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Comparative chewing efficiency in mammalian herbivores

2009, Oikos

Although the relevance of particle size reduction in herbivore digestion is widely appreciated, few studies have investigated digesta particle size across species in relation to body mass or digestive strategy. We investigated faecal particle size, which reflects the size of ingesta particles after both mastication and specialized processes such as rumination. Particle size was measured by wet sieving samples from more than 700 captive individuals representing 193 mammalian species. Using phylogenetic generalized least squares, faecal particle size scaled to body mass with an exponent of 0.22 (95% confidence interval: 0.16Á0.28). In comparisons among different digestive strategies, we found that (1) equids had smaller faecal particles than other hindgut fermenters, (2) non-ruminant foregut fermenters and hindgut fermenters had similar-sized faecal particles (not significantly different), and (3) ruminants had finer faecal particles than non-ruminants. These results confirm that the relationship between chewing efficiency and body mass is modified by morphological adaptations in dental design and physiological adaptations to chewing, such as rumination. This allometric relationship should be considered when investigating the effect of body size on digestive physiology, and digestion studies should include a measure of faecal particle size.

Oikos 118: 16231632, 2009 doi: 10.1111/j.1600-0706.2009.17807.x, # 2009 The Authors. Journal compilation # 2009 Oikos Subject Editor: John Vucetich. Accepted 7 May 2009 Comparative chewing efficiency in mammalian herbivores Julia Fritz, Jürgen Hummel, Ellen Kienzle, Christian Arnold, Charles Nunn and Marcus Clauss J. Fritz and E. Kienzle, Inst. of Animal Physiology, Physiological Chemistry and Animal Nutrition, Faculty of Veterinary Medicine, LudwigMaximilians-Univ. of Munich, Germany.  J. Hummel, Inst. of Animal Science, Univ. of Bonn, Germany.  C. Arnold and C. Nunn, Dept of Anthropology, Peabody Museum, Harvard Univ., Cambridge, MA 02138, USA.  M. Clauss ([email protected]), Clinic for Zoo Animals, Exotic Pets and Wildlife, Vetsuisse Faculty, Univ. of Zurich, CH8057 Zurich, Switzerland. Although the relevance of particle size reduction in herbivore digestion is widely appreciated, few studies have investigated digesta particle size across species in relation to body mass or digestive strategy. We investigated faecal particle size, which reflects the size of ingesta particles after both mastication and specialized processes such as rumination. Particle size was measured by wet sieving samples from more than 700 captive individuals representing 193 mammalian species. Using phylogenetic generalized least squares, faecal particle size scaled to body mass with an exponent of 0.22 (95% confidence interval: 0.160.28). In comparisons among different digestive strategies, we found that (1) equids had smaller faecal particles than other hindgut fermenters, (2) non-ruminant foregut fermenters and hindgut fermenters had similar-sized faecal particles (not significantly different), and (3) ruminants had finer faecal particles than non-ruminants. These results confirm that the relationship between chewing efficiency and body mass is modified by morphological adaptations in dental design and physiological adaptations to chewing, such as rumination. This allometric relationship should be considered when investigating the effect of body size on digestive physiology, and digestion studies should include a measure of faecal particle size. Mammals are the ‘definite chewers’ (Reilly et al. 2001). They have evolved remarkable variations in dental design, a high degree of convergent dental adaptations, and physiological adaptations that involve regurgitating the contents of a proximal gastrointestinal compartment and re-masticating them (i.e. rumination). The latter mechanism is characteristic of ruminants and camelids, where a certain fraction of the forestomach contents is regurgitated. In several other animals, such as some macropods and koalas Phascolarctos cinereus (Hume 1999) and possibly the capybara Hydrochorus hydrochaeris (Lord 1994), food from the simple stomach is sometimes regurgitated and re-masticated; this process is called ‘merycism’, but it is not observed with the same consistency as rumination. Relationships between tooth design, chewing physiology and diet properties have been assumed since antiquity (summarized in Evans et al. 2007). However, comparative tests of chewing efficiency are rare. The relevance of reducing the particle size of ingested food is well understood, particularly in herbivores (Clauss and Hummel 2005). Specifically, smaller food particles can be digested at a much faster rate. Particle size reduction  either by dental mastication (mammals) or by grinding in a gastric mill (birds)  is often considered the key digestive difference between ecto- and endotherms. Although both ecto- and endotherms achieve similar degrees of digestive efficiency per unit of ingested food, endotherms do so at a faster rate, thus allowing for the higher food intake rate necessary to fuel endothermy (Karasov et al. 1986). Within mammals, a tradeoff between ingesta retention time and ingesta particle size has been suggested. In focused comparisons of small groups of species, variation in chewing efficiency has been invoked to explain observations of digestive efficiency that could not be explained by differences in ingesta retention (e.g. among the horse, rhinoceros and elephant (Clauss et al. 2005), the buffalo and hippopotamus (Schwarm et al. 2009), and within the sexually dimorphic ibex (Gross et al. 1996)). Within species, differences in dental efficiency (e.g. due to wear) may be compensated for by different