Beth Gardner

Spatially explicit inference for open populations: estimating demographic parameters from camera-trap studies

We develop a hierarchical capture-recapture model for demographically open populations when auxiliary spatial information about location of capture is obtained. Such spatial capture-recapture data arise from studies based on camera trapping, DNA sampling, and other situations in which a spatial array of devices records encounters of unique individuals. We integrate an individual-based formulation of a Jolly-Seber type model with recently developed spatially explicit capture-recapture models to estimate density and demographic parameters for survival and recruitment. We adopt a Bayesian framework for inference under this model using the method of data augmentation which is implemented in the software program WinBUGS. The model was motivated by a camera trapping study of Pampas cats Leopardus colocolo from Argentina, which we present as an illustration of the model in this paper. We provide estimates of density and the first quantitative assessment of vital rates for the Pampas cat in the High Andes. The precision of these estimates is poor due likely to the sparse data set. Unlike conventional inference methods which usually rely on asymptotic arguments, Bayesian inferences are valid in arbitrary sample sizes, and thus the method is ideal for the study of rare or endangered species for which small data sets are typical.

Estimating black bear density using DNA data from hair snares.

Abstract DNA-based mark–recapture has become a methodological cornerstone of research focused on bear species. The objective of such studies is often to estimate population size; however, doing so is frequently complicated by movement of individual bears. Movement affects the probability of detection and the assumption of closure of the population required in most models. To mitigate the bias caused by movement of individuals, population size and density estimates are often adjusted using ad hoc methods, including buffering the minimum polygon of the trapping array. We used a hierarchical, spatial capture–recapture model that contains explicit components for the spatial-point process that governs the distribution of individuals and their exposure to (via movement), and detection by, traps. We modeled detection probability as a function of each individuals distance to the trap and an indicator variable for previous capture to account for possible behavioral responses. We applied our model to a 2006 hair-snare study of a black bear (Ursus americanus) population in northern New York, USA. Based on the microsatellite marker analysis of collected hair samples, 47 individuals were identified. We estimated mean density at 0.20 bears/km2. A positive estimate of the indicator variable suggests that bears are attracted to baited sites; therefore, including a trap-dependence covariate is important when using bait to attract individuals. Bayesian analysis of the model was implemented in WinBUGS, and we provide the model specification. The model can be applied to any spatially organized trapping array (hair snares, camera traps, mist nests, etc.) to estimate density and can also account for heterogeneity and covariate information at the trap or individual level.

Hierarchical models for estimating density from DNA mark–recapture studies

Genetic sampling is increasingly used as a tool by wildlife biologists and managers to estimate abundance and density of species. Typically, DNA is used to identify individuals captured in an array of traps (e.g., baited hair snares) from which individual encounter histories are derived. Standard methods for estimating the size of a closed population can be applied to such data. However, due to the movement of individuals on and off the trapping array during sampling, the area over which individuals are exposed to trapping is unknown, and so obtaining unbiased estimates of density has proved difficult. We propose a hierarchical spatial capture-recapture model which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to (via movement) and detection by traps. Detection probability is modeled as a function of each individuals distance to the trap. We applied this model to a black bear (Ursus americanus) study conducted in 2006 using a hair-snare trap array in the Adirondack region of New York, USA. We estimated the density of bears to be 0.159 bears/km2, which is lower than the estimated density (0.410 bears/km2) based on standard closed population techniques. A Bayesian analysis of the model is fully implemented in the software program WinBUGS.

Imperfect detection is the rule rather than the exception in plant distribution studies

