Water scarcity is leading to increased focus on water reuse. One common assumption is that the be... more Water scarcity is leading to increased focus on water reuse. One common assumption is that the best way to reduce fresh (raw) water use is to introduce water recycling. The amount of water thereby reused is no longer needed from an external supply. However, it is important to consider wider implications of increased water reuse. We present a generic model of a mine site to examine some limitations to water reuse in coal mining. We consider a discrete-time model of water flow around a mine site, with a single contaminant, salt. Each process is assumed to require water of a minimum quality, which limits the amount of "worked" water able to be used in each process. We quantify the substitution of worked water for raw water for a range of salt tolerances. As reuse increases the water balance becomes more closely coupled to the climate. Finally, we examine the implications of failure in various components of the water infrastructure, caused by limited skills to manage the water system, on the expected water savings. We conclude that moving to water reuse should be accompanied by careful planning to ensure the new water system is appropriately managed.
The survey of plant and animal populations is central to undertaking field ecology. However, dete... more The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.
Active adaptive management is increasingly advocated in natural resource management and conservat... more Active adaptive management is increasingly advocated in natural resource management and conservation biology. Active adaptive management looks at the benefit of employing strategies that may be suboptimal in the near term but which may provide additional information that will facilitate better management in future years. However, when comparing management policies it is traditional to weigh future rewards geometrically (at a constant discount rate) which results in far-distant rewards making a negligible contribution to the total benefit. Under such a discounting scheme active adaptive management is rarely of much benefit, especially if learning is slow. A growing number of authors advocate the use of alternative forms of discounting when evaluating optimal strategies for long-term decisions which have a social component. We consider a theoretical harvested population for which the recovery rate from an unharvestably small population size is unknown and look at the effects on the benefit of experimental management when three different forms of discounting are employed. Under geometric discounting, with a discount rate of 5% per annum, managing to learn actively had little benefit. This study demonstrates that discount functions which weigh future rewards more heavily result in more conservative harvesting strategies, but do not necessarily encourage active learning. Furthermore, the optimal management strategy is not equivalent to employing geometric discounting at a lower rate. If alternative discount functions are made mandatory in calculating optimal management strategies for environmental management then this will affect the structure of optimal management regimes and change when and how much we are willing to invest in learning.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large. Valoración de la Información en Modelos de Manejo Adaptativo Resumen: El manejo adaptativo activo considera los beneficios de la utilización de estrategias que pueden ser subóptimas en el corto plazo pero pueden proporcionar información adicional que facilitará un mejor manejo en el futuro. En muchos problemas de manejo adaptativo que han sido estudiados, las políticasóptimas activas y pasivas (considerar el aprendizaje cuando se diseñan políticas y diseño de políticas con base en la mejor información disponible, respectivamente) son muy similares. Esto parece paradójico; cuando hay incertidumbre sobre la mejor acción, los manejadores deben gastar poca energía en el diseño de programas activos para aprender sobre el sistema que están manejando. Consideramos dos posibles razones por las que las soluciones adaptativas activas y pasivas a menudo son similares. Primero, los beneficios del aprendizaje a menudo están confinados al estudio de caso particular en el escenario modelado, mientras que en la realidad la información obtenida de estudios locales a menudo es aplicada más ampliamente. Segundo, los objetivos de manejo que incorporan la varianza de una estimación pueden poner mayorénfasis en el aprendizaje que los objetivos utilizados más comúnmente que intentan maximizar un valor esperado. Exploramos estos
1. Previous studies that optimize allocation of surveillance resources over space have assumed th... more 1. Previous studies that optimize allocation of surveillance resources over space have assumed that detection rates are constant over time and that travel or survey costs are the same for all sites. Other recent research explicitly accounts for stochastically varying detection rates and distinct travel costs but restricts attention to the optimal number of visits to a single site. Here, we integrate these approaches to construct a model that optimizes the allocation of surveillance effort over both space and time. 2. The solution defines the budget that should be allocated to each site and the number of visits over which that search budget should be expended. We show that the solution has close affinities with that of Hauser and McCarthy (Ecology Letters, 12, 2009, 683), which ignored temporal variation in detection rates and travel costs. We illustrate our approach by finding the optimal allocation of survey effort over space and time that maximizes the expected number of detections of the cascade treefrog (Litoria pearsoniana) in a region. 3. In deriving our model, we also solve an alternative model to Moore et al. (PLoS One, 9, 2014) that considers the trade-off between the number of visits and length of each visit when the detection rate at a site varies over time. We compare the predictions of the original model of Moore et al. (PLoS One, 9, 2014) and the new model using experimental data on detections of two species, showing the two models perform similarly well. 4. Interestingly, when variable detection rates and travel costs are considered using our model, the form of the resulting objective function is very similar to the case in which they are ignored; in both cases, the probability of failed detection at each site is a negative exponential function of effort. However, travel costs impose a disconti-nuity into the solution space making the decision variables semi-continuous (i.e. the optimal surveillance effort at each site is either zero or a value greater than the travel cost). This discontinuity complicates the task of finding the optimal solution. We propose a straightforward algorithm that finds very good approximate solutions.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large.