food intake rates and/ or differences in chewing times (Pérez-Barberı̀a and Gordon 1998b, Logan 2003). A convenient way to assess chewing efficiency is to measure faecal particle size. This measure is independent of further digestive processes, with several studies demonstrating that bacterial fermentation (digestion) has little influence on particle size reduction in the digestive tract of terrestrial mammalian herbivores (Poppi et al. 1980, Murphy and Nicoletti 1984, McLeod and Minson 1988a, Spalinger and Robbins 1992). Similarly, no further reduction in digesta particle size occurs beyond the forestomach from which digesta is regurgitated in the ruminant (and camelid) digestive tract. This finding indicates that other digestive processes (acid and enzymatic digestion in the abomasum and small intestine; bacterial fermentation in the hindgut) have little effect on particle size (Poppi et al. 1980, 1623 Udén and Van Soest 1982, McLeod and Minson 1988b, Lechner-Doll and von Engelhardt 1989, Freudenberger 1992). Fewer studies have been published for non-ruminants, probably because an investigation of digesta particle size along a non-ruminant’s digestive tract is unlikely to reveal differences between different sections. However, existing data for non-ruminant foregut fermenters  macropods (Freudenberger 1992) and sloths (Foley et al. 1995)  indicate little change in ingesta particle size from the forestomach to the faeces. One of the most cited advantages of an increase in body mass (BM) in herbivores is a presumed increase in efficiency of digestion. As gut capacity increases with BM1.00, but energy requirements, and hence food intake, increase with BM0.75, larger animals should have more gut capacity available per unit ingested food, which produces an expected allometric scaling exponent of BM0.25 for ingesta retention time (Parra 1978, Demment and Van Soest 1985, Illius and Gordon 1992, but see Clauss et al. 2007). This suggests that larger animals should experience advantages in terms of digestion. Yet, larger animals might also experience digestive disadvantages (Clauss and Hummel 2005), including an increase in ingesta particle size (Pérez-Barberı̀a and Gordon 1998a). Apart from everyday observations (e.g. on faeces of rabbits and horses), a few studies on limited numbers of species indicate that faecal particle size increases with body mass (Udén and Van Soest 1982, Clauss et al. 2002). The intuitive reason for this is that in the larger teeth of larger mammals, structures responsible for particle size reduction, such as distances between enamel ridges, are of a coarser scale than in smaller animals. In addition to variation in body mass, some mammals possess digestive strategies that enable them to process food more efficiently. These include, for example, dental adaptations in equids, and rumination in other ungulates, which could cause deviations from the underlying allometry of faecal particle size. Although an allometric relationship between ingesta particle size and body mass has been suspected (PérezBarberı̀a and Gordon 1998a), body size considerations have received less attention in the comparative analysis of ingesta particles. Here, we investigated the scaling of ingesta particle size across a dataset of 193 mammalian species. We also performed three nested comparisons in the dataset to further illuminate factors that influence ingesta particle size. First, across the entire dataset, we investigated whether ruminants achieve a smaller ingesta particle size than nonruminants of similar body size. This is an important test because ruminants are thought to possess more efficient digestive capabilities, in part through their method of reducing ingesta particle size by rumination. Second, among the non-ruminants, we investigated whether ingesta particle size differs between foregut and hindgut fermenters. This comparison is important because non-ruminant foregut fermentation has often been equated with ruminant foregut fermentation (Moir 1965, Janis 1976), whereas some comparisons indicate that these groups could be very different in terms of chewing efficiency, with ruminants consistently producing finer particles (Langer 1988, Freudenberger 1992, Clauss et al. 2004, Schwarm et al. 2009). Lastly, among the hindgut fermenters, we tested whether equids generate smaller particles, which we proposed would 1624 occur due to their particularly efficient dental design (Rensberger 1973, Jernvall et al. 1996). Throughout, we used both phylogenetic and non-phylogenetic methods to investigate the comparative patterns. Methods Faecal samples were collected from captive individuals of 193 mammalian species (including previously published data from Clauss et al. 2002), with 118 samples per species, depending on the access to individuals (Appendix 1). Samples originated from apparently healthy, adult animals without a history of dental or digestive disease who were offered a diet that also included a relevant source of fibre. Body mass was either known for the individuals sampled, estimated, or taken from the literature. Especially in the case of small animals, we often had to use group samples, pooling faeces from different individuals (marked as gs in the Appendix 1), to attain the amounts required for analysis. Faeces were analysed by wet sieving. Mean faecal particle size calculated by wet sieving over a series of sieves with mesh sizes of 4, 2, 1, 0.5, 0.25 and 0.125 mm, and subsequent calculation of the mean particle size after fitting a suitable function to the respective sample data using TableCurve 2D v5.01 (Systat Software; Hummel et al. 2008). For each species, an average mean particle size was calculated that was used in the subsequent analyses. Species were classified as hindgut fermenters (i.e. colon or caecum fermenters), non-ruminant foregut fermenters