Spatial uncertainty analysis of population models

This paper describes an approach for conducting spatial uncertainty analysis of spatial population models, and illustrates the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial population models typically simulate birth, death, and migration on an input map that describes habitat. Typically, only a single “reference” map is available, but we can imagine that a collection of other, slightly different, maps could be drawn to represent a particular species’ habitat. As a first approximation, our approach assumes that spatial uncertainty (i.e., the variation among values assigned to a location by such a collection of maps) is constrained by characteristics of the reference map, regardless of how the map was produced. Our approach produces lower levels of uncertainty than alternative methods used in landscape ecology because we condition our alternative landscapes on local properties of the reference map. Simulated spatial uncertainty was higher near the borders of patches. Consequently, average uncertainty was highest for reference maps with equal proportions of suitable and unsuitable habitat, and no spatial autocorrelation. We used two population viability models to evaluate the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial uncertainty produced larger variation among predictions of a spatially explicit model than those of a spatially implicit model. Spatially explicit model predictions of final female population size varied most among landscapes with enough clustered habitat to allow persistence. In contrast, predictions of population growth rate varied most among landscapes with only enough clustered habitat to support a small population, i.e., near a spatially mediated extinction threshold. We conclude that spatial uncertainty has the greatest effect on persistence when the amount and arrangement of suitable habitat are such that habitat capacity is near the minimum required for persistence.     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Replenishable resource management under uncertainty: A reexamination of the U.S. Northern Fishery

This paper partially extends the replenishable resource management literature to the case of uncertainty. Stochastic resource dynamics are defined, studied and estimated. The results of this study suggest that the misallocation of resources into the northern lobster fishery has been greater than was previously believed. While aggregate stochastic influences are small in the lobster fishery, the dynamics of whales appear to be significantly affected by stochastic influences.     

Conditioning uncertainty in ecological models: Assessing the impact of fire management strategies

A simple simulation model has been used to investigate whether large fires in Mediterranean regions are a result of extreme weather conditions or the cumulative effect of a policy of fire suppression over decades. The model reproduced the fire regime characteristics for a wide variety of regions of Mediterranean climate in California, France and Spain. The Generalised Likelihood Uncertainty Estimation (GLUE) methodology was used to assess the possibility of multiple model parameter sets being consistent with the available calibration data. The resulting set of behavioural models was used to assess uncertainty in the predictions. The results suggested that (1) for a given region, the total area burned is much the same whether suppression or prescribed fire policies are used or not; however fire suppression enhances fire intensity and prescribed burning reduces it; (2) the proportion of large fires can be reduced, but not eliminated, using prescribed fires, especially in areas which have the highest proportion of large fires.     

Methods for estimating the uncertainty in emergy table-form models

Emergy studies have suffered criticism due to the lack of uncertainty analysis and this shortcoming may have directly hindered the wider application and acceptance of this methodology. Recently, to fill this gap, the sources of uncertainty in emergy analysis were described and analytical and stochastic methods were put forward to estimate the uncertainty in unit emergy values (UEVs). However, the most common method used to determine UEVs is the emergy table-form model, and only a stochastic method (i.e., the Monte Carlo method) was provided to estimate the uncertainty of values calculated in this way. To simplify the determination of uncertainties in emergy analysis using table-form calculations, we introduced two analytical methods provided by the Guide to the Expression of Uncertainty in Measurement (GUM), i.e., the Variance method and the Taylor method, to estimate the uncertainty of emergy table-form calculations for two different types of data, and compared them with the stochastic method in two case studies. The results showed that, when replicate data are available at the system level, i.e., the same data on inputs and output are measured repeatedly in several independent systems, the Variance method is the simplest and most reliable method for determining the uncertainty of the model output, since it considers the underlying covariance of the inputs and requires no assumptions about the probability distributions of the inputs. However, when replicate data are only available at the subsystem level, i.e., repeat samples are measured on subsystems without specific correspondence between an output and a certain suite of inputs, the Taylor method will be a better option for calculating uncertainty, since it requires less information and is easier to understand and perform than the Monte Carlo method.     

Optimal monitoring and control under state uncertainty: Application to lionfish management

State variables in many renewable resource management problems, such as the abundance of a fish stock, are imperfectly observed over time. In systems characterized by state uncertainty, decision makers often invest in monitoring to learn about the level of a stock. We develop a stochastic bioeconomic model of marine invasive species management under state uncertainty. The decision maker in our model simultaneously evaluates optimal investment in monitoring and population control. Using a recently-devised method for solving continuous-state Partially Observable Markov Decision Processes (POMDPs), we find that the ability to learn through monitoring can alter the role of population control in the optimal policy function, for example by reducing control intensity in favor of monitoring. Optimal monitoring depends on the management context, including in our application lionfish population structure. The rich transient dynamics of our model depend critically on the relationship between the initial conditions for information and invader abundance.     

