Sensitivity of population viability to spatial and nonspatial parameters using GRIP.

Metapopulation dynamics are influenced by spatial parameters including the amount and arrangement of suitable habitat, yet these parameters may be uncertain when deciding how to manage species or their habitats. Sensitivity analyses of population viability analysis (PVA) models can help measure relative parameter influences on predictions, identify research priorities for reducing uncertainty, and evaluate management strategies. Few spatial PVAs, however, include sensitivity analyses of both spatial and nonspatial parameters, perhaps because computationally efficient tools for such analyses are lacking or inaccessible. We developed GRIP, a program to facilitate sensitivity analysis of spatial and nonspatial input parameters for PVAs created in RAMAS Metapop, a widely applied software program. GRIP creates random sets of input files by varying parameters specified in the PVA model including vital rates and their correlations among populations, the number and configuration of populations, dispersal rates, dispersal survival, initial population abundances, carrying capacities, and the probability, intensity, and spatial extent of catastrophes, while drawing on specified parameter distributions. We evaluated GRIP's performance as a tool for sensitivity analysis of spatial PVAs and explored the consequences of varying spatial input parameters for predictions of a published PVA model of the sand lizard (Lacerta agilis). We used GRIP output to generate standardized regression coefficients (SRCs) and nonparametric correlation coefficients as indices of the relative sensitivity of predicted conservation status to input parameters. GRIP performed well; with a single analysis we were able to rank the relative influence of input parameters identified as influential by the PVA's original author, S. A. Berglind, who used three separate forms of sensitivity analysis. Our analysis, however, also underscored the value of exploring the relative influence of spatial parameters on PVA predictions; both SRCs and correlation coefficients indicated that the most influential parameters in the sand lizard model were spatial in nature. We provide annotated code so that GRIP may be modified to reflect particular species biology, customized for more complex spatial PVA models, upgraded to incorporate features added in newer versions of RAMAS Metapop, used as a template to develop similar programs, or used as it is for computationally efficient sensitivity analyses in support of conservation planning.     

Population Viability Analysis with Species Occurrence Data from Museum Collections

Abstract: The most comprehensive data on many species come from scientific collections. Thus, we developed a method of population viability analysis (PVA) in which this type of occurrence data can be used. In contrast to classical PVA, our approach accounts for the inherent observation error in occurrence data and allows the estimation of the population parameters needed for viability analysis. We tested the sensitivity of the approach to spatial resolution of the data, length of the time series, sampling effort, and detection probability with simulated data and conducted PVAs for common, rare, and threatened species. We compared the results of these PVAs with results of standard method PVAs in which observation error is ignored. Our method provided realistic estimates of population growth terms and quasi‐extinction risk in cases in which the standard method without observation error could not. For low values of any of the sampling variables we tested, precision decreased, and in some cases biased estimates resulted. The results of our PVAs with the example species were consistent with information in the literature on these species. Our approach may facilitate PVA for a wide range of species of conservation concern for which demographic data are lacking but occurrence data are readily available.     

The Interplay between Climate Variability and Density Dependence in the Population Viability of Chinook Salmon

Abstract:  The viability of populations is influenced by driving forces such as density dependence and climate variability, but most population viability analyses (PVAs) ignore these factors because of data limitations. Additionally, simplified PVAs produce limited measures of population viability such as annual population growth rate (λ) or extinction risk. Here we developed a "mechanistic" PVA of threatened Chinook salmon ( Oncorhynchus tshawytscha ) in which, based on 40 years of detailed data, we related freshwater recruitment of juveniles to density of spawners, and third-year survival in the ocean to monthly indices of broad-scale ocean and climate conditions. Including climate variability in the model produced important effects: estimated population viability was very sensitive to assumptions of future climate conditions and the autocorrelation contained in the climate signal increased mean population abundance while increasing probability of quasi extinction. Because of the presence of density dependence in the model, however, we could not distinguish among alternative climate scenarios through mean λ values, emphasizing the importance of considering multiple measures to elucidate population viability. Our sensitivity analyses demonstrated that the importance of particular parameters varied across models and depended on which viability measure was the response variable. The density-dependent parameter associated with freshwater recruitment was consistently the most important, regardless of viability measure, suggesting that increasing juvenile carrying capacity is important for recovery.     