and ruminants (including the Ruminantia and the Tylopoda). We investigated the scaling of faecal particle size using both non-phylogenetic tests and phylogenetic generalized least squares (PGLS). PGLS provides an approach to studying correlated evolution (Martins and Hansen 1997, Garland and Ives 2000), and becomes increasingly attractive for comparative biologists due to its flexibility. For phylogenetic tests, we based our analyses on the phylogeny from Bininda-Emonds et al. (2007). Calculation of PGLS was conducted using BayesTraits (Pagel and Meade 2007). Codes reflecting digestion type (ruminants, non-ruminants, non-ruminant foregut fermenters, hindgut fermenters) or taxonomic group (equids) were included as a dummy variable in the regression model. We also investigated whether body mass and faecal particle size showed phylogenetic signal, i.e. whether more closely related species exhibit similar trait values, as calculated in BayesTraits (Pagel and Meade 2007). For this, we calculated the loglikelihood of a model in which l  a measure of phylogenetic signal  was calculated for the data, and then repeated the process when forcing l to equal 0 (Freckleton et al. 2002). Twice the difference in loglikelihoods of these nested models is distributed as a chisquare statistic, with one degree of freedom. We report effects as slopes of the relationship between body mass and digesta particle size (bmass). When investigating the effect of a particular taxonomic group or digestive strategy, we include a second slope estimate (bequid, bhindgut or bruminant) from a multiple regression model that included bmass. The sign of this second slope indicates whether species coded as having state 1 have larger (positive b) or smaller (negative b) digesta particle size than those with state 0, controlling for Figure 1. Association between body mass and mean faecal particle size in the mammalian herbivores (one average value per species) investigated in this study. Regression line based phylogenetic generalized least squares (see text). bmass. All statistical tests reported are two-tailed with significance level (a) of 0.05. We used log-transformed data in all analyses. Results Mean faecal particle size (MPS) increased with body mass across species (Fig. 1), and there was no evident discrepancy between species for which several or only one sample had been available (Fig. 2a). In analyses of species averages, the allometric exponent was estimated as 0.15 (95% CI: 0.10 to 0.19) and was significantly different from zero (t191 6.02, pB0.001, R2 0.16). In analyses of phylogenetic signal, however, we found strong evidence that more closely related species exhibit more similar trait values (l0.97 in a correlated model). The log likelihood in this model was 146.6, which was significantly different from l 0, where the log-likelihood was 410.4 (likelihood ratio test, pB0.0001). Although very close to l 1 (likelihood  170.2), the maximum likelihood estimate of 0.97 was also significantly different from l 1 (p B0.001). Thus, we also investigated the scaling of faecal particle size using a regression model in PGLS with the maximum likelihood estimate of l. This produced a steeper allometric exponent of 0.22 (95% CI: 0.16 to 0.28), which was significantly different from zero (intercept 0.31, t191 7.01, p B 0.001). This bivariate model explained 20% of the variation in ingesta particle size (R2 0.20). Examining ruminants alone, a regression model in PGLS produced a lower allometric exponent of 0.15 (95% CI: 0.08 to 0.22, intercept0.78, t804.46, p B0.0001; R2 0.20). We also investigated three a priori predictions that were nested phylogenetically, as described above. First, among hindgut fermenters, we found that equids produce smaller ingesta particles for their body mass than other hindgut fermenters (bmass 0.25, t91 6.39, pB0.0001, bequid  0.52, t91 2.27, p0.025, R2 0.33, in a statistical model with equids coded as state 1; Fig. 1b). Second, among the non-ruminants, we found no significant difference between foregut and hindgut fermenters (bmass 0.26, t108 6.61, p B0.0001; bhindgut 0.05, Figure 2. Correlation of body mass and mean faecal particle size in (a) mammalian herbivores, ordered according to the number of samples available per species (gsgroup sample); (b) equids (in black) and non-equid hindgut fermenters; (c) non-ruminant foregut fermenters (in black) and hindgut fermenters; (d) functional ruminants (in black) and non-ruminants. 1625 t108 0.39, p0.70, R2 0.29, in a statistical model with hindgut fermenters coded as state 1; Fig. 1c). Lastly, we found that ingesta particle size is significantly smaller in ruminants than in non-ruminants (bmass 0.22, t190  7.74, pB0.0001; bruminant 0.88, t190 4.85, p B 0.0001, R2 0.30, in a statistical model with ruminants coded as state 1; Fig. 1d). Additionally, we used the coefficient from the model that included the ruminants to express faecal MPS as a relative measure. At 4.05 mm/kg0.22, the giant panda had the highest relative MPS in the whole dataset. Among the large mammals, relative MPS decreased from the hippos (3.223.50 mm/kg0.22) to the rhinos (0.972.25 mm/ kg0.22), elephants (1.191.27 mm/kg0.22), tapirs (0.93 1.19 mm/kg0.22), equids (0.150.57 mm/kg0.22) and ruminants and camelids (0.050.34 mm/kg0.22). Rodents had values of 0.091.37 mm/kg0.22; notably, the capybara, at 0.17 mm/kg0.22, resembled ruminants of similar body size. At 0.333.08 mm/kg0.22, primates showed a very large MPS range in this dataset, often surpassing values achieved by equids. Discussion Ingesta particle size is one of the most important factors influencing digestive efficiency, but few studies have investigated the degree to which different species can break down food in broad phylogenetic perspective. Our study is the largest analysis of faecal particle size so far conducted