_sires # 450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data,simdataP9) pedigreep9 <- data.frame (id = simdataP9$id, sire = simdataP9$sire, dam = simdataP9$dam) pedigreep9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep8p7p6p5p4p3p2p1andbase,pedigreep9) 191 ############################################################################## ############################################################################## ## Creating P10 (Year 10) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam18 = nam16+nam17 ############################## ## selecting top 5% sires ## selection of sires averages=by( basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$FItbv, basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$FItbv, basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males10 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 1 & year >= 2006) bulls10 <- males10[order(males10$FItbv), ] selectedmales10 <- bulls10[1:450, ] summary(selectedmales10[ ,7], na.rm=TRUE) nrow(males10) #5687 nrow(selectedmales10) #450 nrow(selectedmales10)/nrow(males10) #0.08 ######################### ## selection of dams ## FIRST: Remove females from year 9 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females10 <- subset(selectedallfemales9, sex == 2 & year > 9) femalesp10 <- females10[sample(1:nrow(females10), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 2 & year == 2007) nrow(heifers) 192 if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$FItbv), ] selectedhfrs <- hfrs[1:n, ] fem10 <- rbind(femalesp10, heifers) selectedallfemales10 <- fem10[sample(1:nrow(fem10), 9000, replace = FALSE),] nrow(femalesp10) #8000 nrow(selectedallfemales10) #10000 damlistp10 = c(selectedallfemales10[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales10) allselectedmales=selectedmales10[rep(seq_len(nrow(selectedmales10)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp10 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales10, selectedallfemales10) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #15073 length(uniqueanimlist) #15073 pedp10 = rbind(subdata[ ,1:3],cbind(c((nam18+1):(nam18+n_progeny)),sirelistp10[1:n_progeny],damlistp10[1:n_progeny ])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) 193 ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P10 progeny, repeating the same code used to create P9. set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam18+1):(nam18+n_progeny)) aid = c(pedp10[ ,1]) sid = c(pedp10[ ,2]) did <- c(pedp10[ ,3]) #number of herds length(unique(selectedallfemales10[ ,6])) iherd=c(selectedallfemales10[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 194 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam19=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales10[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) 195 ################################################################## pedigree10 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree10) dataped <- pedigree10[pedigree10$id>nam18,] simdataP10 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2009, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP10) nrow(simdataP10) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7, P8 and P9) with P10 data file p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP10) ## Data file for basepop and P's (has both observations and TBV) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6 _p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #75255 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$YWT) 196 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p 7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #75245 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,8] > 40) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #75203 #Remove animals with FI less than 0 p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,7] > 1) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #69756 simdataP10 <- subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam18) summary(simdataP10$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. # 40.7 120.8 144.6 146.3 171.0 284.6 summary(simdataP10$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #101.2 226.3 272.5 272.3 316.8 472.7 nrow(simdataP10) #3477 N_sires = length(c(sort(unique(simdataP10$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data,simdataP10) pedigreep10 <- data.frame (id = simdataP10$id, sire = simdataP10$sire, dam = simdataP10$dam) 197 pedigreep10p9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep9p8p7p6p5p4p3p2p1andbase,pedigreep10) ############################################################################## ############################################################################## ## see how many records per sire try <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) nrow(try) ones = c(rep(1,(nrow(try)))) try = data.matrix(try) try = cbind(try,ones) ham=sort(by( try[ ,14], try[ ,2], length)) head(ham) ############################################ ## Final data files ## pedigree file ## ****data file for animals with records (will be used for ****ASREML3.0****) data_anim_with_record <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) summary(data_anim_with_record$FI) #Min. 1st Qu. Median Mean 3rd Qu. Max. #-0.930 4.400 6.160 6.218 7.990 14.260 summary(data_anim_with_record$YWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #76.69 257.10 302.50 304.20 350.70 527.00 summary(data_anim_with_record$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #84.4 171.1 196.3 197.6 222.8 325.9 summary(data_anim_with_record$ADG) # Min. 1st Qu. Median Mean 3rd Qu. Max. #-0.7200 0.4400 0.7200 0.7306 1.0100 2.3100 198 APPENDIX C: R CODE USED TO CREATE SIMULATED DATA FOR SINGLE TRAIT SELECTION ON RESIDUAL FEED INTAKE 199 ##Finalized simulation for RFI selection #R code based on Dr. Larry Schaeffer’s R code for multiple trait models && Hamad Saad's disertation #Creating a simulated data (Selection on decreasing residual feed intake) ## Traits were: Feed intake (RFI), 200 d weight (WWT), 400 d weight (YWT), and average daily gain (ADG) # First creating the base population (No selection) setwd("/Users/Randie/Documents/PhD Research/Simulation") ## To clear environment #RFISimData_v3 rm(list = ls()) ##Run DistFem_USE.R first source("DistFem_USE.R") library(MASS) #Herd effects (50 herds) on RFI, ADG, WWT and YWT set.seed(1234) herdRFI=(rnorm(50,0)) set.seed(1234) herdWW=(rnorm(50,0))*2 set.seed(1234) herdYW=(rnorm(50,0))*10 set.seed(1234) herdADG=(rnorm(50,0))*0.25 ##Crews et al 2006 (SD for ADG) herd=matrix(data = c(herdRFI,herdADG,herdWW,herdYW),byrow = TRUE, nrow = 4) # sex effects (52) herds) on RFI, ADG, WWT, and YWT ##Sex effects for wwt and ywwt from Van Vleck & Cundiff 1998 ##ADG sex effects used Hamad's sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(-0.011,1.473,258.913,479.990) #weighted averages from literature estimates #Matrices are positive definite #eigen values for R: 1.390698e+03 2.940065e+02 3.110134e-01 1.234581e-02 200 #eigen values for G: 7.904835e+02 3.863431e+01 1.715661e-01 5.907012e-04 #ID for animals (founders (10000 dams, 450 sires)) aid = c(1:10400) ##creating fields in the data file for sire (20 progeny each), dams (1 progeny each), herds (size of 200 each), sex (50% females and 50% males) sid = c(numeric(10400),rep(1:400, by=1, each=20)) base.sire <- data.frame(id = c(10001:10400), year = 15, sex = 1) did <- c(numeric(10400),1:10000) bi=c(rep(1,10400),rep(0.5,10000)) set.seed(1234) iherd=c(sample(rep(1:52, by=1, each=200),10400,replace=F)) # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) nam = 10400 # Simulate true breeding values for all animals (founders and their F1 progeny) # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} tbv = jd(nam,4)*0 for(i in 1:nam){ x = LG %*% (sqrt(bi[i])*rnorm(4,0,1)) if(sid[i]>0){ ks=sid[i] kd=did[i] 201 x = x + 0.5*(tbv[ks, ]+tbv[kd, ]) } tbv[i,]=x } nrec=10400 ################################################################## ################################################################### ##Creating base popuation with tbv but no observations ####Use base.females from DistFem_USE.R base.pop <- rbind(base.females, base.sire) simulateddata <- data.frame (id = base.pop$id, sire = c(rep(NA,10400)), dam = c(rep(NA,10400)), sex = base.pop$sex, year = base.pop$year, herd = iherd, RFI = c(rep(NA,10400)), ADG = c(rep(NA,10400)), WWT = c(rep(NA,10400)), YWT = c(rep(NA,10400)), RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simulateddata) animlist = c(simulateddata[ ,1]) detach(simulateddata) uniqueanimlist = c(sort(unique(animlist))) pedigree = data.frame(id = uniqueanimlist, sire = c(rep(NA,10400)), dam = c(rep(NA,10400))) length(uniqueanimlist) #10400 length(pedigree[,1]) #10400 #Header: id sire dam sex year herd RFI ADG WWT YWT RFItbv ADGtbv WWTtbv YWTtbv basepopdata <- simulateddata attach(basepopdata) ############################################################# ## creating P1 (progeny 1) ## Assuming 100% conception ## No selection of RFI. Must use whole population for first 2 generations ############################################################# ## redefine the total number of all animals and number of base population in previous simulation ############################## #total number of all animals (base pop + P1) nam = 20400 #number of sires and dams(founders) (400+10000) in base population nbase = 10400 ############################## ## selecting top 5% sirs and 80% dams (TBV for RFI is the selection criteria) ## selection of sires ## average RFI TBV for sires and dams averages=by( basepopdata$RFItbv, basepopdata$sex, mean) ave1males=averages[1] 202 ave1females=averages[2] ## standard deviation of RFI TBV for sires and dams SDs=by( basepopdata$RFItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## For first selection of cows from P1 only selected 100% of females to be mated to sires females.base <- subset(basepopdata, sex == 2) ##90% Conception Rate selectedallfemales <- females.base[sample(1:nrow(females.base), 9000, replace = FALSE),] nrow(females.base) nrow(selectedallfemales) nrow(selectedallfemales)/nrow(females.base) #0.9 ######################### #### 400 selected males and 10000 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales) n_progeny = n_sel_females # number of females per sire = 22.5 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire # because number of dams per sire is 22.5, then sires will have different numbers of progeny (some will have 22.5 and others will have 23 progeny) rounded_n_females_per_sire = round(n_females_per_sire) rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 22 progeny (200 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 23 progeny (200 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list 203 own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 22 times selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 200 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 10000 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp1 = randomlymatedsires[ ,1] damlistp1 = selectedallfemales[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #9400 length(uniqueanimlist) #9400 ## creating P1 pedigree which include(selected parents and their pedigree + new P1 ID with their selected parents) pedP1 = rbind(subdata[,1:3],cbind(c((nam+1):(nam+n_progeny)),sirelistp1[1:n_progeny],damlistp1[1:n_ progeny])) ################## ############## ## P1 observations library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) 204 herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.040,0.681,1.806,0.04,0.014,0.548,1.231,0.681,0.548,552.753,465.634,1.806,1.231,465.634,1131.95),byrow=TRU E,nrow=4) # G matrix G=matrix(data=c(0.18,0.002,-4.265,-6.994,0.002,0.01,1.014,2.217,4.265,1.014,230.77,327.931,-6.994,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(-0.011,1.473,258.913,479.990) anwr=c((nam+1):(nam+n_progeny)) aid = c(pedP1[ ,1]) sid = c(pedP1[ ,2]) did <- c(pedP1[ ,3]) #number of herds length(unique(selectedallfemales[ ,6])) iherd=c(selectedallfemales[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals 205 # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam1=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree1 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree1) dataped <- pedigree1[pedigree1$id>nam,] simdataP1 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2000, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP1) nrow(simdataP1) #9000 ## combine the data file of (base) with P1 data file p1andbasepopdata <- rbind(basepopdata,simdataP1) ## Data file for basepop and P1 (has both observations and TBV) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1=mean(p1andbasepopdata$WWT) 206 WWTave_base_p1 WWTsd_base_p1=sd(p1andbasepopdata$WWT) WWTsd_base_p1 WWTave_base_p1-(3*WWTsd_base_p1) WWTave_base_p1+(3*WWTsd_base_p1) p1andbasepopdata <- subset(p1andbasepopdata, WWT > (WWTave_base_p1(3*WWTsd_base_p1))) p1andbasepopdata <- subset(p1andbasepopdata, WWT < (WWTave_base_p1+(3*WWTsd_base_p1))) summary(p1andbasepopdata$WWT) nrow(p1andbasepopdata) #8960 # keeping YWT observations within 3 SD YWTave_base_p1=mean(p1andbasepopdata$YWT) YWTave_base_p1 YWTsd_base_p1=sd(p1andbasepopdata$YWT) YWTsd_base_p1 YWTave_base_p1-(3*YWTsd_base_p1) YWTave_base_p1+(3*YWTsd_base_p1) p1andbasepop <- subset(p1andbasepopdata, YWT > (YWTave_base_p1-(3*YWTsd_base_p1))) p1andbasepopdata <- subset(p1andbasepopdata, YWT < (YWTave_base_p1+(3*YWTsd_base_p1))) summary(p1andbasepopdata$YWT) nrow(p1andbasepopdata) #8960 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,10] - p1andbasepopdata[ ,9] > 40) nrow(p1andbasepopdata) #8960 simdataP1 <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nam) summary(simdataP1$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #139.3 222.9 247.8 248.4 273.1 359.4 summary(simdataP1$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #253.5 434.8 479.7 480.9 527.6 666.5 nrow(simdataP1) #8960 N_sires = length(c(sort(unique(simdataP1$sire)))) N_sires #400 basepop_p1_data <- rbind(basepopdata,simdataP1) pedigreep1 <- data.frame (id = simdataP1$id, sire = simdataP1$sire, dam = simdataP1$dam) pedigreep1andbase <- rbind(pedigree,pedigreep1) 207 ############################################################################## ############################################################################## ## Creating P2 (Year 2) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ####Still no selection. No replacements. ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now) nam2 = nam+nam1 ############################## ## selection of sires ## average RFI TBV for sires and dams averages=by( basepopdata$RFItbv, basepopdata$sex, mean) ave1males=averages[1] ave1females=averages[2] ## standard deviation of RFI TBV for sires and dams SDs=by( basepopdata$RFItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## Remove females from year 1 (older than 16 years) females <- subset(selectedallfemales, year > 1) selectedallfemales1 <- females[sample(1:nrow(females), 8100, replace = FALSE),] nrow(selectedallfemales1) nrow(selectedallfemales) nrow(selectedallfemales1)/nrow(selectedallfemales) #0.90 ######################### #### 400 selected males and 8100 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales1) n_progeny = n_sel_females # number of females per sire = 20.25 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire 208 # because number of dams per sire is 20.25, then sires will have different numbers of progeny (some will have 20 and others will have 21 progeny) rounded_n_females_per_sire = round(n_females_per_sire) rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 20 progeny (300 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 21 progeny (100 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 25 times selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 263 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 8100 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp2 = randomlymatedsires[ ,1] damlistp2 = selectedallfemales1[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales1) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) #uniqueanimlist = uniqueanimlist[-1] subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #8500 length(uniqueanimlist) #8500 209 ## creating P2 pedigree which include(selected parents and their pedigree + new P2 ID with their selected parents) pedP2 = rbind(subdata[,1:3],cbind(c((nam2+1):(nam2+n_progeny)),sirelistp2[1:n_progeny],damlistp2[1: n_progeny])) ############## ## For P2, repeating the same code used to create P1. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(-0.011,1.473,258.913,479.990) anwr=c((nam2+1):(nam2+n_progeny)) aid = c(pedP2[ ,1]) sid = c(pedP2[ ,2]) did <- c(pedP2[ ,3]) #number of herds length(unique(selectedallfemales1[ ,6])) iherd=c(selectedallfemales1[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) 210 h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam3=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam3){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales1[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) 211 obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree2 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree2) dataped <- pedigree2[pedigree2$id>nam,] simdataP2 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2001, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP2) nrow(simdataP2) #8100 ## combine the data file of (base and P1) with P2 data file p2_p1_basepopdata <- rbind(p1andbasepopdata,simdataP2) ## Data file for basepop and P1 (has both observations and TBV) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2=mean(p2_p1_basepopdata$WWT) WWTave_base_p1_p2 WWTsd_base_p1_p2=sd(p2_p1_basepopdata$WWT) WWTsd_base_p1_p2 WWTave_base_p1_p2-(3*WWTsd_base_p1_p2) WWTave_base_p1_p2+(3*WWTsd_base_p1_p2) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT > (WWTave_base_p1_p2(3*WWTsd_base_p1_p2))) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT < (WWTave_base_p1_p2+(3*WWTsd_base_p1_p2))) summary(p2_p1_basepopdata$WWT) nrow(p2_p1_basepopdata) #17021 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,10] p2_p1_basepopdata[ ,9] > 40) nrow(p2_p1_basepopdata) #17021 simdataP2 <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nam2) summary(simdataP2$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #137.5 223.0 247.9 248.3 272.5 360.2 summary(simdataP2$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #286.5 434.2 481.4 480.4 526.4 680.6 nrow(simdataP2) #8069 212 N_sires = length(c(sort(unique(simdataP2$sire)))) N_sires #400 basepop_p2_p1_data <- rbind(basepop_p1_data,simdataP2) pedigreep2 <- data.frame (id = simdataP2$id, sire = simdataP2$sire, dam = simdataP2$dam) pedigreep2p1andbase<- rbind(pedigreep1andbase,pedigreep2) ############################################################################## ############################################################################## ## Creating P3 (Year 3) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv # Begin selection for RFI and use replacments from year 2000 ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam4 = nam2+nam3 ############################## ## selecting top 10% sirs and 80% dams ## selection of sires ## sires selection changed to 10% otherwise there were not enough sires averages=by( basepop_p1_data$RFItbv, basepop_p1_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_data$RFItbv, basepop_p1_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males3 <- subset(basepop_p1_data, sex == 1) bulls3 <- males3[order(males3$RFItbv), ] selectedmales3 <- bulls3[1:450, ] summary(selectedmales3[ ,7], na.rm=TRUE) nrow(males3) #4924 nrow(selectedmales3) #450 nrow(selectedmales3)/nrow(males3) #0.09 ######################### ## selection of dams ## FIRST: Remove females from year 2 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss and 90% conception rate 213 females3 <- subset(basepop_p1_data, sex == 2 & year > 2 & year < 2000) femalesp3 <- females3[sample(1:nrow(females3), 8000, replace=FALSE),] hfs <- subset(basepop_p1_data, sex == 2 & year == 2000) nrow(hfs) #4437 if(nrow(hfs) > 2000) { n = 2000 } else { n = nrow(hfs) } hfrs <- hfs[order(hfs$RFItbv), ] selectedhfrs <- hfrs[1:n, ] fem3 <- rbind(femalesp3, selectedhfrs) selectedallfemales3 <- fem3[sample(1:nrow(fem3), 9000, replace = FALSE),] summary(selectedallfemales3[ ,7], na.rm=TRUE) nrow(femalesp3) #8000 nrow(selectedallfemales3) #9000 damlistp3 = c(selectedallfemales3[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales3) allselectedmales=selectedmales3[rep(seq_len(nrow(selectedmales3)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp3 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales3, selectedallfemales3) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_data[basepop_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #10445 length(uniqueanimlist) #10445 pedp3 = rbind(subdata[ ,1:3],cbind(c((nam4+1):(nam4+n_progeny)),sirelistp3[1:n_progeny],damlistp3[1:n_progeny])) ################## 214 RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P3 progeny, repeating the same code used to create P2. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) ####averages: mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam4+1):(nam4+n_progeny)) aid = c(pedp3[ ,1]) sid = c(pedp3[ ,2]) did <- c(pedp3[ ,3]) #number of herds length(unique(selectedallfemales3[ ,6])) iherd=c(selectedallfemales3[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 215 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam5=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam5){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales3[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } 216 obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree3 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree3) dataped <- pedigree3[pedigree3$id>nam4,] simdataP3 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2002, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP3) nrow(simdataP3) #9000 ## combine the data file of (base, P1 and P2) with P3 data file p3_p2_p1_basepopdata <- rbind(p2_p1_basepopdata,simdataP3) ## Data file for basepop and P1 (has both observations and TBV) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3 WWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3 WWTave_base_p1_p2_p3-(3*WWTsd_base_p1_p2_p3) WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3(3*WWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3))) summary(p3_p2_p1_basepopdata$WWT) nrow(p3_p2_p1_basepopdata) #25974 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3 YWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3 YWTave_base_p1_p2_p3-(3*YWTsd_base_p1_p2_p3) YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3(3*YWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3))) 217 summary(p3_p2_p1_basepopdata$YWT) nrow(p3_p2_p1_basepopdata) #25961 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,10] p3_p2_p1_basepopdata[ ,9] > 40) nrow(p3_p2_p1_basepopdata) #25967 simdataP3 <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nam4) summary(simdataP3$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #134.1 214.3 238.9 239.8 264.4 358.0 summary(simdataP3$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 286.3 422.1 468.1 468.9 516.7 660.3 nrow(simdataP3) #8951 N_sires = length(c(sort(unique(simdataP3$sire)))) N_sires #450 basepop_p1_p2_p3_data <- rbind(basepop_p2_p1_data,simdataP3) pedigreep3 <- data.frame (id = simdataP3$id, sire = simdataP3$sire, dam = simdataP3$dam) pedigreep3p2p1andbase <- rbind(pedigreep2p1andbase,pedigreep3) ############################################################################## ############################################################################## ## Creating P4 (Year 4) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1 and P2) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam6 = nam4+nam5 ############################## ## selecting top 5% sires (2000 & 2001) and top heifers for replacements ## selection of sires averages=by( basepop_p2_p1_data$RFItbv, basepop_p2_p1_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p2_p1_data$RFItbv, basepop_p2_p1_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] 218 males4 <- subset(basepop_p2_p1_data, sex == 1 & year >= 2000) bulls4 <- males4[order(males4$RFItbv), ] selectedmales4 <- bulls4[1:450, ] summary(selectedmales4[ ,7], na.rm=TRUE) nrow(males4) #8593 nrow(selectedmales4) #450 nrow(selectedmales4)/nrow(males4) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 3 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss ## Assume 90% Conception Rate females4 <- subset(selectedallfemales3, year > 3) femalesp4 <- females4[sample(1:nrow(females4), 8000, replace=FALSE),] heifers <- subset(basepop_p2_p1_data, sex == 2 & year == 2001) nrow(heifers) #3991 if(nrow(hfs) > 2000) { n = 2000 } else { n = nrow(hfs) } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] fem4 <- rbind(femalesp4, selectedhfrs) selectedallfemales4 <- fem4[sample(1:nrow(fem4), 9000, replace = FALSE),] summary(selectedallfemales4[ ,7], na.rm=TRUE) nrow(femalesp4) #8000 nrow(selectedallfemales4) #9000 damlistp4 = c(selectedallfemales4[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales4) allselectedmales=selectedmales4[rep(seq_len(nrow(selectedmales4)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp4 = randomlymatedsires[ ,1] 219 #################### selectedparents=rbind(selectedmales4, selectedallfemales4) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p2_p1_data[basepop_p2_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #11231 length(uniqueanimlist) #11231 pedp4 = rbind(subdata[ ,1:3],cbind(c((nam6+1):(nam6+n_progeny)),sirelistp4[1:n_progeny],damlistp4[1:n_progeny])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P4 progeny, repeating the same code used to create P3. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) 220 # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam6+1):(nam6+n_progeny)) aid = c(pedp4[ ,1]) sid = c(pedp4[ ,2]) did <- c(pedp4[ ,3]) #number of herds length(unique(selectedallfemales4[ ,6])) iherd=c(selectedallfemales4[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam7=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam7){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } 221 damtbv= selectedallfemales4[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree4 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree4) dataped <- pedigree4[pedigree4$id>nam6,] simdataP4 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2003, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP4) nrow(simdataP4) #9000 ## combine the data file of (base, P1, P2 and P3) with P4 data file p4_p3_p2_p1_basepopdata <- rbind(p3_p2_p1_basepopdata,simdataP4) ## Data file for basepop, P1, P2, P3 and P4 (has both observations and TBV) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4 WWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4 WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4) WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4) 222 p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4))) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$WWT) nrow(p4_p3_p2_p1_basepopdata) #34911 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$YWT) nrow(p4_p3_p2_p1_basepopdata) #34897 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,10] - p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p4_p3_p2_p1_basepopdata) #34897 simdataP4 <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nam6) summary(simdataP4$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #129.8 209.6 235.0 235.6 260.3 356.1 summary(simdataP4$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #280.2 408.0 454.8 455.1 501.7 661.5 nrow(simdataP4) #8951 N_sires = length(c(sort(unique(simdataP4$sire)))) N_sires #450 basepop_p1_p2_p3_p4_data <- rbind(basepop_p1_p2_p3_data,simdataP4) pedigreep4 <- data.frame (id = simdataP4$id, sire = simdataP4$sire, dam = simdataP4$dam) pedigreep4p3p2p1andbase <- rbind(pedigreep3p2p1andbase,pedigreep4) ############################################################################## ############################################################################## ## Creating P5 (Year 5) #1 2 3 4 5 6 7 8 9 10 11 12 13 223 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2 and P3) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam8 = nam6+nam7 ############################## ## selecting top 5% sires and 80% dams ## selection of sires averages=by( basepop_p1_p2_p3_data$RFItbv, basepop_p1_p2_p3_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_data$RFItbv, basepop_p1_p2_p3_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males5 <- subset(basepop_p1_p2_p3_data, sex == 1 & year >= 2001) bulls5 <- males5[order(males5$RFItbv), ] selectedmales5 <- bulls5[1:450, ] summary(selectedmales5[ ,7], na.rm=TRUE) nrow(males5) #8593 nrow(selectedmales5) #450 nrow(selectedmales5)/nrow(males5) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 4 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females5 <- subset(selectedallfemales4, year > 4) femalesp5 <- females5[sample(1:nrow(females5), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_data, sex == 2 & year == 2002) nrow(heifers) #4427 if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$RFItbv), ] 224 selectedhfrs <- hfrs[1:n, ] fem5 <- rbind(femalesp5, selectedhfrs) selectedallfemales5 <- fem5[sample(1:nrow(fem5), 9000, replace = FALSE),] summary(selectedallfemales5[ ,7], na.rm=TRUE) nrow(femalesp5) #8000 nrow(selectedallfemales5) #9000 damlistp5 = c(selectedallfemales5[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales5) allselectedmales=selectedmales5[rep(seq_len(nrow(selectedmales5)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp5 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales5, selectedallfemales5) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_data[basepop_p1_p2_p3_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #12222 length(uniqueanimlist) #12222 pedp5 = rbind(subdata[ ,1:3],cbind(c((nam8+1):(nam8+n_progeny)),sirelistp5[1:n_progeny],damlistp5[1:n_progeny])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P5 progeny, repeating the same code used to create P4. 