... Optimal monitoring for invasive species management. Alana L. Moore, Michael A. McCarthy, and ... more ... Optimal monitoring for invasive species management. Alana L. Moore, Michael A. McCarthy, and Peter G. Taylor. ... We consider finding an optimal combined management strategy for an invasive fox population which specifies both when to monitor and when to control. ...
Conservation biology : the journal of the Society for Conservation Biology, 2014
Biodiversity indices often combine data from different species when used in monitoring programs. ... more Biodiversity indices often combine data from different species when used in monitoring programs. Heuristic properties can suggest preferred indices, but we lack objective ways to discriminate between indices with similar heuristics. Biodiversity indices can be evaluated by determining how well they reflect management objectives that a monitoring program aims to support. For example, the Convention on Biological Diversity requires reporting about extinction rates, so simple indices that reflect extinction risk would be valuable. We developed 3 biodiversity indices that are based on simple models of population viability that relate extinction risk to abundance. We based the first index on the geometric mean abundance of species and the second on a more general power mean. In a third index, we integrated the geometric mean abundance and trend. These indices require the same data as previous indices, but they also relate directly to extinction risk. Field data for butterflies and woodla...
The survey of plant and animal populations is central to undertaking field ecology. However, dete... more The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.
At the heart of our efforts to protect threatened species, there is a controversial debate about ... more At the heart of our efforts to protect threatened species, there is a controversial debate about whether to give priority to cost-effective actions or whether focusing solely on the most endangered species will ultimately lead to preservation of the greatest number of species. By framing this debate within a decisionanalytic framework, we show that allocating resources solely to the most endangered species will typically not minimise the number of extinctions in the long-term, as this does not account for the risk of less endangered species going extinct in the future. It is only favoured when our planning timeframe is short or we have a long-term view and we are optimistic about future conditions. Conservation funding tends to be short-term in nature, which biases allocations to more endangered species. Our work highlights the need to consider resource allocation for biodiversity over the long-term; Ôpreventive conservationÕ, rather than just short-term fire-fighting.
Active adaptive management is increasingly advocated in natural resource management and conservat... more Active adaptive management is increasingly advocated in natural resource management and conservation biology. Active adaptive management looks at the benefit of employing strategies that may be suboptimal in the near term but which may provide additional information that will facilitate better management in future years. However, when comparing management policies it is traditional to weigh future rewards geometrically (at a constant discount rate) which results in far-distant rewards making a negligible contribution to the total benefit. Under such a discounting scheme active adaptive management is rarely of much benefit, especially if learning is slow. A growing number of authors advocate the use of alternative forms of discounting when evaluating optimal strategies for long-term decisions which have a social component. We consider a theoretical harvested population for which the recovery rate from an unharvestably small population size is unknown and look at the effects on the benefit of experimental management when three different forms of discounting are employed. Under geometric discounting, with a discount rate of 5% per annum, managing to learn actively had little benefit. This study demonstrates that discount functions which weigh future rewards more heavily result in more conservative harvesting strategies, but do not necessarily encourage active learning. Furthermore, the optimal management strategy is not equivalent to employing geometric discounting at a lower rate. If alternative discount functions are made mandatory in calculating optimal management strategies for environmental management then this will affect the structure of optimal management regimes and change when and how much we are willing to invest in learning.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large.