and is the first study to use phylogeny-based methods to investigate factors that influence ingesta particle size. We found evidence for negative allometry, with faecal particle size increasing relative to body mass with an exponent of 0.22. We also found support for two of our predictions involving deviations from this allometric relationship. Specifically, particle size was significantly reduced in ruminants (compared to non-ruminants) and equids (compared to other hindgut fermenters). In contrast, we found no significant difference between foregut and hindgut nonruminant fermenters. Our study reveals the importance of controlling for phylogeny. In the non-phylogenetic tests, the allometric exponent was estimated as 0.15, whereas it was 0.22 after controlling for phylogeny. This probably reflects that ruminants, which tend to be larger in body size than many other species and also have smaller ingesta particle sizes, represent the most speciose group in this dataset. This will tend to depress the slope of the association when measured across species without controlling for phylogeny. Coupled with the evidence for strong phylogenetic signal, we suggest that the allometric exponent from the phylogeny-based tests should be preferred to the non-phylogenetic tests. However, even when applying phylogeny-based statistics, we should not consider the resulting allometry as a fixed natural law, but as a snapshot of evolutionary time. Consider, for example, how the sequence of decreasing relative faecal particle size (rhinoelephantequidruminant) somewhat resembles the sequence of the peak radiations of the respective groups (Coppens et al. 1978, MacFadden 1992, Cerdeno 1998, Gentry 2000), leading to the hypothesis that a higher chewing efficiency is a 1626 characteristic of more recently radiated herbivore groups; in other words, these data could suggest that large mammalian herbivore evolution is characterized by a trend toward increasing chewing efficiency. Several limitations of the current study are worth mentioning. For a comparative study that comprises a large variety of species such as the present one, it is not feasible to use one common diet because there is no universal food that will be accepted in a similar manner by all species; additionally, species show clear dental adaptations to different diets (Fortelius 1985, Archer and Sanson 2002). Therefore, ideally, a study like the present one should be performed on faeces from free-ranging animals feeding on their natural diets  a task of enormous logistical challenge. Zoo diets usually consist of varying proportions of a forage material (dried  as hay, or fresh  grass, lucerne, browse, green vegetables), pelleted feeds, and various items such as fruits, bread, grain products. Within a species, faecal particle size will increase with an increasing proportion of forage in the ingested diet (Clauss unpubl., in black rhinoceros). The recording of the different proportions of feeds ingested, which necessitates intake trials of at least three consecutive days per animal, was beyond the scope of this study. As differences in faecal particle size between captive and free-ranging animals of the same species have been demonstrated for browsing as opposed to grazing species (Hummel et al. 2008), conclusions derived from the present dataset must be considered with caution, especially when comparing individual species. Similarly, discrepancies in the body masses of the actual animals and the mass estimates used here could make comparisons between species of similar body mass imprecise. Finally, for some species, only one group sample or material from only one individual was available, which should caution against conclusions focussing on these particular species. We see no reason, however, why these values would bias results of broad scale comparisons using our larger dataset. The results of this study confirm that particle size increases with body mass. Using data from Udén (1978), Pérez-Barberı̀a and Gordon (1998a) found that faecal particle size scaled to BM0.19 in a set of domestic ruminants, rabbits and equids. These authors modelled the scaling of chewing efficiency based on several factors. They suggested that chewing efficiency should, on the one hand, scale to tooth morphology, and, on the other hand, to chewing frequency. Among mammals, teeth scale isometrically, i.e. tooth volume scales to BM1.00, and tooth surface area  the effective part of the tooth  to BM0.67 (Fortelius 1985, Shipley et al. 1994). The number of chews per gram food ingested scales to BM 0.85 (Shipley et al. 1994). Thus, the authors predicted that chewing efficiency scales to BM0.670.85 BM 0.18, or, inversely, that faecal particle size should scale to BM0.18. This exponent lies within the 95% confidence interval determined in our dataset. In contrast, an allometric exponent of 0.33 would have been suspected if it were assumed that particle size, which represents a one-dimensional measure (in mm), should follow the isometric tooth scaling mentioned above (volumeBM1.00, areaBM0.67, distanceBM0.33). However, this exponent was excluded from the 95% confidence interval. Thus, the results could be interpreted to indicate that the whole dental (chewing) surface area and the chewing frequency are important determinants of ingesta particle size, rather than a linear distance between, for example, enamel ridges. After accounting for body mass, the remaining large variation in faecal particle size can be explained by differences in dental design and chewing physiology. The herbivorous mammal with probably the least sophisticated dental and masticatory adaptations to its diet is the giant panda (Sanson 2006), which also had the largest faecal particles in this dataset. Hippos, with interlocking canines that prevent a grinding side-stroke, also had particularly