225 library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam8+1):(nam8+n_progeny)) aid = c(pedp5[ ,1]) sid = c(pedp5[ ,2]) did <- c(pedp5[ ,3]) #number of herds length(unique(selectedallfemales5[ ,6])) iherd=c(selectedallfemales5[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) 226 HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam9=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam9){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales5[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree5 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree5) dataped <- pedigree5[pedigree5$id>nam8,] simdataP5 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2004, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) 227 attach(simdataP5) nrow(simdataP5) #9000 ## combine the data file of (base, P1, P2, P3 and P4) with P5 data file p5_p4_p3_p2_p1_basepopdata <- rbind(p4_p3_p2_p1_basepopdata,simdataP5) ## Data file for basepop and P's (has both observations and TBV) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5 WWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5 WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5) WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43847 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5 YWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5 YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5) YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43836 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,10] - p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p5_p4_p3_p2_p1_basepopdata) #42627 simdataP5 <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nam8) summary(simdataP5$WWT) 228 #Min. 1st Qu. Median Mean 3rd Qu. Max. #129.4 210.1 235.2 236.0 261.2 353.9 summary(simdataP5$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #274.8 409.8 455.5 456.1 502.3 649.9 nrow(simdataP5) #8955 N_sires = length(c(sort(unique(simdataP5$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_data <- rbind(basepop_p1_p2_p3_p4_data,simdataP5) pedigreep5 <- data.frame (id = simdataP5$id, sire = simdataP5$sire, dam = simdataP5$dam) pedigreep5p4p3p2p1andbase <- rbind(pedigreep4p3p2p1andbase,pedigreep5) ############################################################################## ############################################################################## ## Creating P6 (Year 6) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3 and P4) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5 and P5 nam10 = nam8+nam9 ############################## ## selecting top 5% sirs and 80% dams ## selection of sires males6 <- subset(basepop_p1_p2_p3_p4_data, sex == 1 & year >= 2002) bulls6 <- males6[order(males6$RFItbv), ] selectedmales6 <- bulls6[1:450, ] summary(selectedmales6[ ,7], na.rm=TRUE) nrow(males6) #9080 nrow(selectedmales6) #450 nrow(selectedmales6)/nrow(males6) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 5 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females6 <- subset(selectedallfemales5, sex == 2 & year > 5) 229 femalesp6 <- females6[sample(1:nrow(females6), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_data, sex == 2 & year == 2003) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem6 <- rbind(femalesp6, selectedhfrs) selectedallfemales6 <- fem6[sample(1:nrow(fem6), 9000, replace = FALSE),] summary(selectedallfemales6[ ,7], na.rm=TRUE) nrow(femalesp6) #8000 nrow(selectedallfemales6) #9000 damlistp6 = c(selectedallfemales6[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales3) allselectedmales=selectedmales6[rep(seq_len(nrow(selectedmales6)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp6 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales6, selectedallfemales6) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_data[basepop_p1_p2_p3_p4_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #12970 length(uniqueanimlist) #12970 pedp6 = rbind(subdata[ ,1:3],cbind(c((nam10+1):(nam10+n_progeny)),sirelistp6[1:n_progeny],damlistp6[1:n_progeny])) ################## 230 RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P6 progeny, repeating the same code used to create P5. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam10+1):(nam10+n_progeny)) aid = c(pedp6[ ,1]) sid = c(pedp6[ ,2]) did <- c(pedp6[ ,3]) #number of herds length(unique(selectedallfemales6[ ,6])) iherd=c(selectedallfemales6[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 231 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam11=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam11){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales6[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } 232 obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree6 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree6) dataped <- pedigree6[pedigree6$id>nam10,] simdataP6 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2005, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP6) nrow(simdataP6) #9000 ## combine the data file of (base, P1, P2, P3, P4 and P5) with P6 data file p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p5_p4_p3_p2_p1_basepopdata,simdataP6) ## Data file for basepop and P's (has both observations and TBV) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6 WWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6 WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6) WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52789 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6 YWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6 YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6) YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) 233 p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52779 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #57483 simdataP6 <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam10) summary(simdataP6$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #126.8 208.1 233.8 234.5 259.9 353.4 summary(simdataP6$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #270.8 403.3 450.1 450.3 497.4 651.9 nrow(simdataP6) #8953 N_sires = length(c(sort(unique(simdataP6$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_data <- rbind(basepop_p1_p2_p3_p4_p5_data,simdataP6) pedigreep6 <- data.frame (id = simdataP6$id, sire = simdataP6$sire, dam = simdataP6$dam) pedigreep6p5p4p3p2p1andbase <- rbind(pedigreep5p4p3p2p1andbase,pedigreep6) ############################################################################## ############################################################################## ## Creating P7 (Year 7) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4 and P5) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6 and P7 nam12 = nam10+nam11 ############################## ## selecting top 5% sirs and 80% dams ## selection of sires 234 averages=by( basepop_p1_p2_p3_p4_p5_data$RFItbv, basepop_p1_p2_p3_p4_p5_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_p4_p5_data$RFItbv, basepop_p1_p2_p3_p4_p5_data$sex, sd) sd1males=SDs[1] sd1females=SDs[2] males7 <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 1 & year >= 2003) bulls7 <- males7[order(males7$RFItbv), ] selectedmales7 <- bulls7[1:450, ] summary(selectedmales7[ ,7], na.rm=TRUE) nrow(males7) #9067 nrow(selectedmales7) #450 nrow(selectedmales7)/nrow(males7) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 6 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females7 <- subset(selectedallfemales6, sex == 2 & year > 6) femalesp7 <- females7[sample(1:nrow(females7), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 2 & year == 2004) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem7 <- rbind(femalesp7, selectedhfrs) selectedallfemales7 <- fem7[sample(1:nrow(fem7), 9000, replace = FALSE),] summary(selectedallfemales7[ ,7], na.rm=TRUE) nrow(femalesp7) #8000 nrow(selectedallfemales7) #9000 damlistp7 = c(selectedallfemales7[ ,1]) ######################### 235 #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales7) allselectedmales=selectedmales7[rep(seq_len(nrow(selectedmales7)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp7= randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales7, selectedallfemales7) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_data[basepop_p1_p2_p3_p4_p5_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #13850 length(uniqueanimlist) #13850 pedp7 = rbind(subdata[ ,1:3],cbind(c((nam12+1):(nam12+n_progeny)),sirelistp7[1:n_progeny],damlistp7[1:n_progeny])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P7 progeny, repeating the same code used to create P6. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) 236 herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam12+1):(nam12+n_progeny)) aid = c(pedp7[ ,1]) sid = c(pedp7[ ,2]) did <- c(pedp7[ ,3]) #number of herds length(unique(selectedallfemales7[ ,6])) iherd=c(selectedallfemales7[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals 237 # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam13=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam13){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales7[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree7 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree7) dataped <- pedigree7[pedigree7$id>nam12,] simdataP7 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2006, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP7) nrow(simdataP7) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5 and P6) with P7 data file p7_p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p6_p5_p4_p3_p2_p1_basepopdata,simdataP7) ## Data file for basepop, P1, P2, P3, P4, P5, P6 and P7 (has both observations and TBV) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) 238 # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7 WWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7 WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61743 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61726 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61723 simdataP7 <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam12) summary(simdataP7$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #126.5 208.0 233.8 234.5 259.3 352.8 summary(simdataP7$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #278.5 401.4 449.6 449.5 496.8 648.1 nrow(simdataP7) #8954 N_sires = length(c(sort(unique(simdataP7$sire)))) N_sires #450 239 basepop_p1_p2_p3_p4_p5_p6_p7_data <- rbind(basepop_p1_p2_p3_p4_p5_p6_data,simdataP7) pedigreep7 <- data.frame (id = simdataP7$id, sire = simdataP7$sire, dam = simdataP7$dam) pedigreep7p6p5p4p3p2p1andbase <- rbind(pedigreep6p5p4p3p2p1andbase,pedigreep7) ############################################################################## ############################################################################## ## Creating P8 (Year 8) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5 and P6) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7 and P8 nam14 = nam12+nam13 ############################## ## selecting top 5% sires ## selection of sires males8 <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 1 & year >= 2004) bulls8 <- males8[order(males8$RFItbv), ] selectedmales8 <- bulls8[1:450, ] summary(selectedmales8[ ,7], na.rm=TRUE) nrow(males8) #9070 nrow(selectedmales8) #450 nrow(selectedmales8)/nrow(males8) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 7 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females8 <- subset(selectedallfemales7, sex == 2 & year > 7) femalesp8 <- females8[sample(1:nrow(females8), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 2 & year == 2005) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) 240 } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem8 <- rbind(femalesp8, selectedhfrs) selectedallfemales8 <- fem8[sample(1:nrow(fem8), 9000, replace = FALSE),] summary(selectedallfemales8[ ,7], na.rm=TRUE) nrow(femalesp8) #8000 nrow(selectedallfemales8) #9000 damlistp8 = c(selectedallfemales8[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales8) allselectedmales=selectedmales8[rep(seq_len(nrow(selectedmales8)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp8 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales8, selectedallfemales8) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_p6_data[basepop_p1_p2_p3_p4_p5_p6_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #14525 length(uniqueanimlist) #14525 pedp8 = rbind(subdata[ ,1:3],cbind(c((nam14+1):(nam14+n_progeny)),sirelistp8[1:n_progeny],damlistp8[1:n_progeny])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave 241 ############## ############## ## P8 progeny, repeating the same code used to create P7. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) # Traits averages mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam14+1):(nam14+n_progeny)) aid = c(pedp8[ ,1]) sid = c(pedp8[ ,2]) did <- c(pedp8[ ,3]) #number of herds length(unique(selectedallfemales8[ ,6])) iherd=c(selectedallfemales8[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits 242 # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam15=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam15){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales8[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree8 <- data.frame (id = aid, sire = sid, dam = did) 243 attach(pedigree8) dataped <- pedigree8[pedigree8$id>nam14,] simdataP8 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2007, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP8) nrow(simdataP8) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6 and P7) with P8 data file p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP8) ## Data file for basepop and P's (has both observations and TBV) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WW T) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8)) ) summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70676 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT ) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) 244 p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #66130 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70664 simdataP8 <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam14) summary(simdataP8$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #125.5 208.1 232.8 233.7 258.7 351.8 summary(simdataP8$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #266.4 400.1 446.7 447.4 495.0 641.0 nrow(simdataP8) #8951 N_sires = length(c(sort(unique(simdataP8$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_data,simdataP8) pedigreep8 <- data.frame (id = simdataP8$id, sire = simdataP8$sire, dam = simdataP8$dam) pedigreep8p7p6p5p4p3p2p1andbase <- rbind(pedigreep7p6p5p4p3p2p1andbase,pedigreep8) ############################################################################## ############################################################################## ## Creating P9 (Year 9) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam16 = nam14+nam15 ############################## ## selecting top 5% sires 245 ## selection of sires males9 