Water scarcity is leading to increased focus on water reuse. One common assumption is that the be... more Water scarcity is leading to increased focus on water reuse. One common assumption is that the best way to reduce fresh (raw) water use is to introduce water recycling. The amount of water thereby reused is no longer needed from an external supply. However, it is important to consider wider implications of increased water reuse. We present a generic model of a mine site to examine some limitations to water reuse in coal mining. We consider a discrete-time model of water flow around a mine site, with a single contaminant, salt. Each process is assumed to require water of a minimum quality, which limits the amount of "worked" water able to be used in each process. We quantify the substitution of worked water for raw water for a range of salt tolerances. As reuse increases the water balance becomes more closely coupled to the climate. Finally, we examine the implications of failure in various components of the water infrastructure, caused by limited skills to manage the water system, on the expected water savings. We conclude that moving to water reuse should be accompanied by careful planning to ensure the new water system is appropriately managed.
The survey of plant and animal populations is central to undertaking field ecology. However, dete... more The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.
Active adaptive management is increasingly advocated in natural resource management and conservat... more Active adaptive management is increasingly advocated in natural resource management and conservation biology. Active adaptive management looks at the benefit of employing strategies that may be suboptimal in the near term but which may provide additional information that will facilitate better management in future years. However, when comparing management policies it is traditional to weigh future rewards geometrically (at a constant discount rate) which results in far-distant rewards making a negligible contribution to the total benefit. Under such a discounting scheme active adaptive management is rarely of much benefit, especially if learning is slow. A growing number of authors advocate the use of alternative forms of discounting when evaluating optimal strategies for long-term decisions which have a social component. We consider a theoretical harvested population for which the recovery rate from an unharvestably small population size is unknown and look at the effects on the benefit of experimental management when three different forms of discounting are employed. Under geometric discounting, with a discount rate of 5% per annum, managing to learn actively had little benefit. This study demonstrates that discount functions which weigh future rewards more heavily result in more conservative harvesting strategies, but do not necessarily encourage active learning. Furthermore, the optimal management strategy is not equivalent to employing geometric discounting at a lower rate. If alternative discount functions are made mandatory in calculating optimal management strategies for environmental management then this will affect the structure of optimal management regimes and change when and how much we are willing to invest in learning.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large. Valoración de la Información en Modelos de Manejo Adaptativo Resumen: El manejo adaptativo activo considera los beneficios de la utilización de estrategias que pueden ser subóptimas en el corto plazo pero pueden proporcionar información adicional que facilitará un mejor manejo en el futuro. En muchos problemas de manejo adaptativo que han sido estudiados, las políticasóptimas activas y pasivas (considerar el aprendizaje cuando se diseñan políticas y diseño de políticas con base en la mejor información disponible, respectivamente) son muy similares. Esto parece paradójico; cuando hay incertidumbre sobre la mejor acción, los manejadores deben gastar poca energía en el diseño de programas activos para aprender sobre el sistema que están manejando. Consideramos dos posibles razones por las que las soluciones adaptativas activas y pasivas a menudo son similares. Primero, los beneficios del aprendizaje a menudo están confinados al estudio de caso particular en el escenario modelado, mientras que en la realidad la información obtenida de estudios locales a menudo es aplicada más ampliamente. Segundo, los objetivos de manejo que incorporan la varianza de una estimación pueden poner mayorénfasis en el aprendizaje que los objetivos utilizados más comúnmente que intentan maximizar un valor esperado. Exploramos estos
1. Previous studies that optimize allocation of surveillance resources over space have assumed th... more 1. Previous studies that optimize allocation of surveillance resources over space have assumed that detection rates are constant over time and that travel or survey costs are the same for all sites. Other recent research explicitly accounts for stochastically varying detection rates and distinct travel costs but restricts attention to the optimal number of visits to a single site. Here, we integrate these approaches to construct a model that optimizes the allocation of surveillance effort over both space and time. 2. The solution defines the budget that should be allocated to each site and the number of visits over which that search budget should be expended. We show that the solution has close affinities with that of Hauser and McCarthy (Ecology Letters, 12, 2009, 683), which ignored temporal variation in detection rates and travel costs. We illustrate our approach by finding the optimal allocation of survey effort over space and time that maximizes the expected number of detections of the cascade treefrog (Litoria pearsoniana) in a region. 3. In deriving our model, we also solve an alternative model to Moore et al. (PLoS One, 9, 2014) that considers the trade-off between the number of visits and length of each visit when the detection rate at a site varies over time. We compare the predictions of the original model of Moore et al. (PLoS One, 9, 2014) and the new model using experimental data on detections of two species, showing the two models perform similarly well. 4. Interestingly, when variable detection rates and travel costs are considered using our model, the form of the resulting objective function is very similar to the case in which they are ignored; in both cases, the probability of failed detection at each site is a negative exponential function of effort. However, travel costs impose a disconti-nuity into the solution space making the decision variables semi-continuous (i.e. the optimal surveillance effort at each site is either zero or a value greater than the travel cost). This discontinuity complicates the task of finding the optimal solution. We propose a straightforward algorithm that finds very good approximate solutions.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large.