large faecal particles. Equids, who display the most complicated molar design in the collection of ungulate molars presented by Jernvall et al. (1996), had significantly finer particles than the other hindgut fermenters of comparable size in our dataset (Fig. 1b). These examples illustrate how dental design can shift a species away from expectations based on body mass alone. It could be expected that detailed analyses based on morphological (dental design) or ecological (feeding type) correlates, for example within the rodents or the primates, could also lead to more insight into additional factors determining chewing efficiency. The ruminants deserve special attention in this regard. Functional ruminants (true ruminants and camelids) produce finer faecal particles than other mammals (Udén and Van Soest 1982, Freudenberger 1992, Campos-Arceiz et al. 2004; Fig. 1d). This is notably not an effect of having a forestomach per se, as non-ruminant foregut fermenters do not achieve finer faecal particles than hindgut fermenters (Fig. 1c). However, in contrast to what one might expect, rumination is not about chewing food for a longer time; rumination is about sorting (Schwarm et al. 2009). Like many processes in digestive physiology, such as the fermentation of plant material (Hummel et al. 2006), particle size reduction during mastication follows a probability distribution of decreasing returns-the first chew on a new digesta bolus will result in a high degree of particle size reduction, but subsequent chews will be increasingly less effective at reducing particle sizes (Sheine and Kay 1982, Lucas 1994). After a certain number of chews, the probability that food particles that are already sufficiently small will be caught between the chewing blades will be higher than that of catching larger particles, but the small particles are unlikely to be further reduced in their size. Actually, it has been suspected that for any given dentition, a characteristic particle size threshold exists below which particles are very unlikely to be reduced further (Sheine and Kay 1982). In addition, with a higher proportion of already small particles, the probability of fine particles clogging the space between the cutting blades will also increase, thus making further chewing even less efficient. Therefore, after a certain number of chews, swallowing the bolus will be more efficient than continuing to chew; this process intrinsically constrains the advantage that could be gained from increasing chewing time per unit of ingested food. The only mechanism that would significantly increase the efficiency of chewing in this respect would be a separation of fine particles (that need no longer be chewed) from the larger particles (that should ideally be chewed further). Such a separation is not possible within the oral cavity; no ‘sieving’ mechanism prior to swallowing is known in mammals. Only functional ruminants achieve such a separation-not in the oral cavity, but in their elaborate forestomachs. Prolonged chewing of the digesta is costeffective in ruminants, because the ruminant forestomach removes the fine particles from the material that is submitted to repeated mastication (Lechner-Doll et al. 1991). This sorting mechanism is reflected in the fact that the contents of the first sections of the forestomachs of ruminants and camelids comprise not only small particles but also contain larger particles than are found in the distal digestive tract; beyond this point, digesta particle size remains constant and is almost identical to faecal particle size (Udén and Van Soest 1982, Lechner-Doll and von Engelhardt 1989). The sorting mechanisms in ruminants lessens the allometric effect of body size on chewing efficiency, leading to a lower allometric scaling of faecal particle size with body size, thus reducing a potential disadvantage of large size to which other herbivore groups are subjected. It is tempting to speculate that this additional property of the forestomach of functional ruminants was a major factor in the success of this group, particularly the true ruminants, as we know them today. Prinz and Lucas (1997) identified another problem that occurs if one chews too much on the same bolus: the bolus will disintegrate, and hence its travel across the epiglottis will be dangerous because the increase in saliva, and the constant reduction of the large particle fraction, will reach a point where cohesive forces are too low. Actually, in order to safely swallow a bolus, a certain proportion of large particles is needed. In functional ruminants, the large ‘accompanying’ particles will be comminuted later, when more recently ingested large particles will take over the ‘accompanying’ function. To date, in large mammalian herbivores, rumination appears to be the most successful strategy to achieve a high degree of particle size reduction in the digestive tract. Because of the perceived relevance of digesta retention time, numerous studies have investigated this parameter, often in conjunction with digestibility measurements (reviewed by Clauss et al. 2007). In contrast, measures of chewing efficiency, such as faecal particle size, are rarely included in digestion studies (for exceptions see Gross et al. 1995, Pérez-Barberı̀a and Gordon 1998b, Clauss et al. 2004, Pérez-Barberı̀a et al. 2008, Schwarm et al. 2009). A simultaneous evaluation of food intake, ingesta retention time, digestibility, and chewing efficiency will be key for understanding evolutionary variation in digestive physiology. In theory, ingesta retention time should increase with BM0.25 (Introduction). The fact that faecal particle size increased with BM0.22 in this study could indicate that both allometric effects  that of digesta retention time, and that of digesta particle size  could more or less compensate for each other. This