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 1 & year >= 2005) bulls9 <- males9[order(males9$RFItbv), ] selectedmales9 <- bulls9[1:450, ] summary(selectedmales9[ ,7], na.rm=TRUE) nrow(males9) #9065 nrow(selectedmales9) #450 nrow(selectedmales9)/nrow(males9) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 8 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females9 <- subset(selectedallfemales8, sex == 2 & year > 8) femalesp9 <- females9[sample(1:nrow(females9), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 2 & year == 2006) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] nrow(selectedhfrs) fem9 <- rbind(femalesp8, selectedhfrs) selectedallfemales9 <- fem8[sample(1:nrow(fem9), 9000, replace = FALSE),] summary(selectedallfemales9[ ,7], na.rm=TRUE) nrow(femalesp9) #8000 nrow(selectedallfemales9) #10000 damlistp9 = c(selectedallfemales9[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales9) allselectedmales=selectedmales9[rep(seq_len(nrow(selectedmales9)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp9 = randomlymatedsires[ ,1] 246 #################### selectedparents=rbind(selectedmales9, selectedallfemales9) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_p6_p7_data[basepop_p1_p2_p3_p4_p5_p6_p7_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #14636 length(uniqueanimlist) #14636 pedp9 = rbind(subdata[ ,1:3],cbind(c((nam16+1):(nam16+n_progeny)),sirelistp9[1:n_progeny],damlistp9[1:n_progeny])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P9 progeny, repeating the same code used to create P8. library(MASS) set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix 247 R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) ####averages: mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam16+1):(nam16+n_progeny)) aid = c(pedp9[ ,1]) sid = c(pedp9[ ,2]) did <- c(pedp9[ ,3]) #number of herds length(unique(selectedallfemales9[ ,6])) iherd=c(selectedallfemales9[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam17=n_progeny mendelian = jd(nam1,4)*0 248 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales9[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree9 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree9) dataped <- pedigree9[pedigree9$id>nam16,] simdataP9 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2008, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP9) nrow(simdataP9) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7 and P8) with P9 data file p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP9) ## Data file for basepop and P's (has both observations and TBV) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basep opdata$WWT) 249 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_ p8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79617 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepo pdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 _p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79605 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, 250 p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79604 simdataP9 <- subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam16) summary(simdataP9$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #125.5 209.1 233.8 234.4 258.9 350.7 summary(simdataP9$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #268.1 401.7 447.8 449.2 497.0 639.2 nrow(simdataP9) #8950 N_sires = length(c(sort(unique(simdataP9$sire)))) N_sires # 450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data,simdataP9) pedigreep9 <- data.frame (id = simdataP9$id, sire = simdataP9$sire, dam = simdataP9$dam) pedigreep9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep8p7p6p5p4p3p2p1andbase,pedigreep9) ############################################################################## ############################################################################## ## Creating P10 (Year 10) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam18 = nam16+nam17 ############################## ## selecting top 5% sires ## selection of sires averages=by( basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$RFItbv, basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$sex, mean) ave1males=averages[1] ave1females=averages[2] SDs=by( basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$RFItbv, basepop_p1_p2_p3_p4_p5_p6_p7_p8_data$sex, sd) sd1males=SDs[1] 251 sd1females=SDs[2] males10 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 1 & year >= 2006) bulls10 <- males10[order(males10$RFItbv), ] selectedmales10 <- bulls10[1:450, ] summary(selectedmales10[ ,7], na.rm=TRUE) nrow(males10) #9059 nrow(selectedmales10) #450 nrow(selectedmales10)/nrow(males10) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 9 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females10 <- subset(selectedallfemales9, sex == 2 & year > 9) femalesp10 <- females10[sample(1:nrow(females10), 8000, replace=FALSE),] heifers <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 2 & year == 2007) nrow(heifers) if(nrow(heifers) > 2000) { n = 2000 } else { n = nrow(heifers) } hfrs <- heifers[order(heifers$RFItbv), ] selectedhfrs <- hfrs[1:n, ] fem10 <- rbind(femalesp10, heifers) selectedallfemales10 <- fem10[sample(1:nrow(fem10), 9000, replace = FALSE),] nrow(femalesp10) #8000 nrow(selectedallfemales10) #10000 damlistp10 = c(selectedallfemales10[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales10) allselectedmales=selectedmales10[rep(seq_len(nrow(selectedmales10)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp10 = randomlymatedsires[ ,1] #################### 252 selectedparents=rbind(selectedmales10, selectedallfemales10) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #15097 length(uniqueanimlist) #15097 pedp10 = rbind(subdata[ ,1:3],cbind(c((nam18+1):(nam18+n_progeny)),sirelistp10[1:n_progeny],damlistp10[1:n_progeny ])) ################## RFIave=mean(selectedparents[ ,7], na.rm=TRUE) RFIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P10 progeny, repeating the same code used to create P9. set.seed(1234) herdRFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdRFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(0.311,-0.009,0.219,0.579,0.009,0.014,0.548,1.231,0.219,0.548,552.753,465.634,0.579,1.231,465.634,1131.95),byrow=TR UE,nrow=4) 253 # G matrix G=matrix(data=c(0.18,0.0005,-1.372,-2.249,0.0005,0.01,1.014,2.217,1.372,1.014,230.77,327.931,-2.249,2.217,327.931,598.33),byrow=TRUE,nrow=4) ####averages: mu=c(RFIave,ADGave,WWTave,YWTave) anwr=c((nam18+1):(nam18+n_progeny)) aid = c(pedp10[ ,1]) sid = c(pedp10[ ,2]) did <- c(pedp10[ ,3]) #number of herds length(unique(selectedallfemales10[ ,6])) iherd=c(selectedallfemales10[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam19=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } 254 damtbv= selectedallfemales10[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree10 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree10) dataped <- pedigree10[pedigree10$id>nam18,] simdataP10 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2009, herd = iherd, RFI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], RFItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP10) nrow(simdataP10) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7, P8 and P9) with P10 data file p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP10) ## Data file for basepop and P's (has both observations and TBV) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$WWT) 255 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6 _p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88567 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p 7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88558 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,8] > 40) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88558 256 simdataP10 <- subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam18) summary(simdataP10$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #124.2 207.2 232.6 233.4 258.8 351.3 summary(simdataP10$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #264.1 396.6 443.7 443.9 493.0 639.9 nrow(simdataP10) #8962 N_sires = length(c(sort(unique(simdataP10$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data,simdataP10) pedigreep10 <- data.frame (id = simdataP10$id, sire = simdataP10$sire, dam = simdataP10$dam) pedigreep10p9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep9p8p7p6p5p4p3p2p1andbase,pedigreep10) ############################################################################## ############################################################################## ## see how many records per sire try <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) nrow(try) ones = c(rep(1,(nrow(try)))) try = data.matrix(try) try = cbind(try,ones) ham=sort(by( try[ ,14], try[ ,2], length)) head(ham) ############################################ ## Final data files ## pedigree file ## ****data file for animals with records (will be used for ****ASREML3.0****) data_anim_with_record <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) summary(data_anim_with_record$RFI) #Min. 1st Qu. Median Mean 3rd Qu. Max. #-25.310 -11.440 -7.510 -7.425 -3.410 9.020 summary(data_anim_with_record$YWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #253.5 410.4 457.4 457.9 505.7 680.6 summary(data_anim_with_record$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #124.2 211.7 237.0 237.8 262.9 360.2 257 summary(data_anim_with_record$ADG) # Min. 1st Qu. Median Mean 3rd Qu. Max. #-0.120 0.920 1.130 1.143 1.350 2.730 258 APPENDIX D: R CODE USED TO CREATE ECONOMIC SELECTION INDEX PARAMETERS 259 #R code based on Dr. Larry Schaeffer’s R code for multiple trait models && Hamad Saad's disertation #Creating a simulated data (Selection on decreasing feed intake) ## Traits were: Feed intake (FI), 200 d weight (WWT), 400 d weight (YWT), and average daily gain (ADG) # First creating the base population (No selection) setwd("/Users/Randie/Documents/PhD Research/Simulation/SimRCode") ## To clear environment #FISimData_v2 rm(list = ls()) ##Run DistFem_USE.R first source("DistFem_USE.R") #Herd effects (52 herds) on FI, ADG, WWT and YWT ##Simulate observations using G and R matrices for FI. NO SELECTION FOR FI!!! library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages #ID for animals (founders (10000 dams, 400 sires)) aid = c(1:10400) ##creating fields in the data file for sire (20 progeny each), dams (1 progeny each), herds (size of 200 each), sex (50% females and 50% males) sid = c(numeric(10400),rep(1:400, by=1, each=20)) base.sire <- data.frame(id = c(10001:10400), year = 00, sex = 1) 260 did <- c(numeric(10400),1:10000) bi=c(rep(1,10400),rep(0.5,10000)) set.seed(1234) isex=(rbinom(10000, 1, 0.5))+1 set.seed(1234) iherd=c(sample(rep(1:52, by=1, each=200),10400,replace=F)) # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) nam = 10400 # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} tbv = jd(nam,4)*0 for(i in 1:nam){ x = LG %*% (sqrt(bi[i])*rnorm(4,0,1)) if(sid[i]>0){ ks=sid[i] kd=did[i] x = x + 0.5*(tbv[ks, ]+tbv[kd, ]) } tbv[i,]=x } nrec=10400 ################################################################## ################################################################### 261 ##Creating base popuation with tbv but no observations ####Use base.females from DistFem_USE.R base.pop <- rbind(base.females, base.sire) simulateddata <- data.frame (id = base.pop$id, sire = c(rep(NA,10400)), dam = c(rep(NA,10400)), sex = base.pop$sex, year = base.pop$year, herd = iherd, FI = c(rep(NA,10400)), ADG = c(rep(NA,10400)), WWT = c(rep(NA,10400)), YWT = c(rep(NA,10400)), FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simulateddata) animlist = c(simulateddata[ ,1]) detach(simulateddata) uniqueanimlist = c(sort(unique(animlist))) pedigree = data.frame(id = uniqueanimlist, sire = c(rep(NA,10400)), dam = c(rep(NA,10400))) length(uniqueanimlist) #10400 length(pedigree[,1]) #10400 #Header: id sire dam sex year herd FI ADG WWT YWT FItbv ADGtbv WWTtbv YWTtbv basepopdata <- simulateddata attach(basepopdata) ############################################################# ## creating P1 (progeny 1) ## Assuming 100% conception ## No selection of FI. Must use whole population for first 2 generations ############################################################# ## redefine the total number of all animals and number of base population in previous simulation ############################## #total number of all animals (base pop + P1) nam = 20400 #number of sires and dams(founders) (400+10000) in base population nbase = 10400 ############################## ## No Selection for sires to create base pop for SI values. ## Select 5% of sires randomly ## selection of sires ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## For first selection of cows from P1 only selected 100% of females to be mated to sires selectedfemales <- subset(basepopdata, sex == 2) 262 ######################### #### 400 selected males and 10000 selected females ## Create random list of sires with length of 10000 which is number of selected dams allselectedmales=selectedmales[rep(seq_len(nrow(selectedmales)), each=25),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp1 = randomlymatedsires[ ,1] damlistp1 = selectedfemales[ ,1] #################### selectedparents=rbind(selectedmales, selectedfemales) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #10400 length(uniqueanimlist) #10400 ## creating BP (base population for SI values) pedigree which include(selected parents and their pedigree + new BP ID with their selected parents) pedBP = rbind(subdata[,1:3],cbind(c((nam+1):(nam+n_progeny)),sirelistp1[1:n_progeny],damlistp1[1:n_ progeny])) ################## ############## ## P1 observations library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix 263 G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages anwr=c((nam+1):(nam+n_progeny)) aid = c(pedBP[ ,1]) sid = c(pedBP[ ,2]) did <- c(pedBP[ ,3]) #number of herds length(unique(selectedfemales[ ,6])) iherd=c(selectedfemales[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam1=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedfemales[ ,11:14] 264 siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigreeBP <- data.frame (id = aid, sire = sid, dam = did) attach(pedigreeBP) dataped <- pedigreeBP[pedigreeBP$id>nam,] base.pop <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) ## Use base.pop to develop SI values. ## Use only males assuming all were finished in a feedlot ## 10 year averages were used to estimate cattle prices ($/kg), feed cost ($/kg) and average days on feed ## Cattle price: $2.64/kg ## Feed Cost: $0.18/kg ## Day On Feed: 157 d males <- subset(base.pop, sex == 1) y <- males$YWT*2.64 - males$FI*157*0.18 x.FI <- males$FItbv x.ADG <- males$ADGtbv x.WWT <- males$WWTtbv x.YWT <- males$YWTtbv SI.reg <- lm(y ~ x.FI + x.ADG + x.WWT + x.YWT) summary(SI.reg) #Call: 265 #lm(formula = y ~ x.FI + x.ADG + x.WWT + x.YWT) # #Residuals: # Min 1Q Median 3Q Max #-281.585 -52.141 1.002 52.992 298.335 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 1119.42324 1.10451 