Measuring values for environmental resources under uncertainty

The relationship between conventional Hicksian measures of the benefits from changes in environmental amenities under certainty, and corresponding measures of valuation when the conditions of access to an uncertain environmental resource are changed, is considered. The analysis utilizes a contingent commodity framework with the assumption of state-dependent preferences. The findings suggest that the valuation of these changes will depend upon the availability of fair markets for diversifying risk. Moreover, conventional measures of compensating or equivalent surplus will not necessarily bound the individual's valuation of a change in access to an uncertain environmental resource.     

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.     

Planning for alkali land reclamation under rainfall uncertainty

A chance-constrained linear programming model with rainfall as stochastic input has been developed to plan optimal land and water use in alkali soils under reclamation. The model is based on the water balance of a typical alkali catchment in the command area of the Western Jamuna Canal in Haryana (India). The zero-order decision rule has been used to obtain the deterministic equivalent of chance constraint and optimal solutions have been obtained for four levels of rainfall probability. Available water supplies at low rainfall probabilities were found to be inadequate to sustain the high cost reclamation technology. Exploitation of the full potential of agricultural land calls for the augmentation of available water supplies.     

Setting conservation priorities for migratory networks under uncertainty

Conserving migratory species requires protecting connected habitat along the pathways they travel. Despite recent improvements in tracking animal movements, migratory connectivity remains poorly resolved at a population level for the vast majority of species, thus conservation prioritization is hampered. To address this data limitation, we developed a novel approach to spatial prioritization based on a model of potential connectivity derived from empirical data on species abundance and distance traveled between sites during migration. We applied the approach to migratory shorebirds of the East Asian‐Australasian Flyway. Conservation strategies that prioritized sites based on connectivity and abundance metrics together maintained larger populations of birds than strategies that prioritized sites based only on abundance metrics. The conservation value of a site therefore depended on both its capacity to support migratory animals and its position within the migratory pathway; the loss of crucial sites led to partial or total population collapse. We suggest that conservation approaches that prioritize sites supporting large populations of migrants should, where possible, also include data on the spatial arrangement of sites.     

Commercial fisheries under price uncertainty

The deterministic models applied in economics of fisheries are extended to comprise price uncertainty and risk aversion among the fishing units. It is proved that in the open-access fishery both the total fishing effort and the number of fishing units are reduced as the variance of the price increases; that the total fishing effort may be smaller in the open-access fishery than in the optimal fishery at a high variance; that only a fixed producer price system can create a first-best optimum, and that a tax on revenue is more efficient than both fishing unit quotas or tax on catch.     

Environmental policy choice under uncertainty

The Markovian model provides an insightful structure for analyzing environmental policy decisions. This framework is applied to a variety of conceptual issues. The analysis of reswitching phenomena shows that when multiple risks are involved, there is unlikely to be an unambiguous ranking of policies according to their future-mindedness. The discussion of irreversibilities demonstrates that irreversibilities differ only in degree from other probabilistic structures; they create no special analytic complications. In the final section, the Markovian decision framework is extended to incorporate the impact of budgetary constraints on optimal decisions.     

Emission control policies under uncertainty

The paper deals with the problem of optimal environmental policy under uncertainty. Usually, when an environmental policy is considered, only the expected values of the parameters of the marginal benefit and marginal cost functions associated with the policy are known. Thus a relevant question is: In the presence of uncertainty, what is the optimal policy mean for achieving the environmental objective? The study addresses itself to the specific objective of improving air quality although the analysis is generally applicable. The policy means are emission taxes and emission quotas. It is shown that under uncertainty neither of these means is generally optimal, and that specific parameter values of the costs and benefits relations and their distributions determine the optimal policy for each situation.     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

Switching state-space models for modeling penguin population dynamics

Environmental and Ecological Statistics - Tracking individual animals through time using mark-recapture methods is the gold standard for understanding how environmental conditions influence...     