could explain why it has been difficult, so far, to demonstrate an increase in digestive efficiency with increasing body mass across species (Pérez-Barberı̀a et al. 2004, Clauss and Hummel 2005) or within species (Gross et al. 1996, Pérez-Barberı̀a et al. 2008). Actually, the concept that increased digesta retention can compensate for a lack of ingestive particle size reduction has been proposed for the comparison of reptilian and mammalian herbivores (Karasov et al. 1986), and potentially long digesta retention times have been evoked as a compensatory mechanism in 1627 gigantic herbivorous dinosaurs that lacked mechanisms of particle size reduction (Farlow 1987, Franz et al. 2009). It is only with the inclusion of faecal particle size measurements that the associations of these different digestive determinants will be disentangled. Acknowledgements  This work was supported by DFG grant CL 182/3-1 and is contribution no. 53 of the DFG Research Unit 533. 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Lechner-Doll, M. et al. 1991. Factors affecting the mean retention time of particles in the forestomach of ruminants and camelids.  In: Tsuda, T. et al. (eds.), Physiological aspects of digestion and metabolism in ruminants. Academic Press, pp. 455482. Lechner-Doll, M. and von Engelhardt, W. 1989. Particle size and passage from the forestomach in camels compared to cattle and sheep fed a similar diet.  J. Anim. Physiol. Anim. Nutr. 61: 120128. Logan, M. 2003. Effect of tooth wear on the rumination-like behavior, or merycism, of free-ranging koalas (Phascolarctos cinereus).  J. Mammal. 84: 897902. Lord, R. D. 1994. A descriptive account of capybara behavior.  Stud. Neotrop. Fauna Environ. 29: 1122. Lucas, P. W. 1994. Categorisation of food items relevant to oral processing.  In: Chivers, D. J. and Langer, P. (eds), The digestive system in mammals - food, form and function. Cambridge Univ. Press, pp. 197218. MacFadden, B. J. 1992. Fossil horses.  Cambridge Univ. Press. Martins, E. P. and Hansen, T. F. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into analysis of interspecific data.  Am. Nat. 149: 646667. McLeod, M. N. and Minson, D. J. 1988a. Breakdown of large particles in forage by simulated digestion and detrition.  J. Anim. Sci. 66: 10001004. McLeod, M. N. and Minson, D. J. 1988b. Large particle breakdown by cattle eating ryegrass and alfalfa.  J. Anim. Sci. 66: 992999. Moir, R. J. 1965. The comparative physiology of ruminant-like animals.  In: Physiology of digestion in the ruminant. Butterworth, pp. 114. Murphy, M. R. and Nicoletti, J. M. 1984. Potential reduction of forage and rumen digesta particle size by microbial action.  J. Dairy Sci. 67: 12211226. Pagel, M. and Meade, A. 2007. BayesTraits, ver.1.0.  /<www. evolution.rdg.ac.uk>. Parra, R. 1978. Comparison of foregut and hindgut fermentation in herbivores.  In: Montgomery, G. G. (ed.), The ecology of arboreal folivores. Smithsonian Inst. Press, pp. 205229. Pérez-Barberı̀a, F. J. et al. 2004. The evolution of phylogenetic differences in the efficiency of digestion in ruminants.  Proc. R. Soc. Lond. B 271: 10811090. Pérez-Barberı̀a, F. J. and Gordon, I. J. 1998a. Factors affecting food comminution during chewing in ruminants: a review.  Biol. J. Linn. Soc. 63: 233256. Pérez-Barberı̀a, F. J. and Gordon, I. J. 1998b. The influence of molar occlusal surface area on the voluntary intake, digestion, chewing behaviour and diet selection of red deer.  J. Zool. Lond. 245: 307316. Pérez-Barberı̀a, F. J. et al. 2008. Does the Jarman-Bell principle at intra-specific level explain sexual segregation in polygonous ungulates? Sex differences in forage digestibility in Soay sheep.  Oecologia 157: 2130. Poppi, D. P. et al. 1980. The validity of the critical size theory for particles leaving the rumen.  J. Agric. Sci. Cambr. 94: 275 280. Prinz, J. F. and Lucas, P. W. 1997. An optimization model for mastication and swallowing in mammals.  Proc. R. Soc. Lond. B 264: 17151721. Reilly, S. M. et al. 2001. Prey processing in amniotes: biomechanical and behavioral patterns of food reduction.  Comp. Biochem. Physiol. A 128: 397415. Rensberger, J. M. 1973. An occlusal model for mastication and dental wear in herbivorous mammals.  J. Paleontol. 47: 515 528. Sanson, G. D. 2006. The biomechanics of browsing and grazing.  Am. J. Bot. 93: 15311545. Schwarm, A. et al. 2009. More efficient mastication allows increasing intake without compromising digestibility or necessitating a larger gut: comparative feeding trials in banteng (Bos javanicus) and pygmy hippopotamus (Hexaprotodon liberiensis).  Comp. Biochem. Physiol. A 152: 504512. Sheine, W. S. and Kay, R. F. 1982. A model for comparison of masticatory effectiveness in primates.  J. Morphol. 172: 139 149. Shipley, L. A. et al. 1994. The scaling of intake rate in mammalian herbivores.  Am. Nat. 143: 10551082. Spalinger, D. E. and Robbins, C. T. 1992. The dynamics of particle flow in the rumen of mule deer and elk.  Physiol. Zool. 65: 379402. Udén, P. 1978. Comparative studies on rate of passage, particle size, and rate of digestion in ruminants, equines, rabbits, and man.  Cornell Univ. Udén, P. and Van Soest, P. J. 1982. The determination of digesta particle size in some herbivores.  Anim. Feed Sci. Technol. 7: 3544. 