A case study of bats and white‐nose syndrome demonstrating how to model population viability with evolutionary effects

Ecological factors generally affect population viability on rapid time scales. Traditional population viability analyses (PVA) therefore focus on alleviating ecological pressures, discounting potential evolutionary impacts on individual phenotypes. Recent studies of evolutionary rescue (ER) focus on cases in which severe, environmentally induced population bottlenecks trigger a rapid evolutionary response that can potentially reverse demographic threats. ER models have focused on shifting genetics and resulting population recovery, but no one has explored how to incorporate those findings into PVA. We integrated ER into PVA to identify the critical decision interval for evolutionary rescue (DIER) under which targeted conservation action should be applied to buffer populations undergoing ER against extinction from stochastic events and to determine the most appropriate vital rate to target to promote population recovery. We applied this model to little brown bats (Myotis lucifugus) affected by white‐nose syndrome (WNS), a fungal disease causing massive declines in several North American bat populations. Under the ER scenario, the model predicted that the DIER period for little brown bats was within 11 years of initial WNS emergence, after which they stabilized at a positive growth rate (λ = 1.05). By comparing our model results with population trajectories of multiple infected hibernacula across the WNS range, we concluded that ER is a potential explanation of observed little brown bat population trajectories across multiple hibernacula within the affected range. Our approach provides a tool that can be used by all managers to provide testable hypotheses regarding the occurrence of ER in declining populations, suggest empirical studies to better parameterize the population genetics and conservation‐relevant vital rates, and identify the DIER period during which management strategies will be most effective for species conservation.     

Environment-specific elasticity and sensitivity analysis of the stochastic growth rate

For matrix population models, analyses of how sensitive the population growth rate is to changes in vital rates (i.e. perturbations) are important for studies of life history evolution as well as for management and conservation of threatened species. There are two types of sensitivity analyses corresponding to absolute (sensitivity) or relative (elasticity) changes in the vital rates and both types can be applied to both deterministic and stochastic matrix population models. To date, most empirical studies of elasticity and sensitivity of the stochastic growth rate have examined the response to perturbations in the vital rates in a complete set of possible environments. However, it is often of interest to examine the response to perturbations occurring in only a subset of the possible environments. This has been done for periodic time-varying models elsewhere, but here we describe a recently published method for calculating the environment-specific sensitivity and elasticity of the stochastic growth rate and apply this method to data. These environment-specific perturbation analyses provide a logical way of dividing the sensitivity and elasticity among the environments. They give important insight into the selection regime in different environments and can provide valuable information for making management decisions and management evaluations in stochastic environments.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

Actual and Potential Use of Population Viability Analyses in Recovery of Plant Species Listed under the U.S. Endangered Species Act

Use of population viability analyses (PVAs) in endangered species recovery planning has been met with both support and criticism. Previous reviews promote use of PVA for setting scientifically based, measurable, and objective recovery criteria and recommend improvements to increase the framework's utility. However, others have questioned the value of PVA models for setting recovery criteria and assert that PVAs are more appropriate for understanding relative trade‐offs between alternative management actions. We reviewed 258 final recovery plans for 642 plants listed under the U.S. Endangered Species Act to determine the number of plans that used or recommended PVA in recovery planning. We also reviewed 223 publications that describe plant PVAs to assess how these models were designed and whether those designs reflected previous recommendations for improvement of PVAs. Twenty‐four percent of listed species had recovery plans that used or recommended PVA. In publications, the typical model was a matrix population model parameterized with ≤5 years of demographic data that did not consider stochasticity, genetics, density dependence, seed banks, vegetative reproduction, dormancy, threats, or management strategies. Population growth rates for different populations of the same species or for the same population at different points in time were often statistically different or varied by >10%. Therefore, PVAs parameterized with underlying vital rates that vary to this degree may not accurately predict recovery objectives across a species’ entire distribution or over longer time scales. We assert that PVA, although an important tool as part of an adaptive‐management program, can help to determine quantitative recovery criteria only if more long‐term data sets that capture spatiotemporal variability in vital rates become available. Lacking this, there is a strong need for viable and comprehensive methods for determining quantitative, science‐based recovery criteria for endangered species with minimal data availability. Uso Actual y Potencial del Análisis de Viabilidad Poblacional para la Recuperación de Especies de Plantas Enlistadas en el Acta de Especies En Peligro de E.U.A     

