Resolving structural uncertainty in natural resources management using POMDP approaches

In recent years there has been a growing focus on the uncertainties of natural resources management, and the importance of accounting for uncertainty in assessing management effectiveness. This paper focuses on uncertainty in resource management in terms of discrete-state Markov decision processes (MDP) under structural uncertainty and partial observability. It describes the treatment of structural uncertainty with approaches developed for partially observable resource systems. In particular, I show how value iteration for partially observable MDPs (POMDP) can be extended to structurally uncertain MDPs. A key difference between these process classes is that structurally uncertain MDPs require the tracking of system state as well as a probability structure for the structure uncertainty, whereas with POMDPs require only a probability structure for the observation uncertainty. The added complexity of the optimization problem under structural uncertainty is compensated by reduced dimensionality in the search for optimal strategy. A solution algorithm for structurally uncertain processes is outlined for a simple example in conservation biology. By building on the conceptual framework developed for POMDPs, natural resource analysts and decision makers who confront structural uncertainties in natural resources can take advantage of the rapid growth in POMDP methods and approaches, and thereby produce better conservation strategies over a larger class of resource problems.     

The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data

Many methods that study the diversity within hierarchically structured populations have been developed in genetics. Among them, the analysis of molecular variance (AMOVA) (Excoffier et al., 1992) has the advantage of including evolutionary distances between individuals. AMOVA is a special case of a far more general statistical scheme produced by Rao (1982a; 1986) and called the apportionment of quadratic entropy (APQE). It links diversity and dissimilarity and allows the decomposition of diversity according to a given hierarchy. We apply this framework to ecological data showing that APQE may be very useful for studying diversity at various spatial scales. Moreover, the quadratic entropy has a critical advantage over usual diversity indices because it takes into account differences between species. Finally, the differences that can be incorporated in APQE may be either taxonomic or functional (biological traits), which may be of critical interest for ecologists.     

Uncertainty and allocation decisions involving unique environmental resources

The implications of the treatment of uncertainty in the definition of optimal investment criteria for irreversible allocations of unique environmental resources are considered herein. This analysis argues that the single-project, orientation of conventional cost-benefit analysis can lead to inconsistent decisions because it fails to take account of the potential for risk pooling across projects. In the models discussed in this paper uncertainty arises because the planner must estimate the net benefits associated with a mix of developed and preserved natural environments. The results suggest that the criteria for optimal investment plans will be affected by those factors influencing this uncertainty. Both the scale and timing of optimal investments may be altered from those prescribed with the conventional (Fisher-Krutilla-Cicchetti rule) framework when the potential for risk pooling is introduced. Thus, it is important to consider as a part of the specification of the objective function the factors which give rise to uncertainty.     

Incorporating natural enemies in an economic threshold for dynamically optimal pest management

The control of pests by their natural enemies represents an important regulating ecosystem service that helps maintain the stability of crop ecosystems. These services, however, are often ignored in pest management decision making. In addition, the use of broad-spectrum insecticides can damage the populations of natural enemies, reducing the cost-effectiveness of insecticide investment if unaccounted for in treatment decisions.The existing literature on modeling of biological control of insect pests has generally focused on simulations of the population dynamics of pest and natural enemy species and the processes underlying pest control. But agriculture is a managed ecosystem where predator–prey relationships are heavily influenced by human managers. In modeling managerial choices, this study develops an intra-seasonal dynamic bioeconomic optimization model for insecticide-based pest management that explicitly takes into account both the biological control effect of natural enemies on pest density and the nontarget mortality effect of insecticides on the level of natural pest control supplied. The model captures predator–prey interactions, linking them to crop growth and yield damage functions, which in turn are evaluated in a dynamic optimization framework. We introduce a new decision rule for judicious insecticide decisions using a natural enemy-adjusted economic threshold. This threshold represents the pest population density at which insecticide control becomes optimal in spite of the opportunity cost of injury to natural enemies of the target pest. Using field data from Michigan, the model is applied to the case of soybean aphid (Aphis glycines, Matsumura), a recent invasive pest of soybean (Glycine max), whose management is of both economic and environmental importance to the North Central region of the United States. As illustrated by the numerical examples, such natural enemy-adjusted threshold is likely to lead to fewer recommendations for insecticide use than naïve models that ignore natural enemies, resulting in less insecticide use, while maintaining profitability for farmers that rely on chemical pest control methods.The bioeconomic model developed in this study can be used to conduct a wide variety of analyses such as identifying dynamically optimal spray strategies and estimating the implied economic value of natural control services. Furthermore, with the incorporation of inter-year carry-over factors, such as overwintering of pests and natural enemies, the current model can contribute to building multi-year models for studying long-term pest management.     

