A framework for allocating conservation resources among multiple threats and actions.

Land managers decide how to allocate resources among multiple threats that can be addressed through multiple possible actions. Additionally, these actions vary in feasibility, effectiveness, and cost. We sought to provide a way to optimize resource allocation to address multiple threats when multiple management options are available, including mutually exclusive options. Formulating the decision as a combinatorial optimization problem, our framework takes as inputs the expected impact and cost of each threat for each action (including do nothing) and for each overall budget identifies the optimal action to take for each threat. We compared the optimal solution to an easy to calculate greedy algorithm approximation and a variety of plausible ranking schemes. We applied the framework to management of multiple introduced plant species in Australian alpine areas. We developed a model of invasion to predict the expected impact in 50 years for each species-action combination that accounted for each species' current invasion state (absent, localized, widespread); arrival probability; spread rate; impact, if present, of each species; and management effectiveness of each species-action combination. We found that the recommended action for a threat changed with budget; there was no single optimal management action for each species; and considering more than one candidate action can substantially increase the management plan's overall efficiency. The approximate solution (solution ranked by marginal cost-effectiveness) performed well when the budget matched the cost of the prioritized actions, indicating that this approach would be effective if the budget was set as part of the prioritization process. The ranking schemes varied in performance, and achieving a close to optimal solution was not guaranteed. Global sensitivity analysis revealed a threat's expected impact and, to a lesser extent, management effectiveness were the most influential parameters, emphasizing the need to focus research and monitoring efforts on their quantification.

Un Marco de Referencia para Asignar Recursos para la Conservación entre Múltiples Amenazas y Acciones Resumen Los administradores de tierras deciden cómo asignar recursos entre múltiples amenazas que pueden abordarse por medio de múltiples acciones. Adicionalmente, estas acciones varían en viabilidad, efectividad y costo. Buscamos proporcionar una manera para optimizar la asignación de recursos para abordar varias amenazas cuando están disponibles muchas opciones de manejo, incluyendo opciones mutuamente excluyentes. Con una formulación de la decisión como un problema combinatorio de optimización, nuestro marco de referencia toma como entradas el impacto esperado y el costo de cada amenaza para cada acción (incluyendo hacer nada) y para cada presupuesto generalizado identifica la acción óptima a realizar ante cada amenaza. Comparamos la solución óptima con una aproximación de un algoritmo avaricioso fácil de calcular y una variedad de esquemas plausibles de clasificación. Aplicamos el marco de trabajo al manejo de múltiples especies de plantas introducidas en las áreas alpinas de Australia. Desarrollamos un modelo de invasión para predecir el impacto esperado en 50 años para cada combinación de especie-acción que consideró el estado actual de invasión para cada especie (ausente, localizada, ampliamente distribuida), la probabilidad de invasión, la tasa de esparcimiento, el impacto, cuando abundante, de cada especie y la efectividad de manejo de cada combinación especie-acción. Descubrimos que la acción recomendada para una amenaza cambia con el presupuesto, que no existe una acción única de manejo óptimo para cada especie y que considerar más de una acción candidata puede incrementar sustancialmente la eficiencia general del plan de manejo. La solución aproximada (solución clasificada por rentabilidad) tuvo un buen desempeño cuando el presupuesto fue igual al costo de las acciones prioritarias, lo que indica que esta estrategia sería efectiva si el presupuesto está fijado como parte del proceso de priorización. Los esquemas de clasificación variaron en cuanto a desempeño, y lograr una solución cercana a lo óptimo no estuvo garantizado. El análisis de sensibilidad global reveló que el impacto esperado de una amenaza y, a menor grado, la efectividad del manejo no fueron los parámetros con mayor influencia, lo que enfatiza la necesidad de enfocar la investigación y los esfuerzos de monitoreo en la cuantificación del impacto esperado y la efectividad del manejo.

Two-step adaptive management for choosing between two management actions.

Adaptive management is widely advocated to improve environmental management. Derivations of optimal strategies for adaptive management, however, tend to be case specific and time consuming. In contrast, managers might seek relatively simple guidance, such as insight into when a new potential management action should be considered, and how much effort should be expended on trialing such an action. We constructed a two-time-step scenario where a manager is choosing between two possible management actions. The manager has a total budget that can be split between a learning phase and an implementation phase. We use this scenario to investigate when and how much a manager should invest in learning about the management actions available. The optimal investment in learning can be understood intuitively by accounting for the expected value of sample information, the benefits that accrue during learning, the direct costs of learning, and the opportunity costs of learning. We find that the optimal proportion of the budget to spend on learning is characterized by several critical thresholds that mark a jump from spending a large proportion of the budget on learning to spending nothing. For example, as sampling variance increases, it is optimal to spend a larger proportion of the budget on learning, up to a point: if the sampling variance passes a critical threshold, it is no longer beneficial to invest in learning. Similar thresholds are observed as a function of the total budget and the difference in the expected performance of the two actions. We illustrate how this model can be applied using a case study of choosing between alternative rearing diets for hihi, an endangered New Zealand passerine. Although the model presented is a simplified scenario, we believe it is relevant to many management situations. Managers often have relatively short time horizons for management, and might be reluctant to consider further investment in learning and monitoring beyond collecting data from a single time period.

Linking indices for biodiversity monitoring to extinction risk theory.

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 woodland plants and experimental studies of protozoan communities show that the indices correlate with local extinction rates. Applying the index based on the geometric mean to global data on changes in avian abundance suggested that the average extinction probability of birds has increased approximately 1% from 1970 to 2009.

Designing nature reserves in the face of uncertainty.

Conservation reserves are a fundamental tool for managing biodiversity. The so-called SLOSS debate--should we have a Single Large Or Several Small reserves - is central to conservation theory. Population dynamic models suggest that the design that minimizes the risk of extinction of a species is case-specific, with the optimal number of reserves ranging between one and very many. Uncertainty is pervasive in ecology, but, the previous analyses of the SLOSS debate have not considered how uncertainty in the model of extinction risk might influence the optimal design. Herein, we show that when uncertainty is considered, the SLOSS problem is simplified and driven more by the aspirations of the manager than the population dynamics of the species. In this case, the optimal solution is to have in the order of twenty or fewer reserves for any species. This result shows counter-intuitively that considering uncertainty actually simplifies rather than complicates decisions about designing nature reserves.

When should we save the most endangered species?

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 decision-analytic 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; 'preventive conservation', rather than just short-term fire-fighting.

On valuing information in adaptive-management models.

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.

How we value the future affects our desire to learn.

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.

The optimal number of surveys when detectability varies.

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.