Population viability analysis for several populations using multivariate state-space models

The International Union for the Conservation of Nature and Natural Resources (IUCN), the world's largest and most important global conservation network, has listed approximately 16,000 species worldwide as threatened. The most important tool for recognizing and listing species as threatened is population viability analysis (PVA), which estimates the probability of extinction of a population or species over a specified time horizon. The most common PVA approach is to apply it to single time series of population abundance. This approach to population viability analysis ignores covariability of local populations. Covariability can be important because high synchrony of local populations reduces the effective number of local populations and leads to greater extinction risk. Needed is a way of extending PVA to model correlation structure among multiple local populations. Multivariate state-space modeling is applied to this problem and alternative estimation methods are compared. The multivariate state-space technique is applied to endangered populations of pacific salmon, USA. Simulations demonstrated that the correlation structure can strongly influence population viability and is best estimated using restricted maximum likelihood instead of maximum likelihood.     

Longevity can buffer plant and animal populations against changing climatic variability

Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Reliability of Absolute and Relative Predictions of Population Persistence Based on Time Series

Abstract:  Conventional population viability analysis (PVA) is often impractical because data are scarce for many threatened species. For this reason, simple count-based models are being advocated. The simplest of these models requires nothing more than a time series of abundance estimates, from which variance and autocorrelation in growth rate are estimated and predictions of population persistence are generated. What remains unclear, however, is how many years of data are needed to generate reliable estimates of these parameters and hence reliable predictions of persistence. By analyzing published and simulated time series, we show that several decades of data are needed. Predictions based on short time series were very unreliable mainly because limited data yielded biased, unreliable estimates of variance in growth rate, especially when growth rate was strongly autocorrelated. More optimistically, our results suggest that count-based PVA is sometimes useful for relative risk assessment (i.e., for ranking populations by extinction risk), even when time series are only a decade long. However, some conditions consistently lead to backward rankings. We explored the limited conditions under which simple count-based PVA may be useful for relative risk assessment.     

A Behaviorally Explicit Demographic Model Integrating Habitat Selection and Population Dynamics in California Sea Lions

Abstract: Although there has been a call for the integration of behavioral ecology and conservation biology, there are few tools currently available to achieve this integration. Explicitly including information about behavioral strategies in population viability analyses may enhance the ability of conservation biologists to understand and estimate patterns of extinction risk. Nevertheless, most behavioral‐based PVA approaches require detailed individual‐based data that are rarely available for imperiled species. We present a mechanistic approach that incorporates spatial and demographic consequences of behavioral strategies into population models used for conservation. We developed a stage‐structured matrix model that includes the costs and benefits of movement associated with 2 habitat‐selection strategies (philopatry and direct assessment). Using a life table for California sea lions (Zalophus californianus), we explored the sensitivity of model predictions to the inclusion of these behavioral parameters. Including behavioral information dramatically changed predicted population sizes, model dynamics, and the expected distribution of individuals among sites. Estimated population sizes projected in 100 years diverged up to 1 order of magnitude among scenarios that assumed different movement behavior. Scenarios also exhibited different model dynamics that ranged from stable equilibria to cycles or extinction. These results suggest that inclusion of behavioral data in viability models may improve estimates of extinction risk for imperiled species. Our approach provides a simple method for incorporating spatial and demographic consequences of behavioral strategies into population models and may be easily extended to other species and behaviors to understand the mechanisms of population dynamics for imperiled populations.     