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.     

Female choice on male quantitative traits in lizards — why is it so rare?

Female choice on the basis of male traits has been described in an array of taxa but has rarely been demonstrated in reptiles. In the sand lizard (Lacerta agilis), and possibly in other non-territorial reptiles, a male's contribution to a female's fitness is restricted to his genes. In order to choose males of high genetic quality, females have to trade the fitness gain against the costs of active choice. In a Swedish population of sand lizards, long-lived males sired offspring with higher embryonic survival compared to offspring sired by short-lived males. In spite of this female sand lizards did not mate selectively with older and/or larger males. There appeared to be mo reliable cues to male longevity; age-specific male body size was highly variable. Furthermore, estimates of male nuptial coloration did not covary with ectoparasite load and, hence, females cannot use male coloration as a cue to heritable resistance to pathogenic parasite effects. When cues to male genetic quality are poor, or inaccurate, and males make no parental investment, we predict that female choice will be rare. Sand lizard females mating with many partners lay clutches with higher hatching success. Thus, females may obtain good genes for their young by multiple mating, thereby avoiding costs associated with mate choice.     

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.     

From Adaptive Management to Adjustive Management: A Pragmatic Account of Biodiversity Values

Abstract: The conservation of biodiversity poses an exceptionally difficult problem in that it needs to be effective in a context of double uncertainty: scientific (i.e., how to conserve biodiversity) and normative (i.e., which biodiversity to conserve and why). Although adaptive management offers a promising approach to overcome scientific uncertainty, normative uncertainty is seldom tackled by conservation science. We expanded on the approach proposed by adaptive‐management theorists by devising an integrative and iterative approach to conservation that encompasses both types of uncertainty. Inspired by environmental pragmatism, we suggest that moral values at stake in biodiversity conservation are plastic and that a plurality of individual normative positions can coexist and evolve. Moral values should thus be explored through an experimental process as additional parameters to be incorporated in the traditional adaptive‐management approach. As such, moral values should also be monitored by environmental ethicists working side by side with scientists and managers on conservation projects. Acknowledging the diversity of moral values and integrating them in a process of collective deliberation will help overcome the normative uncertainty. We used Dewey's distinction between adaptation and adjustment to offer a new paradigm built around what we call adjustive management, which reflects both the uncertainty and the likely evolution of the moral values humans attribute to biodiversity. We illustrate how this paradigm relates to practical conservation decisions by exploring the case of the Sacred Ibis (Threskiornis aethiopicus), an alien species in France that is the target of an eradication plan undertaken with little regard for moral issues. We propose that a more satisfying result of efforts to control Sacred Ibis could have been reached by rerouting the traditional feedback loop of adaptive management to include a normative inquiry. This adjustive management approach now needs to be tested in real‐case conservation programs.     

Optimal control of Atlantic population Canada geese

Management of Canada geese (Branta canadensis) can be a balance between providing sustained harvest opportunity while not allowing populations to become overabundant and cause damage. In this paper, we focus on the Atlantic population of Canada geese and use stochastic dynamic programming to determine the optimal harvest strategy over a range of plausible models for population dynamics. There is evidence to suggest that the population exhibits significant age structure, and it is possible to reconstruct age structure from surveys. Consequently the harvest strategy is a function of the age composition, as well as the abundance, of the population. The objective is to maximize harvest while maintaining the number of breeding adults in the population between specified upper and lower limits. In addition, the total harvest capacity is limited and there is uncertainty about the strength of density-dependence. We find that under a density-independent model, harvest is maximized by maintaining the breeding population at the highest acceptable abundance. However if harvest capacity is limited, then the optimal long-term breeding population size is lower than the highest acceptable level, to reduce the risk of the population growing to an unacceptably large size. Under the proposed density-dependent model, harvest is maximized by maintaining the breeding population at an intermediate level between the bounds on acceptable population size; limits to harvest capacity have little effect on the optimal long-term population size. It is clear that the strength of density-dependence and constraints on harvest significantly affect the optimal harvest strategy for this population. Model discrimination might be achieved in the long term, while continuing to meet management goals, by adopting an adaptive management strategy.     

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 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.     

