Incorporating Uncertainty of Management Costs in Sensitivity Analyses of Matrix Population Models

The importance of accounting for economic costs when making environmental‐management decisions subject to resource constraints has been increasingly recognized in recent years. In contrast, uncertainty associated with such costs has often been ignored. We developed a method, on the basis of economic theory, that accounts for the uncertainty in population‐management decisions. We considered the case where, rather than taking fixed values, model parameters are random variables that represent the situation when parameters are not precisely known. Hence, the outcome is not precisely known either. Instead of maximizing the expected outcome, we maximized the probability of obtaining an outcome above a threshold of acceptability. We derived explicit analytical expressions for the optimal allocation and its associated probability, as a function of the threshold of acceptability, where the model parameters were distributed according to normal and uniform distributions. To illustrate our approach we revisited a previous study that incorporated cost‐efficiency analyses in management decisions that were based on perturbation analyses of matrix population models. Incorporating derivations from this study into our framework, we extended the model to address potential uncertainties. We then applied these results to 2 case studies: management of a Koala (Phascolarctos cinereus) population and conservation of an olive ridley sea turtle (Lepidochelys olivacea) population. For low aspirations, that is, when the threshold of acceptability is relatively low, the optimal strategy was obtained by diversifying the allocation of funds. Conversely, for high aspirations, the budget was directed toward management actions with the highest potential effect on the population. The exact optimal allocation was sensitive to the choice of uncertainty model. Our results highlight the importance of accounting for uncertainty when making decisions and suggest that more effort should be placed on understanding the distributional characteristics of such uncertainty. Our approach provides a tool to improve decision making.     

On Valuing Information in Adaptive‐Management Models

Abstract: 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.     

Planning for ex situ conservation in the face of uncertainty

Ex situ conservation strategies for threatened species often require long‐term commitment and financial investment to achieve management objectives. We present a framework that considers the decision to adopt ex situ management for a target species as the end point of several linked decisions. We used a decision tree to intuitively represent the logical sequence of decision making. The first decision is to identify the specific management actions most likely to achieve the fundamental objectives of the recovery plan, with or without the use of ex‐situ populations. Once this decision has been made, one decides whether to establish an ex situ population, accounting for the probability of success in the initial phase of the recovery plan, for example, the probability of successful breeding in captivity. Approaching these decisions in the reverse order (attempting to establish an ex situ population before its purpose is clearly defined) can lead to a poor allocation of resources, because it may restrict the range of available decisions in the second stage. We applied our decision framework to the recovery program for the threatened spotted tree frog (Litoria spenceri) of southeastern Australia. Across a range of possible management actions, only those including ex situ management were expected to provide >50% probability of the species’ persistence, but these actions cost more than use of in situ alternatives only. The expected benefits of ex situ actions were predicted to be offset by additional uncertainty and stochasticity associated with establishing and maintaining ex situ populations. Naïvely implementing ex situ conservation strategies can lead to inefficient management. Our framework may help managers explicitly evaluate objectives, management options, and the probability of success prior to establishing a captive colony of any given species.     

The dilemma of pest suppression in the conservation of endangered species

In the conservation of endangered species, suppression of a population of one native species to benefit another poses challenges. Examples include predator control and nest parasite reduction. Less obvious is the control of blood-feeding arthropods. We conducted a case study of the effect of native black flies (Simulium spp.) on reintroduced Whooping Cranes (Grus americana). Our intent was to provide a science-driven approach for determining the effects of blood-feeding arthropods on endangered vertebrates and identifying optimal management actions for managers faced with competing objectives. A multiyear experiment demonstrated that black flies reduce nest success in cranes by driving incubating birds off their nests. We used a decision-analytic approach to develop creative management alternatives and evaluate trade-offs among competing objectives. We identified 4 management objectives: establish a self-sustaining crane population, improve crane well-being, maintain native black flies as functional components of the ecosystem, and minimize costs. We next identified potential management alternatives: do nothing, suppress black flies, force crane renesting to occur after the activity period of black flies, relocate releases of cranes, suppress black flies and relocate releases, or force crane renesting and relocate releases. We then developed predictions on constructed scales of 0 (worst-performing alternative) to 1 (best-performing alternative) to indicate how alternative actions performed in terms of management objectives. The optimal action depended on the relative importance of each objective to a decision maker. Only relocating releases was a dominated alternative, indicating that it was not optimal regardless of the relative importance of objectives. A rational decision maker could choose any other management alternative we considered. Recognizing that decisions involve trade-offs that must be weighed by decision makers is crucial to identifying alternatives that best balance multiple management objectives. Given uncertainty about the population dynamics of blood-feeding arthropods, an adaptive management approach could offer substantial benefits.     