1013.503 <2e-16 *** # x.FI -29.66932 2.90774 -10.204 <2e-16 *** # x.ADG 21.99373 37.28831 0.590 0.555 # x.WWT 0.09652 0.16289 0.593 0.554 # x.YWT 2.55104 0.20261 12.591 <2e-16 *** # --# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # #Residual standard error: 78.5 on 5052 degrees of freedom #Multiple R-squared: 0.3065, Adjusted R-squared: 0.306 #F-statistic: 558.3 on 4 and 5052 DF, p-value: < 2.2e-16 ### SI = -29.66932FItbv + 21.99373ADGtbv + 0.09652WWTtbv + 2.55104YWTtbv ##Sensitivity Testing install.packages("caret") library(caret) konfound(SI.reg, x.FI, to_return = "print", test_all = TRUE) # A tibble: 4 x 8 #var_name t df action inference pct_bias_to_change_inference itcv r_con #<chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> # 1 x.FI -10.2 5053 to_invalidate reject_null 80.6 0.118 0.343 #2 x.ADG 0.590 5053 to_sustain fail_to_reject_null 69.9 -0.019 0.137 #3 x.WWT 0.595 5053 to_sustain fail_to_reject_null 69.6 -0.019 0.137 #4 x.YWT 12.6 5053 to_invalidate reject_null 84.2 0.151 0.388 > 266 APPENDIX E: R CODE USED TO CREATE SIMULATE DATA FOR SELECTION USING AN ECONOMIC SELECTION INDEX 267 #R code based on Dr. Larry Schaeffer’s R code for multiple trait models && Hamad Saad's disertation #Creating a simulated data (Selection on decreasing feed intake) ## Traits were: Feed intake (FI), 200 d weight (WWT), 400 d weight (YWT), and average daily gain (ADG) # First creating the base population (No selection) setwd("/Users/Randie/Documents/PhD Research/Simulation") ## To clear environment #FISimData_v2 rm(list = ls()) ##Run DistFem_USE.R first source("DistFem_USE.R") library(MASS) #Herd effects (50 herds) on FI, ADG, WWT and YWT set.seed(1234) herdFI=(rnorm(50,0)) set.seed(1234) herdWW=(rnorm(50,0))*2 set.seed(1234) herdYW=(rnorm(50,0))*10 set.seed(1234) herdADG=(rnorm(50,0))*0.25 ##Crews et al 2006 (SD for ADG) herd=matrix(data = c(herdFI,herdADG,herdWW,herdYW),byrow = TRUE, nrow = 4) # sex effects (52) herds) on FI, ADG, WWT, and YWT ##Sex effects for wwt and ywwt from Van Vleck & Cundiff 1998 ##ADG sex effects used Hamad's sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages #ID for animals (founders (10000 dams, 450 sires)) aid = c(1:10400) ##creating fields in the data file for sire (20 progeny each), dams (1 progeny each), herds (size of 200 each), sex (50% females and 50% males) 268 sid = c(numeric(10400),rep(1:400, by=1, each=20)) base.sire <- data.frame(id = c(10001:10400), year = 15, sex = 1) did <- c(numeric(10400),1:10000) bi=c(rep(1,10400),rep(0.5,10000)) set.seed(1234) iherd=c(sample(rep(1:52, by=1, each=200),10400,replace=F)) # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) nam = 10400 # Simulate true breeding values for all animals (founders and their F1 progeny) # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} tbv = jd(nam,4)*0 for(i in 1:nam){ x = LG %*% (sqrt(bi[i])*rnorm(4,0,1)) if(sid[i]>0){ ks=sid[i] kd=did[i] x = x + 0.5*(tbv[ks, ]+tbv[kd, ]) } tbv[i,]=x } nrec=10400 ################################################################## ################################################################### ##Creating base popuation with tbv but no observations 269 ####Use base.females from DistFem_USE.R base.pop <- rbind(base.females, base.sire) simulateddata <- data.frame (id = base.pop$id, sire = c(rep(NA,10400)), dam = c(rep(NA,10400)), sex = base.pop$sex, year = base.pop$year, herd = iherd, FI = c(rep(NA,10400)), ADG = c(rep(NA,10400)), WWT = c(rep(NA,10400)), YWT = c(rep(NA,10400)), FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simulateddata) animlist = c(simulateddata[ ,1]) detach(simulateddata) uniqueanimlist = c(sort(unique(animlist))) pedigree = data.frame(id = uniqueanimlist, sire = c(rep(NA,10400)), dam = c(rep(NA,10400))) length(uniqueanimlist) #10400 length(pedigree[,1]) #10400 #Header: id sire dam sex year herd FI ADG WWT YWT FItbv ADGtbv WWTtbv YWTtbv basepopdata <- simulateddata attach(basepopdata) ############################################################# ## creating P1 (progeny 1) ## Assuming 100% conception ## No selection. Must use whole population for first 2 generations ############################################################# ## redefine the total number of all animals and number of base population in previous simulation ############################## #total number of all animals (base pop + P1) nam = 20400 #number of sires and dams(founders) (400+10000) in base population nbase = 10400 ############################## ## selecting top 5% sirs and 80% dams (TBV for FI is the selection criteria) ## selection of sires ## average FI TBV for sires and dams averages=by( basepopdata$FItbv, basepopdata$sex, mean) ave1males=averages[1] ave1females=averages[2] ## standard deviation of FI TBV for sires and dams SDs=by( basepopdata$FItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) 270 ######################### ## selection of all dams ## For first selection of cows from P1 only selected 100% of females to be mated to sires females.base <- subset(basepopdata, sex == 2) ##90% Conception Rate selectedallfemales <- females.base[sample(1:nrow(females.base), 9000, replace = FALSE),] nrow(females.base) nrow(selectedallfemales) nrow(selectedallfemales)/nrow(females.base) #0.9 ######################### #### 400 selected males and 10000 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales) n_progeny = n_sel_females # number of females per sire = 22.5 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire # because number of dams per sire is 22.5, then sires will have different numbers of progeny (some will have 22.5 and others will have 23 progeny) rounded_n_females_per_sire = round(n_females_per_sire) rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 22 progeny (200 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 23 progeny (200 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 22 times selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 200 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times 271 selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 10000 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp1 = randomlymatedsires[ ,1] damlistp1 = selectedallfemales[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #9400 length(uniqueanimlist) #9400 ## creating P1 pedigree which include(selected parents and their pedigree + new P1 ID with their selected parents) pedP1 = rbind(subdata[,1:3],cbind(c((nam+1):(nam+n_progeny)),sirelistp1[1:n_progeny],damlistp1[1:n_ progeny])) ################## ############## ## P1 observations library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) 272 # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages anwr=c((nam+1):(nam+n_progeny)) aid = c(pedP1[ ,1]) sid = c(pedP1[ ,2]) did <- c(pedP1[ ,3]) #number of herds length(unique(selectedallfemales[ ,6])) iherd=c(selectedallfemales[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam1=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } 273 damtbv= selectedallfemales[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree1 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree1) dataped <- pedigree1[pedigree1$id>nam,] simdataP1 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2000, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP1) nrow(simdataP1) #9000 ## combine the data file of (base) with P1 data file p1andbasepopdata <- rbind(basepopdata,simdataP1) ## Data file for basepop and P1 (has both observations and TBV) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1=mean(p1andbasepopdata$WWT) WWTave_base_p1 #231.39 WWTsd_base_p1=sd(p1andbasepopdata$WWT) WWTsd_base_p1 #31.63 WWTave_base_p1-(3*WWTsd_base_p1) #136.49 WWTave_base_p1+(3*WWTsd_base_p1) #326.29 p1andbasepopdata <- subset(p1andbasepopdata, WWT > (WWTave_base_p1(3*WWTsd_base_p1))) 274 p1andbasepopdata <- subset(p1andbasepopdata, WWT < (WWTave_base_p1+(3*WWTsd_base_p1))) summary(p1andbasepopdata$WWT) nrow(p1andbasepopdata) #8954 # keeping YWT observations within 3 SD YWTave_base_p1=mean(p1andbasepopdata$YWT) YWTave_base_p1 #370.82 YWTsd_base_p1=sd(p1andbasepopdata$YWT) YWTsd_base_p1 #54.09 YWTave_base_p1-(3*YWTsd_base_p1) #208.55 YWTave_base_p1+(3*YWTsd_base_p1) #533.08 p1andbasepop <- subset(p1andbasepopdata, YWT > (YWTave_base_p1-(3*YWTsd_base_p1))) p1andbasepopdata <- subset(p1andbasepopdata, YWT < (YWTave_base_p1+(3*YWTsd_base_p1))) summary(p1andbasepopdata$YWT) nrow(p1andbasepopdata) #8954 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p1andbasepopdata <- subset(p1andbasepopdata, p1andbasepopdata[ ,10] - p1andbasepopdata[ ,9] > 40) nrow(p1andbasepopdata) #8938 simdataP1 <- subset(p1andbasepopdata, p1andbasepopdata[ ,1] > nam) summary(simdataP1$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #136.6 222.5 247.5 248.1 272.9 361.4 summary(simdataP1$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #280.1 433.2 480.8 480.5 527.0 660.9 nrow(simdataP1) #8938 N_sires = length(c(sort(unique(simdataP1$sire)))) N_sires #400 basepop_p1_data <- rbind(basepopdata,simdataP1) pedigreep1 <- data.frame (id = simdataP1$id, sire = simdataP1$sire, dam = simdataP1$dam) pedigreep1andbase <- rbind(pedigree,pedigreep1) ############################################################################## ############################################################################## ## Creating P2 (Year 2) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ####Still no selection. No replacements. ############################################################# 275 ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now) nam2 = nam+nam1 ############################## ## selection of sires ## average FI TBV for sires and dams averages=by( basepopdata$FItbv, basepopdata$sex, mean) ave1males=averages[1] ave1females=averages[2] ## standard deviation of FI TBV for sires and dams SDs=by( basepopdata$FItbv, basepopdata$sex, sd) sd1males=SDs[1] sd1females=SDs[2] ## selecting all sires from basepopdata selectedmales <- subset(basepopdata, sex == 1) ######################### ## selection of all dams ## Remove females from year 1 (older than 16 years) females <- subset(selectedallfemales, year > 1) selectedallfemales1 <- females[sample(1:nrow(females), 8100, replace = FALSE),] nrow(selectedallfemales1) nrow(selectedallfemales) nrow(selectedallfemales1)/nrow(selectedallfemales) #0.90 ######################### #### 400 selected males and 8100 selected females n_sel_males = nrow(selectedmales) n_sel_females = nrow(selectedallfemales1) n_progeny = n_sel_females # number of females per sire = 20.25 n_females_per_sire = n_sel_females/n_sel_males n_females_per_sire # because number of dams per sire is 20.25, then sires will have different numbers of progeny (some will have 20 and others will have 21 progeny) rounded_n_females_per_sire = round(n_females_per_sire) rounded_n_females_per_sire if(rounded_n_females_per_sire < n_females_per_sire) { n1records_per_sire = (rounded_n_females_per_sire) 276 n2records_per_sire = (n1records_per_sire)+1 } else { n1records_per_sire = (rounded_n_females_per_sire)-1 n2records_per_sire = (rounded_n_females_per_sire) } #number of sires with 20 progeny (300 out of 400) nsires_with_n1records = (n_sel_males)-((n_sel_females)-(n_sel_males*n1records_per_sire)) #number of sires with 21 progeny (100 out of 400) nsires_with_n2records = (n_sel_males)-(nsires_with_n1records) ##pulling out the first 137 sires of sire list own_record_sires_with_n1records = selectedmales[1:nsires_with_n1records, ] ## replicate each sire 25 times selectedmales1=own_record_sires_with_n1records[rep(seq_len(nrow(own_record_sires_with_n 1records)), each=n1records_per_sire),] ##pulling out the remaining 263 sires of sire list own_record_sires_with_n2records = selectedmales[((nsires_with_n1records)+1):n_sel_males, ] ## replicate each sire 24 times selectedmales2=own_record_sires_with_n2records[rep(seq_len(nrow(own_record_sires_with_n 2records)), each=n2records_per_sire),] ## Create random list of sires with length of 8100 which is number of selected dams allselectedmales=rbind(selectedmales1,selectedmales2) randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp2 = randomlymatedsires[ ,1] damlistp2 = selectedallfemales1[ ,1] #################### selectedparents=rbind(selectedmales, selectedallfemales1) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] # pulling out selected parents and their pedigree animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) #uniqueanimlist = uniqueanimlist[-1] subdata <- basepopdata[basepopdata[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #8500 length(uniqueanimlist) #8500 ## creating P2 pedigree which include(selected parents and their pedigree + new P2 ID with their selected parents) pedP2 = rbind(subdata[,1:3],cbind(c((nam2+1):(nam2+n_progeny)),sirelistp2[1:n_progeny],damlistp2[1: n_progeny])) ############## 277 ## For P2, repeating the same code used to create P1. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(10.007,1.473,258.913,479.990) #weighted averages anwr=c((nam2+1):(nam2+n_progeny)) aid = c(pedP2[ ,1]) sid = c(pedP2[ ,2]) did <- c(pedP2[ ,3]) #number of herds length(unique(selectedallfemales1[ ,6])) iherd=c(selectedallfemales1[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) 278 B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam3=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam3){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales1[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree2 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree2) dataped <- pedigree2[pedigree2$id>nam,] 279 simdataP2 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2001, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP2) nrow(simdataP2) #8100 ## combine the data file of (base and P1) with P2 data file p2_p1_basepopdata <- rbind(p1andbasepopdata,simdataP2) ## Data file for basepop and P1 (has both observations and TBV) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2=mean(p2_p1_basepopdata$WWT) WWTave_base_p1_p2 WWTsd_base_p1_p2=sd(p2_p1_basepopdata$WWT) WWTsd_base_p1_p2 WWTave_base_p1_p2-(3*WWTsd_base_p1_p2) WWTave_base_p1_p2+(3*WWTsd_base_p1_p2) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT > (WWTave_base_p1_p2(3*WWTsd_base_p1_p2))) p2_p1_basepopdata <- subset(p2_p1_basepopdata, WWT < (WWTave_base_p1_p2+(3*WWTsd_base_p1_p2))) summary(p2_p1_basepopdata$WWT) nrow(p2_p1_basepopdata) #17022 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p2_p1_basepopdata <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,10] p2_p1_basepopdata[ ,9] > 40) nrow(p2_p1_basepopdata) #17022 simdataP2 <- subset(p2_p1_basepopdata, p2_p1_basepopdata[ ,1] > nam2) summary(simdataP2$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. # 138.8 223.2 247.2 248.2 272.5 357.9 summary(simdataP2$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #258.1 433.8 482.0 480.5 526.7 682.6 nrow(simdataP2) #8067 N_sires = length(c(sort(unique(simdataP2$sire)))) N_sires #400 basepop_p2_p1_data <- rbind(basepop_p1_data,simdataP2) pedigreep2 <- data.frame (id = simdataP2$id, sire = simdataP2$sire, dam = simdataP2$dam) pedigreep2p1andbase<- rbind(pedigreep1andbase,pedigreep2) 280 ############################################################################## ############################################################################## ## Creating P3 (Year 3) #1 2 3 4 5 6 7 8 9 10 11 12 13 14 # id sire dam sex year herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv # Begin selection for based on Selection Index and use replacments from year 2000 ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population and P1) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam4 = nam2+nam3 ############################## ## selecting top 10% sires and 80% dams ## selection of sires ## sires selection changed to 10% otherwise there were not enough sires males3 <- subset(basepop_p1_data, sex == 1) si.males3 <- data.frame(males3$id, si = -29.66932*males3$FItbv + 21.99373*males3$ADGtbv + 0.09652*males3$WWTtbv + 2.55104*males3$YWTtbv) males3.si <- cbind(males3, si.males3) bulls3 <- males3.si[order(-males3.si$si), ] selectedmales3 <- bulls3[1:450, ] selectedmales3$males3.id <- NULL mean(selectedmales3[ ,15], na.rm=TRUE) selectedmales3$si <- NULL nrow(males3) #4918 nrow(selectedmales3) #450 nrow(selectedmales3)/nrow(males3) #0.09 ######################### ## selection of dams ## FIRST: Remove females from year 2 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss and 90% conception rate females3 <- subset(basepop_p1_data, sex == 2 & year > 2 & year < 2000) femalesp3 <- females3[sample(1:nrow(females3), 8000, replace=FALSE),] hfr <- subset(basepop_p1_data, sex == 2 & year == 2000) nrow(hfr) #4420 if(nrow(hfr) > 2000) { n = 2000 281 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem3 <- rbind(femalesp3, selectedhfrs) selectedallfemales3 <- fem3[sample(1:nrow(fem3), 9000, replace = FALSE),] nrow(femalesp3) #8000 nrow(selectedallfemales3) #9000 damlistp3 = c(selectedallfemales3[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales3) allselectedmales=selectedmales3[rep(seq_len(nrow(selectedmales3)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp3 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales3, selectedallfemales3) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_data[basepop_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #10436 length(uniqueanimlist) #10436 pedp3 = rbind(subdata[ ,1:3],cbind(c((nam4+1):(nam4+n_progeny)),sirelistp3[1:n_progeny],damlistp3[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave 282 ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P3 progeny, repeating the same code used to create P2. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam4+1):(nam4+n_progeny)) aid = c(pedp3[ ,1]) sid = c(pedp3[ ,2]) did <- c(pedp3[ ,3]) #number of herds length(unique(selectedallfemales3[ ,6])) iherd=c(selectedallfemales3[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) 283 rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam5=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam5){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales3[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) 284 obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree3 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree3) dataped <- pedigree3[pedigree3$id>nam4,] simdataP3 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2002, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP3) nrow(simdataP3) #9000 ## combine the data file of (base, P1 and P2) with P3 data file p3_p2_p1_basepopdata <- rbind(p2_p1_basepopdata,simdataP3) ## Data file for basepop and P1 (has both observations and TBV) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3 WWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3 WWTave_base_p1_p2_p3-(3*WWTsd_base_p1_p2_p3) WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3(3*WWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3+(3*WWTsd_base_p1_p2_p3))) summary(p3_p2_p1_basepopdata$WWT) nrow(p3_p2_p1_basepopdata) #25953 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3=mean(p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3 YWTsd_base_p1_p2_p3=sd(p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3 YWTave_base_p1_p2_p3-(3*YWTsd_base_p1_p2_p3) YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3(3*YWTsd_base_p1_p2_p3))) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3+(3*YWTsd_base_p1_p2_p3))) summary(p3_p2_p1_basepopdata$YWT) nrow(p3_p2_p1_basepopdata) #25937 285 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p3_p2_p1_basepopdata <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,10] p3_p2_p1_basepopdata[ ,9] > 40) nrow(p3_p2_p1_basepopdata) #25937 simdataP3 <- subset(p3_p2_p1_basepopdata, p3_p2_p1_basepopdata[ ,1] > nam4) summary(simdataP3$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #145.9 239.4 263.6 264.3 289.1 366.8 summary(simdataP3$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #310.8 463.3 510.0 509.8 556.3 680.4 nrow(simdataP3) #8935 N_sires = length(c(sort(unique(simdataP3$sire)))) N_sires #450 basepop_p1_p2_p3_data <- rbind(basepop_p2_p1_data,simdataP3) pedigreep3 <- data.frame (id = simdataP3$id, sire = simdataP3$sire, dam = simdataP3$dam) pedigreep3p2p1andbase <- rbind(pedigreep2p1andbase,pedigreep3) ############################################################################## ############################################################################## ## Creating P4 (Year 4) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1 and P2) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam6 = nam4+nam5 ############################## ## selecting top 5% sires (2000 & 2001) and top heifers for replacements ## selection of sires males4 <- subset(basepop_p2_p1_data, sex == 1) si.males4 <- data.frame(males4$id, si = -29.66932*males4$FItbv + 21.99373*males4$ADGtbv + 0.09652*males4$WWTtbv + 2.55104*males4$YWTtbv) males4.si <- cbind(males4, si.males4) bulls4 <- males4.si[order(-males4.si$si), ] selectedmales4 <- bulls4[1:450, ] selectedmales4$males4.id <- NULL mean(selectedmales4[ ,15], na.rm=TRUE) selectedmales4$si <- NULL 286 nrow(males4) #9001 nrow(selectedmales4) #450 nrow(selectedmales4)/nrow(males4) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 3 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss ## Assume 90% Conception Rate females4 <- subset(selectedallfemales3, year > 3) femalesp4 <- females4[sample(1:nrow(females4), 8000, replace=FALSE),] hfr <- subset(basepop_p2_p1_data, sex == 2 & year == 2001) nrow(hfr) #3992 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem4 <- rbind(femalesp4, selectedhfrs) selectedallfemales4 <- fem4[sample(1:nrow(fem4), 9000, replace = FALSE),] nrow(femalesp4) #8000 nrow(selectedallfemales4) #9000 damlistp4 = c(selectedallfemales4[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales4) allselectedmales=selectedmales4[rep(seq_len(nrow(selectedmales4)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp4 = randomlymatedsires[ ,1] 287 #################### selectedparents=rbind(selectedmales4, selectedallfemales4) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p2_p1_data[basepop_p2_p1_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #11229 length(uniqueanimlist) #11229 pedp4 = rbind(subdata[ ,1:3],cbind(c((nam6+1):(nam6+n_progeny)),sirelistp4[1:n_progeny],damlistp4[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P4 progeny, repeating the same code used to create P3. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix 288 G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam6+1):(nam6+n_progeny)) aid = c(pedp4[ ,1]) sid = c(pedp4[ ,2]) did <- c(pedp4[ ,3]) #number of herds length(unique(selectedallfemales4[ ,6])) iherd=c(selectedallfemales4[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam7=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam7){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales4[ ,11:14] 289 siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree4 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree4) dataped <- pedigree4[pedigree4$id>nam6,] simdataP4 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2003, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP4) nrow(simdataP4) #9000 ## combine the data file of (base, P1, P2 and P3) with P4 data file p4_p3_p2_p1_basepopdata <- rbind(p3_p2_p1_basepopdata,simdataP4) ## Data file for basepop, P1, P2, P3 and P4 (has both observations and TBV) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4 WWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4 WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4) WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4-(3*WWTsd_base_p1_p2_p3_p4))) 290 p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4+(3*WWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$WWT) nrow(p4_p3_p2_p1_basepopdata) #34893 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4=mean(p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4=sd(p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p4_p3_p2_p1_basepopdata$YWT) nrow(p4_p3_p2_p1_basepopdata) #34882 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p4_p3_p2_p1_basepopdata <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,10] - p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p4_p3_p2_p1_basepopdata) #34835 simdataP4 <- subset(p4_p3_p2_p1_basepopdata, p4_p3_p2_p1_basepopdata[ ,1] > nam6) summary(simdataP4$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #139.8 223.7 249.7 250.4 276.2 365.9 summary(simdataP4$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #303.1 456.2 503.1 503.2 549.7 678.0 nrow(simdataP4) #8952 N_sires = length(c(sort(unique(simdataP4$sire)))) N_sires #450 basepop_p1_p2_p3_p4_data <- rbind(basepop_p1_p2_p3_data,simdataP4) pedigreep4 <- data.frame (id = simdataP4$id, sire = simdataP4$sire, dam = simdataP4$dam) pedigreep4p3p2p1andbase <- rbind(pedigreep3p2p1andbase,pedigreep4) ############################################################################## ############################################################################## ## Creating P5 (Year 5) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# 291 ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2 and P3) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1 and P2 nam8 = nam6+nam7 ############################## ## selecting top 5% sires and 80% dams ## selection of sires males5 <- subset(basepop_p1_p2_p3_data, sex == 1 & year >= 2001) si.males5 <- data.frame(males5$id, si = -29.66932*males5$FItbv + 21.99373*males5$ADGtbv + 0.09652*males5$WWTtbv + 2.55104*males5$YWTtbv) males5.si <- cbind(males5, si.males5) bulls5 <- males5.si[order(-males5.si$si), ] selectedmales5 <- bulls5[1:450, ] selectedmales5$males5.id <- NULL mean(selectedmales5[ ,15], na.rm=TRUE) selectedmales5$si <- NULL nrow(males5) #8571 nrow(selectedmales5) #450 nrow(selectedmales5)/nrow(males5) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 4 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females5 <- subset(selectedallfemales4, year > 4) femalesp5 <- females5[sample(1:nrow(females5), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_data, sex == 2 & year == 2002) nrow(hfr) #4431 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfs <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfs) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] 292 mean(selectedhfrs$si) #72.53 selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem5 <- rbind(femalesp5, selectedhfrs) selectedallfemales5 <- fem5[sample(1:nrow(fem5), 9000, replace = FALSE),] nrow(femalesp5) #8000 nrow(selectedallfemales5) #9000 damlistp5 = c(selectedallfemales5[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales5) allselectedmales=selectedmales5[rep(seq_len(nrow(selectedmales5)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp5 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales5, selectedallfemales5) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_data[basepop_p1_p2_p3_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #12293 length(uniqueanimlist) #12293 pedp5 = rbind(subdata[ ,1:3],cbind(c((nam8+1):(nam8+n_progeny)),sirelistp5[1:n_progeny],damlistp5[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P5 progeny, repeating the same code used to create P4. 293 library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam8+1):(nam8+n_progeny)) aid = c(pedp5[ ,1]) sid = c(pedp5[ ,2]) did <- c(pedp5[ ,3]) #number of herds length(unique(selectedallfemales5[ ,6])) iherd=c(selectedallfemales5[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) 294 HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam9=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam9){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales5[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree5 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree5) dataped <- pedigree5[pedigree5$id>nam8,] simdataP5 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2004, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) 295 attach(simdataP5) nrow(simdataP5) #9000 ## combine the data file of (base, P1, P2, P3 and P4) with P5 data file p5_p4_p3_p2_p1_basepopdata <- rbind(p4_p3_p2_p1_basepopdata,simdataP5) ## Data file for basepop and P's (has both observations and TBV) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5 WWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5 WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5) WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5-(3*WWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5+(3*WWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43812 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5=mean(p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5 YWTsd_base_p1_p2_p3_p4_p5=sd(p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5 YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5) YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5-(3*YWTsd_base_p1_p2_p3_p4_p5))) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5+(3*YWTsd_base_p1_p2_p3_p4_p5))) summary(p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p5_p4_p3_p2_p1_basepopdata) #43787 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p5_p4_p3_p2_p1_basepopdata <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,10] - p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p5_p4_p3_p2_p1_basepopdata) #43747 simdataP5 <- subset(p5_p4_p3_p2_p1_basepopdata, p5_p4_p3_p2_p1_basepopdata[ ,1] > nam8) summary(simdataP5$WWT) 296 #Min. 1st Qu. Median Mean 3rd Qu. Max. #140.9 243.5 268.6 269.0 294.8 372.1 summary(simdataP5$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #328.0 478.1 526.3 525.7 572.1 694.6 nrow(simdataP5) #8917 N_sires = length(c(sort(unique(simdataP5$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_data <- rbind(basepop_p1_p2_p3_p4_data,simdataP5) pedigreep5 <- data.frame (id = simdataP5$id, sire = simdataP5$sire, dam = simdataP5$dam) pedigreep5p4p3p2p1andbase <- rbind(pedigreep4p3p2p1andbase,pedigreep5) ############################################################################## ############################################################################## ## Creating P6 (Year 6) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3 and P4) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5 and P5 nam10 = nam8+nam9 ############################## ## selecting top 5% sirs and 80% dams ## selection of sires males6 <- subset(basepop_p1_p2_p3_p4_data, sex == 1 & year >= 2002) si.males6 <- data.frame(males6$id, si = -29.66932*males6$FItbv + 21.99373*males6$ADGtbv + 0.09652*males6$WWTtbv + 2.55104*males6$YWTtbv) males6.si <- cbind(males6, si.males6) bulls6 <- males6.si[order(-males6.si$si), ] selectedmales6 <- bulls6[1:450, ] selectedmales6$males6.id <- NULL mean(selectedmales6[ ,15], na.rm=TRUE) selectedmales6$si <- NULL nrow(males6) #9013 nrow(selectedmales6) #450 nrow(selectedmales6)/nrow(males6) #0.05 ######################### ## selection of dams 297 ## FIRST: Remove females from year 5 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females6 <- subset(selectedallfemales5, sex == 2 & year > 5) femalesp6 <- females6[sample(1:nrow(females6), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_p4_data, sex == 2 & year == 2003) nrow(hfr) #4424 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem6 <- rbind(femalesp6, selectedhfrs) selectedallfemales6 <- fem6[sample(1:nrow(fem6), 9000, replace = FALSE),] nrow(femalesp6) #8000 nrow(selectedallfemales6) #9000 damlistp6 = c(selectedallfemales6[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales6) allselectedmales=selectedmales6[rep(seq_len(nrow(selectedmales6)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp6 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales6, selectedallfemales6) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] 298 subdata <- basepop_p1_p2_p3_p4_data[basepop_p1_p2_p3_p4_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #13098 length(uniqueanimlist) #13098 pedp6 = rbind(subdata[ ,1:3],cbind(c((nam10+1):(nam10+n_progeny)),sirelistp6[1:n_progeny],damlistp6[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P6 progeny, repeating the same code used to create P5. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam10+1):(nam10+n_progeny)) 299 aid = c(pedp6[ ,1]) sid = c(pedp6[ ,2]) did <- c(pedp6[ ,3]) #number of herds length(unique(selectedallfemales6[ ,6])) iherd=c(selectedallfemales6[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam11=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam11){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales6[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals 300 obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree6 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree6) dataped <- pedigree6[pedigree6$id>nam10,] simdataP6 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2005, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP6) nrow(simdataP6) #9000 ## combine the data file of (base, P1, P2, P3, P4 and P5) with P6 data file p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p5_p4_p3_p2_p1_basepopdata,simdataP6) ## Data file for basepop and P's (has both observations and TBV) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6 WWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6 WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6) WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6-(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6+(3*WWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52728 # keeping YWT observations within 3 SD 301 YWTave_base_p1_p2_p3_p4_p5_p6=mean(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6 YWTsd_base_p1_p2_p3_p4_p5_p6=sd(p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6 YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6) YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6-(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6+(3*YWTsd_base_p1_p2_p3_p4_p5_p6))) summary(p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52714 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p6_p5_p4_p3_p2_p1_basepopdata <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p6_p5_p4_p3_p2_p1_basepopdata) #52714 simdataP6 <- subset(p6_p5_p4_p3_p2_p1_basepopdata, p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam10) summary(simdataP6$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #144.6 245.7 270.4 271.4 297.3 375.0 summary(simdataP6$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #322.2 489.0 535.7 536.1 583.5 704.4 nrow(simdataP6) #8936 N_sires = length(c(sort(unique(simdataP6$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_data <- rbind(basepop_p1_p2_p3_p4_p5_data,simdataP6) pedigreep6 <- data.frame (id = simdataP6$id, sire = simdataP6$sire, dam = simdataP6$dam) pedigreep6p5p4p3p2p1andbase <- rbind(pedigreep5p4p3p2p1andbase,pedigreep6) ############################################################################## ############################################################################## ## Creating P7 (Year 7) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4 and P5) in previous simulation ############################## 302 #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6 and P7 nam12 = nam10+nam11 ############################## ## selecting top 5% sires and 80% dams ## selection of sires males7 <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 1 & year >= 2003) si.males7 <- data.frame(males7$id, si = -29.66932*males7$FItbv + 21.99373*males7$ADGtbv + 0.09652*males7$WWTtbv + 2.55104*males7$YWTtbv) males7.si <- cbind(males7, si.males7) bulls7 <- males7.si[order(-males7.si$si), ] selectedmales7 <- bulls7[1:450, ] selectedmales7$males7.id <- NULL mean(selectedmales7[ ,15], na.rm=TRUE) #142.43 selectedmales7$si <- NULL nrow(males7) #9007 nrow(selectedmales7) #450 nrow(selectedmales7)/nrow(males7) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 5 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females7 <- subset(selectedallfemales6, sex == 2 & year > 6) femalesp7 <- females7[sample(1:nrow(females7), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_p4_p5_data, sex == 2 & year == 2004) nrow(hfr) #4413 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL 303 selectedhfrs$si <- NULL fem7 <- rbind(femalesp7, selectedhfrs) selectedallfemales7 <- fem7[sample(1:nrow(fem7), 9000, replace = FALSE),] nrow(femalesp7) #8000 nrow(selectedallfemales7) #9000 damlistp7 = c(selectedallfemales7[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales7) allselectedmales=selectedmales7[rep(seq_len(nrow(selectedmales7)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp7= randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales7, selectedallfemales7) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_data[basepop_p1_p2_p3_p4_p5_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #13856 length(uniqueanimlist) #13856 pedp7 = rbind(subdata[ ,1:3],cbind(c((nam12+1):(nam12+n_progeny)),sirelistp7[1:n_progeny],damlistp7[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P7 progeny, repeating the same code used to create P6. 304 library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam12+1):(nam12+n_progeny)) aid = c(pedp7[ ,1]) sid = c(pedp7[ ,2]) did <- c(pedp7[ ,3]) #number of herds length(unique(selectedallfemales7[ ,6])) iherd=c(selectedallfemales7[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B 305 HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam13=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam13){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales7[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree7 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree7) dataped <- pedigree7[pedigree7$id>nam12,] simdataP7 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2006, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP7) 306 nrow(simdataP7) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5 and P6) with P7 data file p7_p6_p5_p4_p3_p2_p1_basepopdata <- rbind(p6_p5_p4_p3_p2_p1_basepopdata,simdataP7) ## Data file for basepop, P1, P2, P3, P4, P5, P6 and P7 (has both observations and TBV) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7 WWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7 WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61639 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7=mean(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4 YWTsd_base_p1_p2_p3_p4_p5_p6_p7=sd(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) YWTsd_base_p1_p2_p3_p4 YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4) YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4-(3*YWTsd_base_p1_p2_p3_p4))) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4+(3*YWTsd_base_p1_p2_p3_p4))) summary(p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61494 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p7_p6_p5_p4_p3_p2_p1_basepopdata) #61494 simdataP7 <- subset(p7_p6_p5_p4_p3_p2_p1_basepopdata, p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam12) summary(simdataP7$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. 307 #149.8 255.5 280.6 280.8 306.2 380.6 summary(simdataP7$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #308.7 506.1 552.6 552.6 600.9 685.9 nrow(simdataP7) #8824 N_sires = length(c(sort(unique(simdataP7$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_data <- rbind(basepop_p1_p2_p3_p4_p5_p6_data,simdataP7) pedigreep7 <- data.frame (id = simdataP7$id, sire = simdataP7$sire, dam = simdataP7$dam) pedigreep7p6p5p4p3p2p1andbase <- rbind(pedigreep6p5p4p3p2p1andbase,pedigreep7) ############################################################################## ############################################################################## ## Creating P8 (Year 8) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5 and P6) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7 and P8 nam14 = nam12+nam13 ############################## ## selecting top 5% sires ## selection of sires males8 <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 1 & year >= 2004) si.males8 <- data.frame(males8$id, si = -29.66932*males8$FItbv + 21.99373*males8$ADGtbv + 0.09652*males8$WWTtbv + 2.55104*males8$YWTtbv) males8.si <- cbind(males8, si.males8) bulls8 <- males8.si[order(-males8.si$si), ] selectedmales8 <- bulls8[1:450, ] selectedmales8$males8.id <- NULL mean(selectedmales8[ ,15], na.rm=TRUE) selectedmales8$si <- NULL nrow(males8) #8997 nrow(selectedmales8) #450 nrow(selectedmales8)/nrow(males8) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 7 (older than 16 years) 308 ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females8 <- subset(selectedallfemales7, sex == 2 & year > 7) femalesp8 <- females8[sample(1:nrow(females8), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_p4_p5_p6_data, sex == 2 & year == 2005) nrow(hfr) #4419 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem8 <- rbind(femalesp8, selectedhfrs) selectedallfemales8 <- fem8[sample(1:nrow(fem8), 9000, replace = FALSE),] nrow(femalesp8) #8000 nrow(selectedallfemales8) #9000 damlistp8 = c(selectedallfemales8[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales8) allselectedmales=selectedmales8[rep(seq_len(nrow(selectedmales8)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp8 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales8, selectedallfemales8) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_p6_data[basepop_p1_p2_p3_p4_p5_p6_data[ ,1] %in% uniqueanimlist, ] 309 subdata <- data.matrix(subdata) length(subdata[,1]) #14556 length(uniqueanimlist) #14556 pedp8 = rbind(subdata[ ,1:3],cbind(c((nam14+1):(nam14+n_progeny)),sirelistp8[1:n_progeny],damlistp8[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P8 progeny, repeating the same code used to create P7. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) # Traits averages mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam14+1):(nam14+n_progeny)) aid = c(pedp8[ ,1]) sid = c(pedp8[ ,2]) 310 did <- c(pedp8[ ,3]) #number of herds length(unique(selectedallfemales8[ ,6])) iherd=c(selectedallfemales8[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam15=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam15){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales8[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ 311 kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree8 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree8) dataped <- pedigree8[pedigree8$id>nam14,] simdataP8 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2007, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP8) nrow(simdataP8) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6 and P7) with P8 data file p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP8) ## Data file for basepop and P's (has both observations and TBV) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WW T) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8)) ) 312 summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70411 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8=mean(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$ YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8=sd(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT ) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8-(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8))) summary(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70378 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] - p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #70378 simdataP8 <- subset(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam14) summary(simdataP8$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #150.6 265.3 290.1 290.9 316.4 386.5 summary(simdataP8$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #346.1 526.2 573.0 572.5 620.2 729.9 nrow(simdataP8) #8895 N_sires = length(c(sort(unique(simdataP8$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_data,simdataP8) pedigreep8 <- data.frame (id = simdataP8$id, sire = simdataP8$sire, dam = simdataP8$dam) pedigreep8p7p6p5p4p3p2p1andbase <- rbind(pedigreep7p6p5p4p3p2p1andbase,pedigreep8) ############################################################################## 313 ############################################################################## ## Creating P9 (Year 9) #1 2 3 4 5 6 7 8 9 10 11 12 13 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam16 = nam14+nam15 ############################## ## selecting top 5% sires ## selection of sires males9 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 1 & year >= 2005) si.males9 <- data.frame(males9$id, si = -29.66932*males9$FItbv + 21.99373*males9$ADGtbv + 0.09652*males9$WWTtbv + 2.55104*males9$YWTtbv) males9.si <- cbind(males9, si.males9) bulls9 <- males9.si[order(-males9.si$si), ] selectedmales9 <- bulls9[1:450, ] selectedmales9$males9.id <- NULL mean(selectedmales9[ ,15], na.rm=TRUE) selectedmales9$si <- NULL nrow(males9) #8899 nrow(selectedmales9) #450 nrow(selectedmales9)/nrow(males9) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 8 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females9 <- subset(selectedallfemales8, sex == 2 & year > 8) femalesp9 <- females9[sample(1:nrow(females9), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_data, sex == 2 & year == 2006) nrow(hfr) #4434 if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } 314 si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem9 <- rbind(femalesp9, selectedhfrs) selectedallfemales9 <- fem9[sample(1:nrow(fem9), 9000, replace = FALSE),] nrow(femalesp9) #8000 nrow(selectedallfemales9) #9000 damlistp9 = c(selectedallfemales9[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales9) allselectedmales=selectedmales9[rep(seq_len(nrow(selectedmales9)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp9 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales9, selectedallfemales9) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <- basepop_p1_p2_p3_p4_p5_p6_p7_data[basepop_p1_p2_p3_p4_p5_p6_p7_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #15070 length(uniqueanimlist) #15070 pedp9 = rbind(subdata[ ,1:3],cbind(c((nam16+1):(nam16+n_progeny)),sirelistp9[1:n_progeny],damlistp9[1:n_progeny])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) 315 WWTave YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P9 progeny, repeating the same code used to create P8. library(MASS) set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam16+1):(nam16+n_progeny)) aid = c(pedp9[ ,1]) sid = c(pedp9[ ,2]) did <- c(pedp9[ ,3]) #number of herds length(unique(selectedallfemales9[ ,6])) iherd=c(selectedallfemales9[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 316 # correlations among traits # Function to calculate correlations from a covariance matrix CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam17=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales9[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) 317 ################################################################## pedigree9 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree9) dataped <- pedigree9[pedigree9$id>nam16,] simdataP9 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2008, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP9) nrow(simdataP9) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7 and P8) with P9 data file p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP9) ## Data file for basepop and P's (has both observations and TBV) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basep opdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_ p8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79271 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=mean(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepo pdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9=sd(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdat a$YWT) 318 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8 _p9) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9))) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p 8_p9))) summary(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79239 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,10] p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] > 40) nrow(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #79409 simdataP9 <- subset(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam16) summary(simdataP9$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #161.5 275.4 300.2 300.0 325.4 393.6 summary(simdataP9$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #342.0 544.8 591.9 591.0 638.8 746.2 nrow(simdataP9) #8862 N_sires = length(c(sort(unique(simdataP9$sire)))) N_sires # 450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data,simdataP9) pedigreep9 <- data.frame (id = simdataP9$id, sire = simdataP9$sire, dam = simdataP9$dam) pedigreep9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep8p7p6p5p4p3p2p1andbase,pedigreep9) ############################################################################## ############################################################################## ## Creating P10 (Year 10) #1 2 3 4 5 6 7 8 9 10 11 12 13 319 # id sire dam sex herd CE BW ww pwg CEtbv BWtbv wwtbv pwgtbv ############################################################# ############################################################# ## redefine (the total number of all animals) and (number of base population, P1, P2, P3, P4, P5, P6, P7 and P8) in previous simulation ############################## #total number of all animals (Used unique IDs up to now): basepop, P1, P2, P3, P4, P5, P6, P7, P8 and P9 nam18 = nam16+nam17 ############################## ## selecting top 5% sires and 80% dams ## selection of sires males10 <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 1 & year >= 2006) si.males10 <- data.frame(males10$id, si = -29.66932*males10$FItbv + 21.99373*males10$ADGtbv + 0.09652*males10$WWTtbv + 2.55104*males10$YWTtbv) males10.si <- cbind(males10, si.males10) bulls10 <- males10.si[order(-males10.si$si), ] selectedmales10 <- bulls10[1:450, ] selectedmales10$males10.id <- NULL mean(selectedmales10[ ,15], na.rm=TRUE) selectedmales10$si <- NULL nrow(males10) #8866 nrow(selectedmales10) #450 nrow(selectedmales10)/nrow(males10) #0.05 ######################### ## selection of dams ## FIRST: Remove females from year 9 (older than 16 years) ## SECOND: Selection of cows and replace with 2000 heifers ## Assume 20% loss females10 <- subset(selectedallfemales9, sex == 2 & year > 9) femalesp10 <- females10[sample(1:nrow(females10), 8000, replace=FALSE),] hfr <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_data, sex == 2 & year == 2007) nrow(hfr) if(nrow(hfr) > 2000) { n = 2000 } else { n = nrow(hfr) } si.hfr <- data.frame(hfr$id, si = -29.66932*hfr$FItbv + 21.99373*hfr$ADGtbv + 0.09652*hfr$WWTtbv + 2.55104*hfr$YWTtbv) 320 hfs.si <- cbind(hfr, si.hfr) hfrs <- hfs.si[order(-hfs.si$si), ] selectedhfrs <- hfrs[1:n, ] mean(selectedhfrs$si) selectedhfrs$hfr.id <- NULL selectedhfrs$si <- NULL fem10 <- rbind(femalesp10, selectedhfrs) selectedallfemales10 <- fem10[sample(1:nrow(fem10), 9000, replace = FALSE),] nrow(femalesp10) #8000 nrow(selectedallfemales10) #9000 damlistp10 = c(selectedallfemales10[ ,1]) ######################### #### 450 selected males and 9000 selected females n_progeny = nrow(selectedallfemales10) allselectedmales=selectedmales10[rep(seq_len(nrow(selectedmales10)), each=20),] randomlymatedsires=allselectedmales[sample(nrow(allselectedmales)),] sirelistp10 = randomlymatedsires[ ,1] #################### selectedparents=rbind(selectedmales10, selectedallfemales10) sortedselectedparents <- selectedparents[order(selectedparents[ ,1]),] animlist = c(selectedparents[ ,1],selectedparents[ ,2], selectedparents[ ,3]) uniqueanimlist = c(sort(unique(animlist))) uniqueanimlist = uniqueanimlist[-1] subdata <basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[basepop_p1_p2_p3_p4_p5_p6_p7_p8_data[ ,1] %in% uniqueanimlist, ] subdata <- data.matrix(subdata) length(subdata[,1]) #15624 length(uniqueanimlist) #15624 pedp10 = rbind(subdata[ ,1:3],cbind(c((nam18+1):(nam18+n_progeny)),sirelistp10[1:n_progeny],damlistp10[1:n_progeny ])) ################## FIave=mean(selectedparents[ ,7], na.rm=TRUE) FIave ADGave=mean(selectedparents[ ,8], na.rm=TRUE) ADGave WWTave=mean(selectedparents[ ,9], na.rm=TRUE) WWTave 321 YWTave=mean(selectedparents[ ,10], na.rm=TRUE) YWTave ############## ############## ## P10 progeny, repeating the same code used to create P9. set.seed(1234) herdFI=(rnorm(52,0)) set.seed(1234) herdWW=(rnorm(52,0))*25 set.seed(1234) herdYW=(rnorm(52,0))*10 set.seed(1234) herdADG=(rnorm(52,0))*0.25 herd=matrix(data=c(herdFI,herdADG,herdWW,herdYW),byrow=TRUE,nrow=4) sex=matrix(data=c(0,0,0.060,-0.040,10,-7,50,-40),byrow=TRUE,nrow=4) # Residual matrix R=matrix(data=c(1.05,0.049,0.528,17.749,0.049,0.014,0.287,1.982,0.528,0.287,552.75,465.63,1 7.749,1.982,465.63,1131.95),byrow=TRUE,nrow=4) # G matrix G=matrix(data=c(0.694,0.050,9.945,18.845,0.050,0.005,0.709,1.550,9.945,0.709,230.77,327.934 ,18.845,1.550,327.934,598.327),byrow=TRUE,nrow=4) ####averages: mu=c(FIave,ADGave,WWTave,YWTave) anwr=c((nam18+1):(nam18+n_progeny)) aid = c(pedp10[ ,1]) sid = c(pedp10[ ,2]) did <- c(pedp10[ ,3]) #number of herds length(unique(selectedallfemales10[ ,6])) iherd=c(selectedallfemales10[ ,6]) set.seed(123) isex=(rbinom(n_progeny, 1, 0.5))+1 # heritability of traits gd=diag(G) rd=diag(R) h2=gd/(gd+rd) h2 # correlations among traits # Function to calculate correlations from a covariance matrix 322 CORMAT=function(Q) { D = diag(Q) D = sqrt(D) B = diag(1/D) HC = B %*% Q %*% B HC } CORMAT(R) CORMAT(G) # Get cholesky decompositions of G and R LG = t(chol(G)) LR = t(chol(R)) # Simulate true breeding values for all animals # J MATRIX FUNCTION jd = function(n,m){ matrix(c(1),nrow=n,ncol=m)} nam19=n_progeny mendelian = jd(nam1,4)*0 for(i in 1:nam1){ mendelian[i, ] = LG %*% (rnorm(4,0,1)) } damtbv= selectedallfemales10[ ,11:14] siretbv= randomlymatedsires[ ,11:14] parentsaveragetbv=0.5*(damtbv + siretbv) tbv=mendelian+parentsaveragetbv nrec=n_progeny # Make an observation for all traits for all animals obser = jd(nrec,4)*0 for(k in 1:nrec){ kherd=iherd[k] ksex=isex[k] obser[k, ]=mu + herd[ ,kherd] + sex[ ,ksex] res = LR %*% rnorm(4,0,1) obser[k, ]=obser[k, ] + res } obs = obser + tbv obs[ ,1] = round(obs[ ,1], digits=2) obs[ ,2] = round(obs[ ,2], digits=2) obs[ ,3] = round(obs[ ,3], digits=2) obs[ ,4] = round(obs[ ,4], digits = 2) ################################################################## pedigree10 <- data.frame (id = aid, sire = sid, dam = did) attach(pedigree10) 323 dataped <- pedigree10[pedigree10$id>nam18,] simdataP10 <- data.frame (id = dataped$id, sire = dataped$sire, dam = dataped$dam, sex = isex, year = 2009, herd = iherd, FI = obs[ ,1], ADG = obs[ ,2], WWT = obs[ ,3], YWT = obs[ ,4], FItbv = tbv[ ,1], ADGtbv = tbv[ ,2], WWTtbv = tbv[ ,3], YWTtbv = tbv[ ,4]) attach(simdataP10) nrow(simdataP10) #9000 ## combine the data file of (base, P1, P2, P3, P4, P5, P6, P7, P8 and P9) with P10 data file p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <rbind(p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata,simdataP10) ## Data file for basepop and P's (has both observations and TBV) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nbase) # keeping WWT observations within 3 SD WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$WWT) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$WWT) WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT > (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*WWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, WWT < (WWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*WWTsd_base_p1_p2_p3_p4_p5_p6 _p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$WWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88106 # keeping YWT observations within 3 SD YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=mean(p10_p9_p8_p7_p6_p5_p4_p3_p2_ p1_basepopdata$YWT) YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10=sd(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_b asepopdata$YWT) YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10) 324 YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p 7_p8_p9_p10) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT > (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10(3*YWTsd_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10))) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, YWT < (YWTave_base_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10+(3*YWTsd_base_p1_p2_p3_p4_p5_p6_ p7_p8_p9_p10))) summary(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata$YWT) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88068 #Remove animals with less than 40kg (88lbs) gain from wwt to ywt (might be too small to reproduce anyway) p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata <subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,9] p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,8] > 40) nrow(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata) #88312 simdataP10 <- subset(p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata, p10_p9_p8_p7_p6_p5_p4_p3_p2_p1_basepopdata[ ,1] > nam18) summary(simdataP10$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #167.9 288.2 313.0 313.0 338.8 403.4 summary(simdataP10$YWT) # Min. 1st Qu. Median Mean 3rd Qu. Max. #381.2 568.3 615.1 614.3 661.3 765.6 nrow(simdataP10) #8829 N_sires = length(c(sort(unique(simdataP10$sire)))) N_sires #450 basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data <rbind(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_data,simdataP10) pedigreep10 <- data.frame (id = simdataP10$id, sire = simdataP10$sire, dam = simdataP10$dam) pedigreep10p9p8p7p6p5p4p3p2p1andbase <rbind(pedigreep9p8p7p6p5p4p3p2p1andbase,pedigreep10) ############################################################################## ############################################################################## ## see how many records per sire try <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) nrow(try) 325 ones = c(rep(1,(nrow(try)))) try = data.matrix(try) try = cbind(try,ones) ham=sort(by( try[ ,14], try[ ,2], length)) head(ham) ############################################ ## Final data files ## pedigree file data_anim_with_record <- subset(basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data, basepop_p1_p2_p3_p4_p5_p6_p7_p8_p9_p10_data[ ,1] > nbase) summary(data_anim_with_record$FI) #Min. 1st Qu. Median Mean 3rd Qu. Max. #2.96 9.64 11.07 11.11 12.55 20.10 summary(data_anim_with_record$YWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #258.1 482.3 536.5 537.0 590.6 765.6 summary(data_anim_with_record$WWT) #Min. 1st Qu. Median Mean 3rd Qu. Max. #136.6 244.1 273.0 273.8 303.1 403.4 summary(data_anim_with_record$ADG) # Min. 1st Qu. Median Mean 3rd Qu. Max. #0.340 1.200 1.360 1.381 1.540 2.610 ##SI for each year's progeny P1.si <- data.frame(id = simdataP1$id, si = -29.66932*simdataP1$FItbv + 21.99373*simdataP1$ADGtbv + 0.09652*simdataP1$WWTtbv + 2.55104*simdataP1$YWTtbv) P2.si <- data.frame(id = simdataP2$id, si = -29.66932*simdataP2$FItbv + 21.99373*simdataP2$ADGtbv + 0.09652*simdataP2$WWTtbv + 2.55104*simdataP2$YWTtbv) P3.si <- data.frame(id = simdataP3$id, si = -29.66932*simdataP3$FItbv + 21.99373*simdataP3$ADGtbv + 0.09652*simdataP3$WWTtbv + 2.55104*simdataP$YWTtbv) P4.si <- data.frame(id = simdataP4$id, si = -29.66932*simdataP4$FItbv + 21.99373*simdataP4$ADGtbv + 0.09652*simdataP4$WWTtbv + 2.55104*simdataP4$YWTtbv) P5.si <- data.frame(id = simdataP5$id, si = -29.66932*simdataP5$FItbv + 21.99373*simdataP5$ADGtbv + 0.09652*simdataP5$WWTtbv + 2.55104*simdataP5$YWTtbv) P6.si <- data.frame(id = simdataP6$id, si = -29.66932*simdataP6$FItbv + 21.99373*simdataP6$ADGtbv + 0.09652*simdataP6$WWTtbv + 2.55104*simdataP6$YWTtbv) P7.si <- data.frame(id = simdataP7$id, si = -29.66932*simdataP7$FItbv + 21.99373*simdataP7$ADGtbv + 0.09652*simdataP7$WWTtbv + 2.55104*simdataP7$YWTtbv) P8.si <- data.frame(id = simdataP8$id, si = -29.66932*simdataP8$FItbv + 21.99373*simdataP8$ADGtbv + 0.09652*simdataP8$WWTtbv + 2.55104*simdataP8$YWTtbv) P9.si <- data.frame(id = simdataP9$id, si = -29.66932*simdataP9$FItbv + 21.99373*simdataP9$ADGtbv + 0.09652*simdataP9$WWTtbv + 2.55104*simdataP9$YWTtbv) 326 P10.si <- data.frame(id = simdataP10$id, si = -29.66932*simdataP10$FItbv + 21.99373*simdataP10$ADGtbv + 0.09652*simdataP10$WWTtbv + 2.55104*simdataP10$YWTtbv) 327