The Sensitivity of Population Viability Analysis to Uncertainty about Habitat Requirements: Implications for the Management of the Endangered Southern Brown Bandicoot

Abstract:  Whenever population viability analysis (PVA) models are built to help guide decisions about the management of rare and threatened species, an important component of model building is the specification of a habitat model describing how a species is related to landscape or bioclimatic variables. Model-selection uncertainty may arise because there is often a great deal of ambiguity about which habitat model structure best approximates the true underlying biological processes. The standard approach to incorporate habitat models into PVA is to assume the best habitat model is correct, ignoring habitat-model uncertainty and alternative model structures that may lead to quantitatively different conclusions and management recommendations. Here we provide the first detailed examination of the influence of habitat-model uncertainty on the ranking of management scenarios from a PVA model. We evaluated and ranked 6 management scenarios for the endangered southern brown bandicoot ( Isoodon obesulus ) with PVA models, each derived from plausible competing habitat models developed with logistic regression. The ranking of management scenarios was sensitive to the choice of the habitat model used in PVA predictions. Our results demonstrate the need to incorporate methods into PVA that better account for model uncertainty and highlight the sensitivity of PVA to decisions made during model building. We recommend that researchers search for and consider a range of habitat models when undertaking model-based decision making and suggest that routine sensitivity analyses should be expanded to include an analysis of the impact of habitat-model uncertainty and assumptions.     

A critical appraisal of population viability analysis

Population viability analysis (PVA) is useful in management of imperiled species. Applications range from research design, threat assessment, and development of management frameworks. Given the importance of PVAs, it is essential that they be rigorous and adhere to widely accepted guidelines; however, the quality of published PVAs is rarely assessed. We evaluated the quality of 160 PVAs of 144 species of birds and mammals published in peer-reviewed journals from 1990 to 2017. We hypothesized that PVA quality would be lower with generic programs than with custom-built programs; be higher for those developed for imperiled species; change over time; and be higher for those published in journals with high impact factors (IFs). Each included study was evaluated based on answers to an evaluation framework containing 32 questions reflecting whether and to what extent the PVA study adhered to published PVA guidelines or contained important PVA components. All measures of PVA quality were generally lower for studies based on generic programs. Conservation status of the species did not affect any measure of PVA quality, but PVAs published in high IF journals were of higher quality. Quality generally declined over time, suggesting the quantitative literacy of PVA practitioners has not increased over time or that PVAs developed by unskilled users are being published in peer-reviewed journals. Only 18.1% of studies were of high quality (score >75%), which is troubling because poor-quality PVAs could misinform conservation decisions. We call for increased scrutiny of PVAs by journal editors and reviewers. Our evaluation framework can be used for this purpose. Because poor-quality PVAs continue to be published, we recommend caution while using PVA results in conservation decision making without thoroughly assessing the PVA quality.     

Incorporating evolutionary processes into population viability models

We examined how ecological and evolutionary (eco‐evo) processes in population dynamics could be better integrated into population viability analysis (PVA). Complementary advances in computation and population genomics can be combined into an eco‐evo PVA to offer powerful new approaches to understand the influence of evolutionary processes on population persistence. We developed the mechanistic basis of an eco‐evo PVA using individual‐based models with individual‐level genotype tracking and dynamic genotype–phenotype mapping to model emergent population‐level effects, such as local adaptation and genetic rescue. We then outline how genomics can allow or improve parameter estimation for PVA models by providing genotypic information at large numbers of loci for neutral and functional genome regions. As climate change and other threatening processes increase in rate and scale, eco‐evo PVAs will become essential research tools to evaluate the effects of adaptive potential, evolutionary rescue, and locally adapted traits on persistence.     

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     

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.     

Predictive vegetation modeling for conservation: impact of error propagation from digital elevation data.

The effect of digital elevation model (DEM) error on environmental variables, and subsequently on predictive habitat models, has not been explored. Based on an error analysis of a DEM, multiple error realizations of the DEM were created and used to develop both direct and indirect environmental variables for input to predictive habitat models. The study explores the effects of DEM error and the resultant uncertainty of results on typical steps in the modeling procedure for prediction of vegetation species presence/absence. Results indicate that all of these steps and results, including the statistical significance of environmental variables, shapes of species response curves in generalized additive models (GAMs), stepwise model selection, coefficients and standard errors for generalized linear models (GLMs), prediction accuracy (Cohen's kappa and AUC), and spatial extent of predictions, were greatly affected by this type of error. Error in the DEM can affect the reliability of interpretations of model results and level of accuracy in predictions, as well as the spatial extent of the predictions. We suggest that the sensitivity of DEM-derived environmental variables to error in the DEM should be considered before including them in the modeling processes.     