Making conservation decisions under uncertainty for the persistence of multiple species.

Population models for multiple species provide one of the few means of assessing the impact of alternative management options on the persistence of biodiversity, but they are inevitably uncertain. Is it possible to use population models in multiple-species conservation planning given the associated uncertainties? We use information-gap decision theory to explore the impact of parameter uncertainty on the conservation decision when planning for the persistence of multiple species. An information-gap approach seeks robust outcomes that are most immune from error. We assess the impact of uncertainty in key model parameters for three species, whose extinction risks under four alternative management scenarios are estimated using a metapopulation model. Three methods are described for making conservation decisions across the species, taking into account uncertainty. We find that decisions based on single species are relatively robust to uncertainty in parameters, although the estimates of extinction risk increase rapidly with uncertainty. When identifying the best conservation decision for the persistence of all species, the methods that rely on the rankings of the management options by each species result in decisions that are similarly robust to uncertainty. Methods that depend on absolute values of extinction risk are sensitive to uncertainty, as small changes in extinction risk can alter the ranking of the alternative scenarios. We discover that it is possible to make robust conservation decisions even when the uncertainties of the multiple-species problem appear overwhelming. However, the decision most robust to uncertainty is likely to differ from the best decision when uncertainty is ignored, illustrating the importance of incorporating uncertainty into the decision-making process.     

Accounting for Uncertainty in Making Species Protection Decisions

Abstract:  Uncertainty gives rise to two decision errors in implementing the U.S. Endangered Species Act: listing species that are not in danger of extinction and delisting species that are in danger of extinction. I evaluated four methods (minimum standard, precautionary principle, minimax regret criterion, adaptive management) for deciding whether to list or delist a species when there is uncertainty about how those decisions are likely to influence survival of the species. A safe minimum standard criterion preserves some minimum amount or safe standard (population) of a species unless maintaining that amount generates unacceptable social cost. The precautionary principle favors not delisting a species when there is insufficient evidence on the efficacy of state management plans for protecting them. A minimax regret criterion selects the delisting decision that minimizes the maximum loss likely to occur under alternative ecosystem states. When the cost of making a correct decision is less than the cost of making an incorrect decision, the minimax regret criteria indicates that delisting is the optimal decision. Active adaptive management employs statistically valid experiments to test hypotheses about the likely impacts of delisting decisions. Safe minimum standard and minimax regret criterion are not compatible with the U.S. Endangered Species Act. The precautionary principle comes closest to describing how federal agencies make delisting decisions. Active adaptive management is scientifically superior to the other methods but is costly and time consuming and may not be compatible with the U.S. National Environmental Policy Act.     

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.     

Adaptive resource management and the value of information

The value of information is a general and broadly applicable concept that has been used for several decades to aid in making decisions in the face of uncertainty. Yet there are relatively few examples of its use in ecology and natural resources management, and almost none that are framed in terms of the future impacts of management decisions. In this paper we discuss the value of information in a context of adaptive management, in which actions are taken sequentially over a timeframe and both future resource conditions and residual uncertainties about resource responses are taken into account. Our objective is to derive the value of reducing or eliminating uncertainty in adaptive decision making. We describe several measures of the value of information, with each based on management objectives that are appropriate for adaptive management. We highlight some mathematical properties of these measures, discuss their geometries, and illustrate them with an example in natural resources management. Accounting for the value of information can help to inform decisions about whether and how much to monitor resource conditions through time.     