1629 Appendix 1. Original data from this study. DTdigestion type (Hhindgut fermenter, Fnonruminant foregut fermenter, Rruminant); n is the number of faecal samples analysed (gs group sample pooled from a group of animals; BMbody mass (mean if actually measured) in kg, followed by the SDstandard deviation (if body mass was actually measured); MPSmean particle size in mm, followed by the SD; rMPSrelative mean particle size, expressed in mm/kg0.22. Species Monodelphis domestica Phascolarctos cinereus Vombatus ursinus Bettongia penicillata Dendrolagus matschiei Macropus agilis Macropus fuliginosus Macropus giganteus Macropus parma Macropus rufogriseus Macropus rufus Wallabia bicolor Hapalemur griseus Lemur catta Varecia variegata Alouatta palliata Lagothrix lagotricha Pithecia pithecia Cercopithecus pygerythrus Macaca sylvanus Mandrillus sphinx Presbytis obscurus Presbytis entellus Presbytis cristata Pygathrix nemaeus Theropithecus gelada Hylobates lar Hylobates lar moloch Hylobates syndactylus Gorilla gorilla Pan paniscus Pan troglodytes Pongo pygmaeus Choloepus didactylus Lepus europaeus Oryctolagus cuniculus Cynomys ludovicianus Marmota bobac Marmota marmota Sciurus carolinensis Sciurus variegatoides Xerus inauris Castor canadensis Castor fiber Pedetes capensis Jaculus jaculus Acomys russatus Lemniscomys barbarus Mastomys natalensis Micromys minutus Mus musculus Cricetomys emini Cricetulus griseus Gerbillus perpallidus Graphiurus murinus Hypogeomys antimena Microtus brandti Microtus fortis Phodopus roborovskii Phodopus sungorus Seketamys calurus Ctenodactylus gundi Atherurus africanus Hystrix africaeaustralis Hystrix cristata Hystrix indica Petromus typicus Heterocephalus glaber Chinchilla chinchilla 1630 Didelphimorphia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Diprodontia Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Primates Xenarthra Lagomorpha Lagomorpha Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Didelphidae Phascolarctidae Vombatidae Potoridae Macropodidae Macropodidae Macropodidae Macropodidae Macropodidae Macropodidae Macropodidae Macropodidae Lemuridae Lemuridae Lemuridae Cebidae Cebidae Cebidae Cercopithecidae Cercopithecidae Cercopithecidae Cercopithecidae Cercopithecidae Cercopithecidae Cercopithecidae Cercopithecidae Hylobatidae Hylobatidae Hylobatidae Pongidae Pongidae Pongidae Pongidae Megalonychidae Leporidae Leporidae Sciuridae Sciuridae Sciuridae Sciuridae Sciuridae Sciuridae Castoridae Castoridae Pedetidae Dipodidae Muridae Muridae Muridae Muridae Muridae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Cricetidae Ctenodactylidae Hystricidae Hystricidae Hystricidae Hystricidae Petromuridae Bathyergidae Chinchillidae DT n H H H F F F F F F F F F H H H H H H H H H F F F F H H H H H H H H F H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H 2 (gs) 5 3 2 (gs) 3 2 1 3 2 (gs) 3 2 2 1 3 4 1 2 2 1 1 2 1 2 (gs) 3 (gs) 5 6 2 2 4 8 5 5 5 5 5 5 1 (gs) 1 1 1 1 1 (gs) 2 3 1 (gs) 1 (gs) 2 (gs) 1 (gs) 1 (gs) 2 (gs) 1 1 (gs) 1 (gs) 2 (gs) 1 (gs) 2 1 (gs) 1 (gs) 2 (gs) 3 (gs) 1 (gs) 1 1 (gs) 1 (gs) 5 (gs) 2 (gs) 1 2 (gs) 3 (gs) BM 0.100 6.190 40.000 1.250 13.000 15.000 50.000 60.000 6.000 16.500 62.500 15.000 1.200 3.330 4.000 7.000 7.500 1.800 5.500 24.000 27.500 7.000 20.000 13.170 9.000 17.500 5.500 5.500 12.500 97.560 39.120 52.220 60.000 10.000 4.500 4.000 1.150 5.000 5.000 0.450 0.550 0.750 30.000 30.000 3.500 0.055 0.045 0.040 0.065 0.006 0.020 1.250 0.040 0.040 0.025 1.350 0.050 0.050 0.030 0.040 0.060 0.250 1.750 15.000 20.000 15.000 0.200 0.050 0.550 SD  1.128  0.354    25.000  0.866    0.289   4.243 0.283   0.707  1.414 2.021 1.414   0.707 1.683 55.537 9.366 26.187 37.495 1.414                                   0.050 MPS SD rMPS 0.3096 0.2684 0.4195 0.5253 0.7902 0.7302 0.9027 0.6619 0.257 0.8935 1.2745 0.5967 1.3616 1.9137 2.1139 4.2799 1.4689 0.3734 0.5246 0.7321 1.2757 0.8022 0.7557 0.9121 0.692 2.3431 2.6485 1.4543 5.3762 3.5757 2.8217 2.887 2.4292 0.4726 0.3134 0.3464 0.7907 0.1501 1.0513 0.2941 0.2928 0.5029 2.4945 2.887 0.2508 0.2095 0.4119 0.308 0.382 0.238 0.2085 0.3611 0.3046 0.2615 0.4441 0.4323 0.1164 0.131 0.2911 0.3074 0.4073 0.1871 0.3483 1.3612 1.9895 1.005 0.2471 0.5468 0.1502 0.2087 0.0482 0.0716 0.5419 0.0884 0.0285  0.4235 0.1152 0.0916 0.3221 0.1061  0.6248 0.8335  0.5602 0.0283   0.4009  0.0244 0.1149 0.2713 0.9424 0.8821 0.2147 3.8075 1.5837 0.5834 1.1119 1.6022 0.1887 0.0903 0.0427       0.2709 0.3855   0.0702   0.0416    0.0169  0.1427   0.0586 0.0034     0.9872 0.0754  0.1048 0.0547 0.51 0.18 0.19 0.50 0.45 0.40 0.38 0.27 0.17 0.48 0.51 0.33 1.31 1.47 1.56 2.79 0.94 0.33 0.36 0.36 0.62 0.52 0.39 0.52 0.43 1.25 1.82 1.00 3.08 1.31 1.26 1.21 0.99 0.28 0.23 0.26 0.77 0.11 0.74 0.35 0.33 0.54 1.18 1.37 0.19 0.40 0.81 0.63 0.70 0.73 0.49 0.34 0.62 0.53 1.00 0.40 0.22 0.25 0.63 0.62 0.76 0.25 0.31 0.75 1.03 0.55 0.35 1.06 0.17 Appendix 1 (Continued) Species Lagostomus maximus Cavia aperea Cavia aperea f. porcellus Dolichotis patagonum Galea musteloides Kerodon rupestris Hydrochaerus hydrochaeris Dasyprocta azarae Dasyprocta leporina Octodon degus Spalacopus cyanus Capromys pilorides Myocastor coypus Procavia capensis Elephas maximus Loxodonta africana Trichechus manatus Equus africanus f. asinus Equus africanus somalicus Equus grevyi Equus hemionus kiang Equus hemionus kulan Equus hemionus onager Equus przewalskii Equus przewalskii f. caballus Equus quagga antiquorum Equus quagga boehmi Equus quagga burchelli Equus quagga chapmani Equus zebra hartmannae Ceratotherium simum Diceros bicornis Rhinoceros unicornis Tapirus indicus Tapirus terrestris Ailuropoda melanoleuca Ailurus fulgens Babyrousa babyrussa Phacochoerus aethiopicus Tayassu tajacu Choeropsis liberiensis Hippopotamus amphibius Camelus dromedarius Camelus ferus Lama guanicoe Lama guanicoe f. glaman Lama guanicoe f. pacos Lama vicugna Tragulus javanicus Antilocapra americana Giraffa camelopardalis Okapia johnstoni Alces alces Axis axis Blastocerus dichotomus Capreolus capreolus Cervus albirostris Cervus elaphus Cervus eldi Cervus nippon Cervus timorensis Cervus unicolor Dama dama Elaphodus cephalophus Muntiacus muntjak Muntiacus reevesi Odocoileus hemionus Odocoileus virginianus Ozotoceros beoarticus Pudu pudu Rangifer tarandus Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Rodentia Hyracoidea Proboscidea Proboscidea Sirenia Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Perissodactyla Carnivora