Identifying robust strategies for assisted migration in a competitive stochastic metacommunity

Assisted migration (AM) is the translocation of species beyond their historical range to locations that are expected to be more suitable under future climate change. However, a relocated population may fail to establish in its donor community if there is high uncertainty in decision-making, climate, and interactions with the recipient ecological community. To quantify the benefit to persistence and risk of establishment failure of AM under different management scenarios (e.g., choosing target species, proportion of population to relocate, and optimal location to relocate), we built a stochastic metacommunity model to simulate several species reproducing, dispersing, and competing on a temperature gradient as temperature increases over time. Without AM, the species were vulnerable to climate change when they had low population sizes, short dispersal, and strong poleward competition. When relocating species that exemplified these traits, AM increased the long-term persistence of the species most when relocating a fraction of the donor population, even if the remaining population was very small or rapidly declining. This suggests that leaving behind a fraction of the population could be a robust approach, allowing managers to repeat AM in case they move the species to the wrong place and at the wrong time, especially when it is difficult to identify a species’ optimal climate. We found that AM most benefitted species with low dispersal ability and least benefited species with narrow thermal tolerances, for which AM increased extinction risk on average. Although relocation did not affect the persistence of nontarget species in our simple competitive model, researchers will need to consider a more complete set of community interactions to comprehensively understand invasion potential.     

Climate change threatens polar bear populations: a stochastic demographic analysis

The polar bear (Ursus maritimus) depends on sea ice for feeding, breeding, and movement. Significant reductions in Arctic sea ice are forecast to continue because of climate warming. We evaluated the impacts of climate change on polar bears in the southern Beaufort Sea by means of a demographic analysis, combining deterministic, stochastic, environment-dependent matrix population models with forecasts of future sea ice conditions from IPCC general circulation models (GCMs). The matrix population models classified individuals by age and breeding status; mothers and dependent cubs were treated as units. Parameter estimates were obtained from a capture-recapture study conducted from 2001 to 2006. Candidate statistical models allowed vital rates to vary with time and as functions of a sea ice covariate. Model averaging was used to produce the vital rate estimates, and a parametric bootstrap procedure was used to quantify model selection and parameter estimation uncertainty. Deterministic models projected population growth in years with more extensive ice coverage (2001-2003) and population decline in years with less ice coverage (2004-2005). LTRE (life table response experiment) analysis showed that the reduction in lambda in years with low sea ice was due primarily to reduced adult female survival, and secondarily to reduced breeding. A stochastic model with two environmental states, good and poor sea ice conditions, projected a declining stochastic growth rate, log lambdas, as the frequency of poor ice years increased. The observed frequency of poor ice years since 1979 would imply log lambdas approximately - 0.01, which agrees with available (albeit crude) observations of population size. The stochastic model was linked to a set of 10 GCMs compiled by the IPCC; the models were chosen for their ability to reproduce historical observations of sea ice and were forced with "business as usual" (A1B) greenhouse gas emissions. The resulting stochastic population projections showed drastic declines in the polar bear population by the end of the 21st century. These projections were instrumental in the decision to list the polar bear as a threatened species under the U.S. Endangered Species Act.     

A noninvasive demographic assessment of sea lions based on stage-specific abundances

A pressing need exists to develop new approaches for obtaining information on demographic rates without causing further threats to imperiled animal populations. In this paper, we illustrate and apply a data-fitting technique based on quadratic programming that uses stage-specific abundance data to estimate demographic rates and asymptotic population growth rates (lambda). We used data from seven breeding colonies of California sea lions (Zalophus californianus) in the Gulf of California, Mexico. Estimates of lambda were similar to those from previous studies relying on a diffusion approximation using trends in total abundance. On average, predicted abundances were within 24% of the observed value for the inverse estimation method and within 29% of the observed value for the diffusion approximation. Our results suggest that three of the seven populations are declining (lambda < 1), but as many as six may be at risk. Elasticity and sensitivity analyses suggest that population management in most sites should focus on the protection of adults, whose survival generally contributes the most to lambda. The quadratic programming approach is a promising noninvasive technique for estimating demographic rates and assessing the viability of populations of imperiled species.     

Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories

Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life-history traits in the two ecotypes, which, in turn, affect population dynamics. M-slow populations have evolved life-history traits that buffer fitness against direct effects of variation in reproduction and that spread lifetime reproduction across a greater number of reproductive bouts. These results highlight the importance of long-term demographic and environmental monitoring and of incorporating temporal dynamics into empirical studies of life-history evolution.     

Importance of individual and environmental variation for invasive species spread: a spatial integral projection model

Plant survival, growth, and flowering are size dependent in many plant populations but also vary among individuals of the same size. This individual variation, along with variation in dispersal caused by differences in, e.g., seed release height, seed characteristics, and wind speed, is a key determinant of the spread rate of species through homogeneous landscapes. Here we develop spatial integral projection models (SIPMs) that include both demography and dispersal with continuous state variables. The advantage of this novel approach over discrete-stage spread models is that the effect of variation in plant size and size-dependent vital rates can be studied at much higher resolution. Comparing Neubert-Caswell matrix models to SIPMs allowed us to assess the importance of including individual variation in the models. As a test case we parameterized a SIPM with previously published data on the invasive monocarpic thistle Carduus nutans in New Zealand. Spread rate (c*) estimates were 34% lower than for standard spatial matrix models and stabilized with as few as seven evenly distributed size classes. The SIPM allowed us to calculate spread rate elasticities over the range of plant sizes, showing the size range of seedlings that contributed most to c* through their survival, growth and reproduction. The annual transitions of these seedlings were also the most important ones for local population growth (lambda). However, seedlings that reproduced within a year contributed relatively more to c* than to lambda. In contrast, plants that grow over several years to reach a large size and produce many more seeds, contributed relatively more to lambda than to c*. We show that matrix models pick up some of these details, while other details disappear within wide size classes. Our results show that SIPMs integrate various sources of variation much better than discrete-stage matrix models. Simpler, heuristic models, however, remain very valuable in studies where the main goal is to investigate the general impact of a life history stage on population dynamics. We conclude with a discussion of future extensions of SIPMs, including incorporation of continuous time and environmental drivers.     

Multi-model analysis of tree competition along environmental gradients in southern New England forests.

Robust predictions of competitive interactions among canopy trees and variation in tree growth along environmental gradients represent key challenges for the management of mixed-species, uneven-aged forests. We analyzed the effects of competition on tree growth along environmental gradients for eight of the most common tree species in southern New England and southeastern New York using forest inventory and analysis (FIA) data, information theoretic decision criteria, and multi-model inference to evaluate models. The suite of models estimated growth of individual trees as a species-specific function of average potential diameter growth, tree diameter at breast height, local environmental conditions, and crowding by neighboring trees. We used ordination based on the relative basal area of species to generate a measure of site conditions in each plot. Two ordination axes were consistent with variation in species abundance along moisture and fertility gradients. Estimated potential growth varied along at least one of these axes for six of the eight species; peak relative abundance of less shade-tolerant species was in all cases displaced away from sites where they showed maximum potential growth. Our crowding functions estimate the strength of competitive effects of neighbors; only one species showed support for the hypothesis that all species of competitors have equivalent effects on growth. The relative weight of evidence (Akaike weights) for the best models varied from a low of 0.207 for Fraxinus americana to 0.747 for Quercus rubra. In such cases, model averaging provides a more robust platform for prediction than that based solely on the best model. We show that predictions based on the selected best models dramatically overestimated differences between species relative to predictions based on the averaged set of models.     

Nonlinear relationships between vital rates and state variables in demographic models

To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.     