A comparison of models for predicting population persistence

We consider a range of models that may be used to predict the future persistence of populations, particularly those based on discrete-state Markov processes. While the mathematical theory of such processes is very well-developed, they may be difficult to work with when attempting to estimate parameters or expected times to extinction. Hence, we focus on diffusion and other approximations to these models, presenting new and recent developments in parameter estimation for density dependent processes, and the calculation of extinction times for processes subject to catastrophes. We illustrate these and other methods using data from simulated and real time series. We give particular attention to a procedure, due to Ross et al. [Ross, J.V., Taimre, T., Pollett, P.K. On parameter estimation in population models, Theor. Popul. Biol., in press], for estimating the parameters of the stochastic SIS logistic model, and demonstrate ways in which these parameters may be used to estimate expected extinction times. Although the stochastic SIS logistic model is strictly density dependent and allows only for birth and death events, it nonetheless may be used to predict extinction times with some accuracy even for populations that are only weakly density dependent, or that are subject to catastrophes.     

Graph theory as a proxy for spatially explicit population models in conservation planning.

Spatially explicit population models (SEPMs) are often considered the best way to predict and manage species distributions in spatially heterogeneous landscapes. However, they are computationally intensive and require extensive knowledge of species' biology and behavior, limiting their application in many cases. An alternative to SEPMs is graph theory, which has minimal data requirements and efficient algorithms. Although only recently introduced to landscape ecology, graph theory is well suited to ecological applications concerned with connectivity or movement. This paper compares the performance of graph theory to a SEPM in selecting important habitat patches for Wood Thrush (Hylocichla mustelina) conservation. We use both models to identify habitat patches that act as population sources and persistent patches and also use graph theory to identify patches that act as stepping stones for dispersal. Correlations of patch rankings were very high between the two models. In addition, graph theory offers the ability to identify patches that are very important to habitat connectivity and thus long-term population persistence across the landscape. We show that graph theory makes very similar predictions in most cases and in other cases offers insight not available from the SEPM, and we conclude that graph theory is a suitable and possibly preferable alternative to SEPMs for species conservation in heterogeneous landscapes.     

Definition and calculation of uncertainty in ecological process models

We present a method of multi-criteria assessment for the analysis of process model uncertainty that combines analysis of model structure, parameters and data requirements. There are three components in calculation and definition of uncertainty.

(1)

Assessment criteria: Uncertainty in a process model is reduced as the model can simultaneously simulate an increased number of assessment criteria selected to test specific aspects of the theory being investigated, and within acceptable limits set for those criteria. This reduces incomplete specification of the model—the characteristic that a model may explain some, but not all, of the observed features of a phenomenon. The calculation required is computation of the Pareto set which provides the list of simultaneously achieved criteria within specified ranges.     

Testing the robustness of management decisions to uncertainty: Everglades restoration scenarios.

To effectively manage large natural reserves, resource managers must prepare for future contingencies while balancing the often conflicting priorities of different stakeholders. To deal with these issues, managers routinely employ models to project the response of ecosystems to different scenarios that represent alternative management plans or environmental forecasts. Scenario analysis is often used to rank such alternatives to aid the decision making process. However, model projections are subject to uncertainty in assumptions about model structure, parameter values, environmental inputs, and subcomponent interactions. We introduce an approach for testing the robustness of model-based management decisions to the uncertainty inherent in complex ecological models and their inputs. We use relative assessment to quantify the relative impacts of uncertainty on scenario ranking. To illustrate our approach we consider uncertainty in parameter values and uncertainty in input data, with specific examples drawn from the Florida Everglades restoration project. Our examples focus on two alternative 30-year hydrologic management plans that were ranked according to their overall impacts on wildlife habitat potential. We tested the assumption that varying the parameter settings and inputs of habitat index models does not change the rank order of the hydrologic plans. We compared the average projected index of habitat potential for four endemic species and two wading-bird guilds to rank the plans, accounting for variations in parameter settings and water level inputs associated with hypothetical future climates. Indices of habitat potential were based on projections from spatially explicit models that are closely tied to hydrology. For the American alligator, the rank order of the hydrologic plans was unaffected by substantial variation in model parameters. By contrast, simulated major shifts in water levels led to reversals in the ranks of the hydrologic plans in 24.1-30.6% of the projections for the wading bird guilds and several individual species. By exposing the differential effects of uncertainty, relative assessment can help resource managers assess the robustness of scenario choice in model-based policy decisions.     

Dynamic aspects of effluent taxation under uncertainty

The optimal adjustment process for an effluent charge is derived when the firm's response to the charge is uncertain. The optimal process is shown to exhibit the dual effects of caution and probing. Because of uncertainty, society should be risk averse or cautious when setting the charge. However, because of the possibility of generating information for improved future control, this caution is balanced by the incentive to probe for additional information. Finally, if the uncertain parameters of the firm's response function are nonautonomous, their change over time must be explicitly considered to avoid bias in estimation.