Effect of risk aversion on prioritizing conservation projects

Conservation outcomes are uncertain. Agencies making decisions about what threat mitigation actions to take to save which species frequently face the dilemma of whether to invest in actions with high probability of success and guaranteed benefits or to choose projects with a greater risk of failure that might provide higher benefits if they succeed. The answer to this dilemma lies in the decision maker's aversion to risk—their unwillingness to accept uncertain outcomes. Little guidance exists on how risk preferences affect conservation investment priorities. Using a prioritization approach based on cost effectiveness, we compared 2 approaches: a conservative probability threshold approach that excludes investment in projects with a risk of management failure greater than a fixed level, and a variance‐discounting heuristic used in economics that explicitly accounts for risk tolerance and the probabilities of management success and failure. We applied both approaches to prioritizing projects for 700 of New Zealand's threatened species across 8303 management actions. Both decision makers’ risk tolerance and our choice of approach to dealing with risk preferences drove the prioritization solution (i.e., the species selected for management). Use of a probability threshold minimized uncertainty, but more expensive projects were selected than with variance discounting, which maximized expected benefits by selecting the management of species with higher extinction risk and higher conservation value. Explicitly incorporating risk preferences within the decision making process reduced the number of species expected to be safe from extinction because lower risk tolerance resulted in more species being excluded from management, but the approach allowed decision makers to choose a level of acceptable risk that fit with their ability to accommodate failure. We argue for transparency in risk tolerance and recommend that decision makers accept risk in an adaptive management framework to maximize benefits and avoid potential extinctions due to inefficient allocation of limited resources. El Efecto de la Aversión de Riesgo sobre la Priorización de Proyectos de Conservación     

A density projection approach for non-trivial information dynamics: Adaptive management of stochastic natural resources

We demonstrate a density projection approximation method for solving resource management problems with imperfect state information. The method expands the set of partially-observed Markov decision process (POMDP) problems that can be solved with standard dynamic programming tools by addressing dimensionality problems in the decision maker's belief state. Density projection is suitable for uncertainty over both physical states (e.g. resource stock) and process structure (e.g. biophysical parameters). We apply the method to an adaptive management problem under structural uncertainty in which a fishery manager's harvest policy affects both the stock of fish and the belief state about the process governing reproduction. We solve for the optimal endogenous learning policy—the active adaptive management approach—and compare it to passive learning and non-learning strategies. We demonstrate how learning improves efficiency but typically follows a period of costly short-run investment.     

A Strategy for Monitoring and Managing Declines in an Amphibian Community

Although many taxa have declined globally, conservation actions are inherently local. Ecosystems degrade even in protected areas, and maintaining natural systems in a desired condition may require active management. Implementing management decisions under uncertainty requires a logical and transparent process to identify objectives, develop management actions, formulate system models to link actions with objectives, monitor to reduce uncertainty and identify system state (i.e., resource condition), and determine an optimal management strategy. We applied one such structured decision‐making approach that incorporates these critical elements to inform management of amphibian populations in a protected area managed by the U.S. National Park Service. Climate change is expected to affect amphibian occupancy of wetlands and to increase uncertainty in management decision making. We used the tools of structured decision making to identify short‐term management solutions that incorporate our current understanding of the effect of climate change on amphibians, emphasizing how management can be undertaken even with incomplete information. Estrategia para Monitorear y Manejar Disminuciones en una Comunidad de Anfibios     

Resource allocation in two species systems: Is it worth acknowledging species interactions?

It is becoming increasingly popular to consider species interactions when managing ecological foodwebs. Such an approach is useful in determining how management can affect multiple species, with either beneficial or detrimental consequences. Identifying such actions is particularly valuable in the context of conservation decision making as funding is severely limited. This paper outlines a new approach that simplifies the resource allocation problem in a two species system for a range of species interactions: independent, mutualism, predator-prey, and competitive exclusion. We assume that both species are endangered and we do not account for decisions over time. We find that optimal funding allocation is to the conservation of the species with the highest marginal gain in expected probability of survival and that, across all except mutualist interaction types, optimal conservation funding allocation differs between species. Loss in efficiency from ignoring species interactions was most severe in predator-prey systems. The funding problem we address, where an ecosystem includes multiple threatened species, will only become more commonplace as increasing numbers of species worldwide become threatened.     

Adaptive Decision Rules for the Acquisition of Nature Reserves

Abstract:  Although reserve-design algorithms have shown promise for increasing the efficiency of conservation planning, recent work casts doubt on the usefulness of some of these approaches in practice. Using three data sets that vary widely in size and complexity, we compared various decision rules for acquiring reserve networks over multiyear periods. We explored three factors that are often important in real-world conservation efforts: uncertain availability of sites for acquisition, degradation of sites, and overall budget constraints. We evaluated the relative strengths and weaknesses of existing optimal and heuristic decision rules and developed a new set of adaptive decision rules that combine the strengths of existing optimal and heuristic approaches. All three of the new adaptive rules performed better than the existing rules we tested under virtually all scenarios of site availability, site degradation, and budget constraints. Moreover, the adaptive rules required no additional data beyond what was readily available and were relatively easy to compute.     