Ultrastructural and chemical characterization of egg surface of honeybee worker and queen-laid eggs

Summary. Worker policing in honeybees predicts the evolution of a mechanism to discriminate between queenand worker-born eggs. Although it has been postulated that this discrimination is based on an egg recognition pheromone, neither the chemistry nor the glandular source were elucidated. To verify whether egg discrimination might be based on structural differences, we compared the ultrastructure surface of queen-laid diploid and haploid eggs to that of worker-laid eggs using SEM. Only small differences between the different types of eggs were found. Thus, at least based on the fine structure of the egg surface, queen eggs are indistinguishable from worker-laid eggs.To explore the chemosensory hypothesis for egg discrimination, we conducted a detailed comparative chemical analysis of the different egg types. The coating of all egg types was dominated by linear alkanes, but queen eggs, diploid and haploid, differed from those of workers on two accounts: 1. The diversity of compounds found on queenlaid eggs was much greater than found on worker-laid eggs, mainly due to the number of hydrocarbons. 2. Acetates of some fatty alcohols, alkenes and especially monomethylalkanes were characteristic to queen eggs. The origin of the two latter substances and the acetates is still unknown. Whether these compounds constitute the signal that enables police workers to discriminate between queen- and workerborn eggs remains to be investigated.     

Using environmental and geographic data to optimize ex situ collections and preserve evolutionary potential

Maintenance of biodiversity through seed banks and botanical gardens, where the wealth of species’ genetic variation may be preserved ex situ, is a major goal of conservation. However, challenges can persist in optimizing ex situ collections if trade-offs exist among cost, effort, and conserving species evolutionary potential, particularly when genetic data are not available. We evaluated the genetic consequences of population preservation informed by geographic (isolation by distance [IBD]) and environmental (isolation by environment [IBE]) distance for ex situ collections for which population provenance is available. We used 19 genetic and genomic data sets from 15 plant species to assess the proportion of population genetic differentiation explained by geographic and environmental factors and to simulate ex situ collections prioritizing source populations based on pairwise geographic distance, environmental distance, or both. Specifically, we tested the impact prioritizing sampling based on these distances may have on the capture of neutral, functional, or putatively adaptive genetic diversity and differentiation. Individually, IBD and IBE explained limited population genetic differences across all 3 genetic marker classes (IBD, 10–16%; IBE, 1–5.5%). Together, they explained a substantial proportion of population genetic differences for functional (45%) and adaptive (71%) variation. Simulated ex situ collections revealed that inclusion of IBD, IBE, or both increased allelic diversity and genetic differentiation captured among populations, particularly for loci that may be important for adaptation. Thus, prioritizing population collections based on environmental and geographic distance data can optimize genetic variation captured ex situ. For the vast majority of plant species for which there is no genetic information, these data are invaluable to conservation because they can guide preservation of genetic variation needed to maintain evolutionary potential within collections.     

Incorporating known sources of uncertainty to determine precautionary harvests of saltwater crocodiles.

It has been demonstrated repeatedly that the degree to which regulation operates and the magnitude of environmental variation in an exploited population will together dictate the type of sustainable harvest achievable. Yet typically, harvest models fail to incorporate uncertainty in the underlying dynamics of the target population by assuming a particular (unknown) form of endogenous control. We use a novel approach to estimate the sustainable yield of saltwater crocodile (Crocodylus porosus) populations from major river systems in the Northern Territory, Australia, as an example of a system with high uncertainty. We used multimodel inference to incorporate three levels of uncertainty in yield estimation: (1) uncertainty in the choice of the underlying model(s) used to describe population dynamics, (2) the error associated with the precision and bias of model parameter estimation, and (3) environmental fluctuation (process error). We demonstrate varying strength of evidence for density regulation (1.3-96.7%) for crocodiles among 19 river systems by applying a continuum of five dynamical models (density-independent with and without drift and three alternative density-dependent models) to time series of density estimates. Evidence for density dependence increased with the number of yearly transitions over which each river system was monitored. Deterministic proportional maximum sustainable yield (PMSY) models varied widely among river systems (0.042-0.611), and there was strong evidence for an increasing PMSY as support for density dependence rose. However, there was also a large discrepancy between PMSY values and those produced by the full stochastic simulation projection incorporating all forms of uncertainty, which can be explained by the contribution of process error to estimates of sustainable harvest. We also determined that a fixed-quota harvest strategy (up to 0.2K, where K is the carrying capacity) reduces population size much more rapidly than proportional harvest (the latter strategy requiring temporal monitoring of population size to adjust harvest quotas) and greatly inflates the risk of resource depletion. Using an iconic species recovering from recent extreme overexploitation to examine the potential for renewed sustainable harvest, we have demonstrated that incorporating major forms of uncertainty into a single quantitative framework provides a robust approach to modeling the dynamics of exploited populations.     