Carnivora Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Chinchillidae Caviidae Caviidae Caviidae Caviidae Caviidae Hydrochaeridae Dasyproctidae Dasyproctidae Octodontidae Octodontidae Capromyidae Myocastoridae Procaviidae Elephantidae Elephantidae Trichechidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Equidae Rhinocerotidae Rhinocerotidae Rhinocerotidae Tapiridae Tapiridae Ailuridae Ailuridae Suidae Suidae Tayassuidae Hippopotamidae Hippopotamidae Camelidae Camelidae Camelidae Camelidae Camelidae Camelidae Tragulidae Antilocapridae Giraffidae Giraffidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae Cervidae DT n BM SD MPS SD rMPS H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H F H H F F R R R R R R R R R R R R R R R R R R R R R R R R R R R R R 5 (gs) (gs) (gs) (gs) 1 3 1 (gs) 2 (gs) 2 (gs) 1 3 5 (gs) 2 (gs) 18 13 4 11 4 5 6 5 2 5 37 3 6 2 5 5 8 12 6 5 10 8 5 (gs) 3 5 5 9 6 5 5 5 5 5 (gs) 5 5 (gs) 3 14 9 3 3 2 3 7 3 3 3 3 3 3 3 4 5 3 3 2 2 3 4.130 0.630 0.780 7.500 0.450 0.750 40.000 3.000 3.250 0.230 0.090 5.000 7.600 3.080 3183.670 2764.620 850.000 216.360 268.750 342.000 245.000 250.000 250.000 292.000 460.000 216.670 275.000 215.000 290.000 314.000 1938.750 985.000 2150.000 275.000 195.500 98.750 5.000 60.000 85.000 23.000 250.000 2391.600 460.000 650.000 90.000 120.000 65.000 51.000 2.000 40.000 672.140 243.330 320.000 85.000 80.000 25.000 130.000 170.000 120.000 70.000 150.000 200.000 60.000 35.000 25.000 11.400 80.000 70.000 35.000 12.000 180.000 0.790  0.075 0.354        0.500 0.894 0.106 821.540 1014.656 57.735 113.227 23.936 10.955 5.477   40.866 223.709 28.868 27.386 21.213 22.361 21.909 370.769 200.839 151.658 17.678 17.552 9.910      263.686 22.361     2.236   327.459 32.596              4.219      0.1375 0.1099 0.1228 0.2308 0.1051 0.2233 0.3868 0.9024 0.5393 0.1441 0.2852 0.126 0.765 1.4364 7.0195 7.2848 6.7287 1.0646 1.3898 1.6918 0.6449 0.9464 0.9268 0.5305 1.1642 1.4914 1.9624 1.0146 1.4985 1.1418 10.0477 10.2459 5.227 4.1099 2.968 11.115 1.0317 3.555 2.1359 0.5969 11.788 17.807 0.4436 0.5656 0.199 0.1378 0.1441 0.3996 0.2681 0.2866 0.7398 0.7485 0.716 0.3924 0.4733 0.2265 0.4613 0.4713 0.3671 0.3554 0.3379 0.3904 0.2892 0.4472 0.283 0.2754 0.2922 0.2128 0.4471 0.5857 0.2936 0.0114 0.0215 0.0102 0.0464   0.0578  0.3939 0.0164  0.0297 0.3442 1.0848 3.7525 2.9278 3.8258 0.5555 0.4776 0.9495 0.1583 0.3523 0.0483 0.0814 0.5327 0.7224 0.8105 0.0114 1.2459 0.4181 2.8326 4.9816 2.3469 1.934 1.3287 8.9169 0.4037 1.5333 0.228 0.1019 3.0969 8.892 0.1036 0.1337 0.0842 0.0431 0.0557 0.5334 0.0693 0.0092 0.3228 0.3613 0.2035 0.1853 0.1138 0.0311 0.178 0.1264 0.2418 0.0678 0.1031 0.0762 0.0425 0.1705 0.07 0.1668 0.1006 0.0219 0.1717 0.4249 0.0237 0.10 0.12 0.13 0.15 0.13 0.24 0.17 0.71 0.42 0.20 0.48 0.09 0.49 1.12 1.19 1.27 1.53 0.33 0.41 0.47 0.19 0.28 0.28 0.15 0.30 0.46 0.57 0.31 0.43 0.32 1.90 2.25 0.97 1.19 0.93 4.05 0.72 1.44 0.80 0.30 3.50 3.22 0.12 0.14 0.07 0.05 0.06 0.17 0.23 0.13 0.18 0.22 0.20 0.15 0.18 0.11 0.16 0.15 0.13 0.14 0.11 0.12 0.12 0.20 0.14 0.16 0.11 0.08 0.20 0.34 0.09 3 6 5 1 1631 Appendix 1 (Continued) Species Addax nasomaculatus Aepyceros melampus Alcelaphus buselaphus Antidorcas marsupialis Antilope cervicapra Bison bison Bison bonasus Bos frontalis Bos grunniens Bos javanicus Bos primigenius f. taurus Boselaphus tragocamelus Bubalus arnee Bubalus depressicornis Budorcas taxicolor Capra falconeri Capra hircus Capra ibex Cephalophus monticola Cephalophus natalensis Cervus duvauceli Connochaetes gnou Damaliscus pygargus Dorcatragus megalotis Elaphurus davidianus Gazella dama Gazella dorcas Gazella subgutturosa Hippotragus equinus Hippotragus niger Kobus ellipsiprymnus Kobus leche Litocranius walleri Madoqua kirki Nemorhaedus goral Oreamnos americanus Oreotragus oreotragus Oryx dammah Oryx gazella Ovibos moschatus Ovis ammon aries Ovis ammon musimon Pseudois nayaur Redunca redunca Rupicapra rupicapra Saiga tartarica Syncerus caffer Tragelaphus angasi Tragelaphus eurycerus Tragelaphus imberbis Tragelaphus oryx Tragelaphus spekei Tragelaphus strepsiceros 1632 Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Cetartiodactyla Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae Bovidae DT n BM SD MPS SD rMPS R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R 3 3 3 6 3 3 3 3 3 3 6 4 3 2 3 3 3 3 3 5 (gs) 4 3 3 1 3 2 3 3 3 3 3 4 2 2 3 3 4 3 2 5 3 3 2 3 3 3 3 3 3 3 3 4 5 85.000 55.000 180.000 30.000 33.000 650.000 600.000 800.000 400.000 600.000 661.670 220.000 900.000 150.000 270.000 50.000 40.000 60.000 7.000 12.400 200.000 160.000 65.000 10.000 120.000 50.000 18.000 27.000 270.000 220.000 190.000 90.000 37.000 4.750 35.000 60.000 13.750 180.000 200.000 252.000 25.000 40.000 27.000 50.000 50.000 35.000 600.000 100.000 250.000 95.000 500.000 95.000 230.000           510.624         0.894              0.354   0.500   56.303              0.3139 0.2818 0.4226 0.3498 0.492 0.4499 0.459 0.3989 0.4623 0.4023 0.2539 0.7075 0.6085 0.2581 0.339 0.3216 0.1929 0.409 0.1521 0.2617 0.2185 0.2942 0.1712 0.2144 0.274 0.4539 0.2481 0.2705 0.3811 0.4944 0.3848 0.3145 0.2104 0.264 0.2205 0.2137 0.2924 0.6202 0.2802 0.3318 0.3504 0.3095 0.3217 0.2945 0.4014 0.2244 0.4652 0.5392 0.4984 0.6063 0.7036 0.4471 0.7294 0.1071 0.0181 0.1225 0.0935 0.0471 0.199 0.1574 0.1299 0.0872 0.0932 0.0644 0.2317 0.1229 0.0008 0.1799 0.0407 0.0455 0.035 0.0245 0.0219 0.0552 0.0536 0.0259  0.0898 0.1117 0.0048 0.0195 0.0267 0.2089 0.1166 0.07 0.0127 0.0009 0.0304 0.0943 0.0608 0.2916 0.0022 0.1887 0.1027 0.0501 0.2978 0.1635 0.0844 0.0308 0.0697 0.1736 0.0692 0.1419 0.2758 0.1551 0.256 0.12 0.12 0.13 0.17 0.23 0.11 0.11 0.09 0.12 0.10 0.06 0.22 0.14 0.09 0.10 0.14 0.09 0.17 0.10 0.15 0.07 0.10 0.07 0.13 0.10 0.19 0.13 0.13 0.11 0.15 0.12 0.12 0.10 0.19 0.10 0.09 0.16 0.20 0.09 0.10 0.17 0.14 0.16 0.12 0.17 0.10 0.11 0.20 0.15 0.22 0.18 0.16 0.22