An Adaptive‐Management Framework for Optimal Control of Hiking Near Golden Eagle Nests in Denali National Park

Abstract: Unintended effects of recreational activities in protected areas are of growing concern. We used an adaptive‐management framework to develop guidelines for optimally managing hiking activities to maintain desired levels of territory occupancy and reproductive success of Golden Eagles (Aquila chrysaetos) in Denali National Park (Alaska, U.S.A.). The management decision was to restrict human access (hikers) to particular nesting territories to reduce disturbance. The management objective was to minimize restrictions on hikers while maintaining reproductive performance of eagles above some specified level. We based our decision analysis on predictive models of site occupancy of eagles developed using a combination of expert opinion and data collected from 93 eagle territories over 20 years. The best predictive model showed that restricting human access to eagle territories had little effect on occupancy dynamics. However, when considering important sources of uncertainty in the models, including environmental stochasticity, imperfect detection of hares on which eagles prey, and model uncertainty, restricting access of territories to hikers improved eagle reproduction substantially. An adaptive management framework such as ours may help reduce uncertainty of the effects of hiking activities on Golden Eagles.     

Incorporating the Effects of Socioeconomic Uncertainty into Priority Setting for Conservation Investment

Abstract:  Uncertainty in the implementation and outcomes of conservation actions that is not accounted for leaves conservation plans vulnerable to potential changes in future conditions. We used a decision-theoretic approach to investigate the effects of two types of investment uncertainty on the optimal allocation of global conservation resources for land acquisition in the Mediterranean Basin. We considered uncertainty about (1) whether investment will continue and (2) whether the acquired biodiversity assets are secure, which we termed transaction uncertainty and performance uncertainty, respectively. We also developed and tested the robustness of different rules of thumb for guiding the allocation of conservation resources when these sources of uncertainty exist. In the presence of uncertainty in future investment ability (transaction uncertainty), the optimal strategy was opportunistic, meaning the investment priority should be to act where uncertainty is highest while investment remains possible. When there was a probability that investments would fail (performance uncertainty), the optimal solution became a complex trade-off between the immediate biodiversity benefits of acting in a region and the perceived longevity of the investment. In general, regions were prioritized for investment when they had the greatest performance certainty, even if an alternative region was highly threatened or had higher biodiversity value. The improved performance of rules of thumb when accounting for uncertainty highlights the importance of explicitly incorporating sources of investment uncertainty and evaluating potential conservation investments in the context of their likely long-term success.     

Subpopulation Triage: How to Allocate Conservation Effort among Populations

Abstract:  Threatened species often exist in a small number of isolated subpopulations. Given limitations on conservation spending, managers must choose from strategies that range from managing just one subpopulation and risking all other subpopulations to managing all subpopulations equally and poorly, thereby risking the loss of all subpopulations. We took an economic approach to this problem in an effort to discover a simple rule of thumb for optimally allocating conservation effort among subpopulations. This rule was derived by maximizing the expected number of extant subpopulations remaining given n subpopulations are actually managed. We also derived a spatiotemporally optimized strategy through stochastic dynamic programming. The rule of thumb suggested that more subpopulations should be managed if the budget increases or if the cost of reducing local extinction probabilities decreases. The rule performed well against the exact optimal strategy that was the result of the stochastic dynamic program and much better than other simple strategies (e.g., always manage one extant subpopulation or half of the remaining subpopulation). We applied our approach to the allocation of funds in 2 contrasting case studies: reduction of poaching of Sumatran tigers ( Panthera tigris sumatrae ) and habitat acquisition for San Joaquin kit foxes ( Vulpes macrotis mutica ). For our estimated annual budget for Sumatran tiger management, the mean time to extinction was about 32 years. For our estimated annual management budget for kit foxes in the San Joaquin Valley, the mean time to extinction was approximately 24 years. Our framework allows managers to deal with the important question of how to allocate scarce conservation resources among subpopulations of any threatened species.     