Temporal patterns of populations in a warming world: a modelling framework

In this paper, we present an approach for describing the environmentally induced temporal pattern of structured populations by partial integro-differential equations. Populations are structured according to size or stage. Growth, energy allocation and stage transitions are affected by environmental conditions of which temperature, photoperiod, water depth and food supply were taken into account. The resulting modelling framework was applied to describe, analyse and predict alterations in populations with continuous development, populations with distinct state structures and interacting populations. Our exemplary applications consider populations of freshwater Amphipoda, Isopoda and Odonata. The model was capable of simulating life cycle alterations in dependence on temperature in interaction with other environmental factors: (1) population dynamics, (2) seasonal regulation, (3) water depth-dependent dispersal, (4) intraguild predation and (5) consumer-resource dynamics.     

Unraveling the complexities of variation in female mate preference for vertical bars in the swordtail, Xiphophorus cortezi

Investigations into the nature of mate choice suggest that variation in female mate preferences is often context dependent, varying in response to genetic and environmental influences on female condition as well as to external environmental stimuli. Determining whether variation in female mate preference is adaptive requires understanding the variables involved that produce this variation and how they interact. Comparative, multivariate studies of wild-caught adult females can be used as initial assessments of variation in female mate preferences, providing valuable insights into the parameters that influence female preferences under natural conditions. We examined variation in female preferences for the pigment pattern vertical bars across five populations of the swordtail, Xiphophorus cortezi. The populations we examined are genetically differentiated and varied in the frequency of males and females with bars. We also considered a variable indicative of within-individual variation (size, as influenced by age) and a variable that varies across individuals (genotype for vertical bars: barred or barless). Using Akaike information criterion, all candidate models explaining variation in strength of preference included female bar state, female size, and population. We suggest that a combination of genetic (bar state) and environmental (female size) conditions influenced how they responded to experience with both male phenotypes in X. cortezi. Future studies should examine the possibility that barred and barless females respond differently over an environmental gradient.     

An optimization approach for sustainable release of e-flows for lake restoration and preservation: Model development and a case study of Baiyangdian Lake, China

In this paper, we describe the development of a model for the sustainable release of e-flows from the regional water resource infrastructure (e.g., reservoirs, rivers with available water) for lake restoration and preservation, and use the model in a case study of Baiyangdian Lake, China. First, we define the sustainable environmental flows (e-flows), with an emphasis on the ecological importance of temporal variation in factors such as water level (depth). By analyzing historical data on the suitable range of water levels in the lake, we evaluated fluctuations using canonical correspondence analysis and frequency distribution analysis. The temporal variations required by the ecosystem of the lake were also assessed. Based on this approach, we developed an optimization model for sustainable release of e-flows. We used the adaptive genetic algorithm approach to solve the model and determine the required release of e-flows. Scenario analysis then provided a range of potential management strategies for the e-flows. The optimal results are helpful to the lake managers to establish sustainable e-flow release schemes for the lake restoration and preservation.     

MHC, health, color, and reproductive success in sand lizards

Good genes are genetic elements that contribute to lifetime reproductive success, regardless of an individuals additional genotype. Their existence is debated, and most work has targeted their viability benefits to the offspring of choosy females. In the present study, we analyze a case of potential good genes effects in adult male sand lizards (Lacerta agilis). We show that males with a particular RFLP (Restriction Fragment Length Polymorphism) MHC genotype (O-males), as opposed to those that lack this genetic element (NO-males), have less ectoparasites under increasing physiological stress (indexed by baseline corticosterone level), and are not constrained by parasites at production of status coloration. Furthermore, O-males are more successful at mate acquisition and guard their partners longer. Ultimately, they have a higher genetic reproductive success as assigned by microsatellites.Communicated by W. Cooper     

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.     

Incorporating Uncertainty into Management Models for Marine Mammals

Abstract: Good management models and good models for understanding biology differ in basic philosophy. Management models must facilitate management decisions despite large amounts of uncertainty about the managed populations. Such models must be based on parameters that can be estimated readily, must explicitly account for uncertainty, and should be simple to understand and implement. In contrast, biological models are designed to elucidate the workings of biology and should not be constrained by management concerns. We illustrate the need to incorporate uncertainty in management models by reviewing the inadequacy of using standard biological models to manage marine mammals in the United States. Past management was based on a simple model that, although it may have represented population dynamics adequately, failed as a management tool because the parameter that triggered management action was extremely difficult to estimate for the majority of populations. Uncertainty in parameter estimation resulted in few conservation actions. We describe a recently adopted management scheme that incorporates uncertainty and its resulting implementation. The approach used in this simple management scheme, which was tested by using simulation models, incorporates uncertainty and mandates monitoring abundance and human-caused mortality. Although the entire scheme may be suitable for application to some terrestrial and marine problems, two features are broadly applicable: the incorporation of uncertainty through simulations of management and the use of quantitative management criteria to translate verbal objectives into levels of acceptable risk.