Effects of uncertainty and variability on population declines and IUCN Red List classifications

The International Union for Conservation of Nature (IUCN) Red List Categories and Criteria is a quantitative framework for classifying species according to extinction risk. Population models may be used to estimate extinction risk or population declines. Uncertainty and variability arise in threat classifications through measurement and process error in empirical data and uncertainty in the models used to estimate extinction risk and population declines. Furthermore, species traits are known to affect extinction risk. We investigated the effects of measurement and process error, model type, population growth rate, and age at first reproduction on the reliability of risk classifications based on projected population declines on IUCN Red List classifications. We used an age‐structured population model to simulate true population trajectories with different growth rates, reproductive ages and levels of variation, and subjected them to measurement error. We evaluated the ability of scalar and matrix models parameterized with these simulated time series to accurately capture the IUCN Red List classification generated with true population declines. Under all levels of measurement error tested and low process error, classifications were reasonably accurate; scalar and matrix models yielded roughly the same rate of misclassifications, but the distribution of errors differed; matrix models led to greater overestimation of extinction risk than underestimations; process error tended to contribute to misclassifications to a greater extent than measurement error; and more misclassifications occurred for fast, rather than slow, life histories. These results indicate that classifications of highly threatened taxa (i.e., taxa with low growth rates) under criterion A are more likely to be reliable than for less threatened taxa when assessed with population models. Greater scrutiny needs to be placed on data used to parameterize population models for species with high growth rates, particularly when available evidence indicates a potential transition to higher risk categories.     

Implications of different population model structures for management of threatened plants

Population viability analysis (PVA) is a reliable tool for ranking management options for a range of species despite parameter uncertainty. No one has yet investigated whether this holds true for model uncertainty for species with complex life histories and for responses to multiple threats. We tested whether a range of model structures yielded similar rankings of management and threat scenarios for 2 plant species with complex postfire responses. We examined 2 contrasting species from different plant functional types: an obligate seeding shrub and a facultative resprouting shrub. We exposed each to altered fire regimes and an additional, species‐specific threat. Long‐term demographic data sets were used to construct an individual‐based model (IBM), a complex stage‐based model, and a simple matrix model that subsumes all life stages into 2 or 3 stages. Agreement across models was good under some scenarios and poor under others. Results from the simple and complex matrix models were more similar to each other than to the IBM. Results were robust across models when dominant threats are considered but were less so for smaller effects. Robustness also broke down as the scenarios deviated from baseline conditions, likely the result of a number of factors related to the complexity of the species’ life history and how it was represented in a model. Although PVA can be an invaluable tool for integrating data and understanding species’ responses to threats and management strategies, this is best achieved in the context of decision support for adaptive management alongside multiple lines of evidence and expert critique of model construction and output.     

Forecasting extinction risk with nonstationary matrix models.

Matrix population growth models are standard tools for forecasting population change and for managing rare species, but they are less useful for predicting extinction risk in the face of changing environmental conditions. Deterministic models provide point estimates of lambda, the finite rate of increase, as well as measures of matrix sensitivity and elasticity. Stationary matrix models can be used to estimate extinction risk in a variable environment, but they assume that the matrix elements are randomly sampled from a stationary (i.e., non-changing) distribution. Here we outline a method for using nonstationary matrix models to construct realistic forecasts of population fluctuation in changing environments. Our method requires three pieces of data: (1) field estimates of transition matrix elements, (2) experimental data on the demographic responses of populations to altered environmental conditions, and (3) forecasting data on environmental drivers. These three pieces of data are combined to generate a series of sequential transition matrices that emulate a pattern of long-term change in environmental drivers. Realistic estimates of population persistence and extinction risk can be derived from stochastic permutations of such a model. We illustrate the steps of this analysis with data from two populations of Sarracenia purpurea growing in northern New England. Sarracenia purpurea is a perennial carnivorous plant that is potentially at risk of local extinction because of increased nitrogen deposition. Long-term monitoring records or models of environmental change can be used to generate time series of driver variables under different scenarios of changing environments. Both manipulative and natural experiments can be used to construct a linking function that describes how matrix parameters change as a function of the environmental driver. This synthetic modeling approach provides quantitative estimates of extinction probability that have an explicit mechanistic basis.     

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.