Population dynamics and control of invasive Spartina alterniflora: inference and forecasting under uncertainty

Managing invaded ecosystems entails making decisions about control strategies in the face of scientific uncertainty and ecological stochasticity. Statistical tools such as model selection and Bayesian decision analysis can guide decision-making by estimating probabilities of outcomes under alternative management scenarios, but these tools have seldom been applied in invasion ecology. We illustrate the use of model selection and Bayesian methods in a case study of smooth cordgrass (Spartina alterniflora) invading Willapa Bay, Washington. To address uncertainty in model structure, we quantified the weight of evidence for two previously proposed hypotheses, that S. alterniflora recruitment varies with climatic conditions (represented by sea surface temperature) and that recruitment is subject to an Allee effect due to pollen limitation. By fitting models to time series data, we found strong support for climate effects, with higher per capita seedling production in warmer years, but no evidence for an Allee effect based on either the total area invaded or the mean distance between neighboring clones. We used the best-supported model to compare alternative control strategies, incorporating uncertainty in parameter estimates and population dynamics. For a fixed annual removal effort, the probability of eradication in 10 years was highest, and final invaded area lowest, if removals targeted the smallest clones rather than the largest or randomly selected clones. The relationship between removal effort and probability of eradication was highly nonlinear, with a sharp threshold separating -0% and -100% probability of success, and this threshold was 95% lower in simulations beginning early rather than late in the invasion. This advantage of a rapid response strategy is due to density-dependent population growth, which produces alternative stable equilibria depending on the initial invasion size when control begins. Our approach could be applied to a wide range of invasive species management problems where appropriate data are available.     

Male influence on sex allocation in the parasitoid wasp Nasonia vitripennis

Sex allocation is an important reproductive decision for parents. However, it is often assumed that females have substantial control over sex allocation decisions, and this is particularly true in haplodiploid insects, in which females apparently determine sex by deciding whether to fertilise an egg (and produce a diploid daughter) or not (and produce a haploid son). Mechanisms by which males may influence sex allocation are not so straightforward, and their potential influence on sex ratios has been somewhat neglected. Here, we test whether males influence offspring sex ratios in the parasitoid wasp Nasonia vitripennis. We show that some of the variation in observed sex ratios can be attributed to males when comparing the affect of male strain on sex ratio. We did not find among-male variation in sex ratio with a less powerful experiment using males from only one strain or an effect of male mating environment. Our data suggest that males can influence female sex ratios and contribute to the variation around the sex ratios optimal for females. However, the influence is not large, suggesting that females have more influence on sex allocation than do males. We conclude by considering whether male influences on sex ratio represent differences in male reproductive competence or deliberate attempts by males to increase their fitness by influencing daughter production.     

Deconstructing adaptive management: criteria for applications to environmental management.

The concept of adaptive management has, for many ecologists, become a foundation of effective environmental management for initiatives characterized by high levels of ecological uncertainty. Yet problems associated with its application are legendary, and many of the initiatives promoted as examples of adaptive management appear to lack essential characteristics of the approach. In this paper we propose explicit criteria for helping managers and decision makers to determine the appropriateness of either passive or active adaptive-management strategies as a response to ecological uncertainty in environmental management. Four categories of criteria--dealing with spatial and temporal scale, dimensions of uncertainty, the evaluation of costs and benefits, and institutional and stakeholder support--are defined and applied using hypothetical yet realistic case-study scenarios that illustrate a range of environmental management problems. We conclude that many of the issues facing adaptive management may have less to do with the approach itself than with the indiscriminate choice of contexts within which it is now applied.     

Combining Structured Decision Making and Value‐of‐Information Analyses to Identify Robust Management Strategies

Abstract: Structured decision making and value‐of‐information analyses can be used to identify robust management strategies even when uncertainty about the response of the system to management is high. We used these methods in a case study of management of the non‐native invasive species gray sallow willow (Salix cinerea) in alpine Australia. Establishment of this species is facilitated by wildfire. Managers are charged with developing a management strategy despite extensive uncertainty regarding the frequency of fires, the willow's demography, and the effectiveness of management actions. We worked with managers in Victoria to conduct a formal decision analysis. We used a dynamic model to identify the best management strategy for a range of budgets. We evaluated the robustness of the strategies to uncertainty with value‐of‐information analyses. Results of the value‐of‐information analysis indicated that reducing uncertainty would not change which management strategy was identified as the best unless budgets increased substantially. This outcome suggests there would be little value in implementing adaptive management for the problem we analyzed. The value‐of‐information analyses also highlighted that the main driver of gray sallow willow invasion (i.e., fire frequency) is not necessarily the same factor that is most important for decision making (i.e., willow seed dispersal distance). Value of‐information analyses enables managers to better target monitoring and research efforts toward factors critical to making the decision and to assess the need for adaptive management.