Using demography and movement behavior to predict range expansion of the southern sea otter

In addition to forecasting population growth, basic demographic data combined with movement data provide a means for predicting rates of range expansion. Quantitative models of range expansion have rarely been applied to large vertebrates, although such tools could be useful for restoration and management of many threatened but recovering populations. Using the southern sea otter (Enhydra lutris nereis) as a case study, we utilized integro-difference equations in combination with a stage-structured projection matrix that incorporated spatial variation in dispersal and demography to make forecasts of population recovery and range recolonization. In addition to these basic predictions, we emphasize how to make these modeling predictions useful in a management context through the inclusion of parameter uncertainty and sensitivity analysis. Our models resulted in hind-cast (1989-2003) predictions of net population growth and range expansion that closely matched observed patterns. We next made projections of future range expansion and population growth, incorporating uncertainty in all model parameters, and explored the sensitivity of model predictions to variation in spatially explicit survival and dispersal rates. The predicted rate of southward range expansion (median = 5.2 km/yr) was sensitive to both dispersal and survival rates; elasticity analysis indicated that changes in adult survival would have the greatest potential effect on the rate of range expansion, while perturbation analysis showed that variation in subadult dispersal contributed most to variance in model predictions. Variation in survival and dispersal of females at the south end of the range contributed most of the variance in predicted southward range expansion. Our approach provides guidance for the acquisition of further data and a means of forecasting the consequence of specific management actions. Similar methods could aid in the management of other recovering populations.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

Incorporating landscape stochasticity into population viability analysis.

The importance of incorporating landscape dynamics into population viability analysis (PVA) has previously been acknowledged, but the need to repeat the landscape generation process to encapsulate landscape stochasticity in model outputs has largely been overlooked. Reasons for this are that (1) there is presently no means for quantifying the relative effects of landscape stochasticity and population stochasticity on model outputs, and therefore no means for determining how to allocate simulation time optimally between the two; and (2) the process of generating multiple landscapes to incorporate landscape stochasticity is tedious and user-intensive with current PVA software. Here we demonstrate that landscape stochasticity can be an important source of variance in model outputs. We solve the technical problems with incorporating landscape stochasticity by deriving a formula that gives the optimal ratio of population simulations to landscape simulations for a given model, and by providing a computer program that incorporates the formula and automates multiple landscape generation in a dynamic landscape metapopulation (DLMP) model. Using a case study of a bird population, we produce estimates of DLMP model output parameters that are up to four times more precise than those estimated from a single landscape in the same amount of total simulation time. We use the DLMP modeling software RAMAS Landscape to run the landscape and metapopulation models, though our method is general and could be applied to any PVA platform. The results of this study should motivate DLMP modelers to consider landscape stochasticity in their analyses.     

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.     

Hierarchical Bayesian Spatial Models for Multispecies Conservation Planning and Monitoring

Abstract: Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence–absence data derived from regional monitoring programs to develop models with both landscape and site‐level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence–absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad‐scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km² hexagons), can increase the relevance of habitat models to multispecies conservation planning.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

GIS and geostatistics: Essential partners for spatial analysis

Initially, geographical information systems (GIS) concentrated on two issues: automated map making, and facilitating the comparison of data on thematic maps. The first required high quality graphics, vector data models and powerful data bases, the second is based on grid cells that can be manipulated by suites of mathematical operators collectively termed map algebra. Both kinds of GIS are widely available and are taught in many universities and technical colleges. After more than 20 years of development, most standard GIS provide both kinds of functionality and good quality graphic display, but until recently they have not included the methods of statistics and geostatistics as tools for spatial analysis. Recently, standard statistical packages have been linked to GIS for both exploratory data analysis and statistical analysis and hypothesis testing. Standard statistical packages include methods for the analysis of random samples of cases or objects that are not necessarily co-located in space—if the results of statistical analysis display a spatial pattern then that is because the underlying data also share that pattern. Geostatistics addresses the need to make predictions of sampled attributes (i.e., maps) at unsampled locations from sparse, often expensive data. To make up for lack of hard data geostatistics has concentrated on the development of powerful methods based on stochastic theory. Though there have been recent moves to incorporate ancillary data in geostatistical analyses, insufficient attention has been paid to using modern methods of data display for the visualization of results. GIS can serve geostatistics by aiding geo-registration of data, facilitating spatial exploratory data analysis, providing a spatial context for interpolation and conditional simulation, as well as providing easy-to-use and effective tools for data display and visualization. The value of geostatistics for GIS lies in the provision of reliable interpolation methods with known errors, methods of upscaling and generalization, and for supplying multiple realizations of spatial patterns that can be used in environmental modeling. These stochastic methods are improving understanding of how errors in models of spatial processes accrue from errors in data or incompleteness in the structure of the models. New developments in GIS, based on ideas taken from map algebra, cellular automata and image analysis are providing high level programming languages for modeling dynamic processes such as erosion or the development of alluvial fans and deltas. Research has demonstrated that these models need stochastic inputs to yield realistic results. Non-stochastic tools such as fuzzy subsets have been shown to be useful for spatial analysis when probabilistic approaches are inappropriate or impossible. The conclusion is that in spite of differences in history and approach, the linkage of GIS, statistics and geostatistics provides a powerful, and complementary suite of tools for spatial analysis in the agricultural, earth and environmental sciences.