... Optimal monitoring for invasive species management. Alana L. Moore, Michael A. McCarthy, and ... more ... Optimal monitoring for invasive species management. Alana L. Moore, Michael A. McCarthy, and Peter G. Taylor. ... We consider finding an optimal combined management strategy for an invasive fox population which specifies both when to monitor and when to control. ...
Conservation biology : the journal of the Society for Conservation Biology, 2014
Biodiversity indices often combine data from different species when used in monitoring programs. ... more Biodiversity indices often combine data from different species when used in monitoring programs. Heuristic properties can suggest preferred indices, but we lack objective ways to discriminate between indices with similar heuristics. Biodiversity indices can be evaluated by determining how well they reflect management objectives that a monitoring program aims to support. For example, the Convention on Biological Diversity requires reporting about extinction rates, so simple indices that reflect extinction risk would be valuable. We developed 3 biodiversity indices that are based on simple models of population viability that relate extinction risk to abundance. We based the first index on the geometric mean abundance of species and the second on a more general power mean. In a third index, we integrated the geometric mean abundance and trend. These indices require the same data as previous indices, but they also relate directly to extinction risk. Field data for butterflies and woodla...
The survey of plant and animal populations is central to undertaking field ecology. However, dete... more The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.
At the heart of our efforts to protect threatened species, there is a controversial debate about ... more At the heart of our efforts to protect threatened species, there is a controversial debate about whether to give priority to cost-effective actions or whether focusing solely on the most endangered species will ultimately lead to preservation of the greatest number of species. By framing this debate within a decisionanalytic framework, we show that allocating resources solely to the most endangered species will typically not minimise the number of extinctions in the long-term, as this does not account for the risk of less endangered species going extinct in the future. It is only favoured when our planning timeframe is short or we have a long-term view and we are optimistic about future conditions. Conservation funding tends to be short-term in nature, which biases allocations to more endangered species. Our work highlights the need to consider resource allocation for biodiversity over the long-term; Ôpreventive conservationÕ, rather than just short-term fire-fighting.
Active adaptive management is increasingly advocated in natural resource management and conservat... more Active adaptive management is increasingly advocated in natural resource management and conservation biology. Active adaptive management looks at the benefit of employing strategies that may be suboptimal in the near term but which may provide additional information that will facilitate better management in future years. However, when comparing management policies it is traditional to weigh future rewards geometrically (at a constant discount rate) which results in far-distant rewards making a negligible contribution to the total benefit. Under such a discounting scheme active adaptive management is rarely of much benefit, especially if learning is slow. A growing number of authors advocate the use of alternative forms of discounting when evaluating optimal strategies for long-term decisions which have a social component. We consider a theoretical harvested population for which the recovery rate from an unharvestably small population size is unknown and look at the effects on the benefit of experimental management when three different forms of discounting are employed. Under geometric discounting, with a discount rate of 5% per annum, managing to learn actively had little benefit. This study demonstrates that discount functions which weigh future rewards more heavily result in more conservative harvesting strategies, but do not necessarily encourage active learning. Furthermore, the optimal management strategy is not equivalent to employing geometric discounting at a lower rate. If alternative discount functions are made mandatory in calculating optimal management strategies for environmental management then this will affect the structure of optimal management regimes and change when and how much we are willing to invest in learning.
Active adaptive management looks at the benefit of using strategies that may be suboptimal in the... more Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive-management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay-off for learning about their benefits is large.
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Papers by Alana Moore