Summary 1. Imperfect detection can seriously bias conventional estimators of species distributions and species richness. Plant traits, survey-specific conditions and site-specific characteristics may influence plant detection probability. However, the generality of the problems induced by imperfect detection in plants and the magnitude of this challenge for plant distribution studies are currently unknown. 2. We address this question based on data from the Swiss Biodiversity Monitoring, in which vascular plants are surveyed twice in the same year along a 2.5-km transect in 451 1-km 2 quadrats. Overall, 1700 species were recorded. We chose a random sample of 100 species from the 1700 species to determine general detection levels. To examine the relationship of covariates on detection, we chose a stratified random sample of 100 species from 886 species that were detected in at least 18 locations, with 25 each from four life-forms (LF): grass, forb, shrub and tree. Using a Bayesian multispecies site-occupancy model, we estimated occurrence and detection probability of these species and their relation to covariates. 3. Based on the random sample of 100 species, detection probability during the first survey ranged 0.03–0.99 (median 0.74) and during the second survey, 0.03–0.99 (median 0.82). Based on the stratified random sample of 100 species, detection probability during the first survey ranged 0.02–0.99 (median 0.87) and during the second survey, 0.01–1 (median 0.89). Detection probability differed slightly among the four LFs. In 60 species, survey season or elevation had significant effects on detection. We illustrated detection probability maps for Switzerland based on the modelled relationships with environmental covariates. 4. Synthesis. Our findings suggest that even in a standardized monitoring program, imperfect detection of plants may be common. With the absence of a correction for detection errors, maps in plant distribution studies will be confounded with spatial patterns in detection probability. We presume that these problems will be much more widespread in the data sets that are used for conventional plant species distribution modelling. Imperfect detection should be estimated, even in distribution studies of plants and other sessile organisms, to better control detection errors that may compromise the results of species distribution studies.

How does spatial study design influence density estimates from spatial capture-recapture models?

When estimating population density from data collected on non-invasive detector arrays, recently developed spatial capture-recapture (SCR) models present an advance over non-spatial models by accounting for individual movement. While these models should be more robust to changes in trapping designs, they have not been well tested. Here we investigate how the spatial arrangement and size of the trapping array influence parameter estimates for SCR models. We analysed black bear data collected with 123 hair snares with an SCR model accounting for differences in detection and movement between sexes and across the trapping occasions. To see how the size of the trap array and trap dispersion influence parameter estimates, we repeated analysis for data from subsets of traps: 50% chosen at random, 50% in the centre of the array and 20% in the South of the array. Additionally, we simulated and analysed data under a suite of trap designs and home range sizes. In the black bear study, we found that results were similar across trap arrays, except when only 20% of the array was used. Black bear density was approximately 10 individuals per 100 km2. Our simulation study showed that SCR models performed well as long as the extent of the trap array was similar to or larger than the extent of individual movement during the study period, and movement was at least half the distance between traps. SCR models performed well across a range of spatial trap setups and animal movements. Contrary to non-spatial capture-recapture models, they do not require the trapping grid to cover an area several times the average home range of the studied species. This renders SCR models more appropriate for the study of wide-ranging mammals and more flexible to design studies targeting multiple species.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

The ecology of religious beliefs

Significance Here we show that the spatial prevalence of human societies that believe in moralizing high gods can be predicted with a high level of accuracy (91%) from historical, social, and ecological data. Using high-resolution datasets, we systematically estimate the relative effects of resource abundance, ecological risk, cultural diffusion, shared ancestry, and political complexity on the global distribution of beliefs in moralizing high gods. The methods presented in this paper provide a blueprint for how to leverage the increasing wealth of ecological, linguistic, and historical data to understand the forces that have shaped the behavior of our own species. Although ecological forces are known to shape the expression of sociality across a broad range of biological taxa, their role in shaping human behavior is currently disputed. Both comparative and experimental evidence indicate that beliefs in moralizing high gods promote cooperation among humans, a behavioral attribute known to correlate with environmental harshness in nonhuman animals. Here we combine fine-grained bioclimatic data with the latest statistical tools from ecology and the social sciences to evaluate the potential effects of environmental forces, language history, and culture on the global distribution of belief in moralizing high gods (n = 583 societies). After simultaneously accounting for potential nonindependence among societies because of shared ancestry and cultural diffusion, we find that these beliefs are more prevalent among societies that inhabit poorer environments and are more prone to ecological duress. In addition, we find that these beliefs are more likely in politically complex societies that recognize rights to movable property. Overall, our multimodel inference approach predicts the global distribution of beliefs in moralizing high gods with an accuracy of 91%, and estimates the relative importance of different potential mechanisms by which this spatial pattern may have arisen. The emerging picture is neither one of pure cultural transmission nor of simple ecological determinism, but rather a complex mixture of social, cultural, and environmental influences. Our methods and findings provide a blueprint for how the increasing wealth of ecological, linguistic, and historical data can be leveraged to understand the forces that have shaped the behavior of our own species.

A spatial mark–resight model augmented with telemetry data

Abundance and population density are fundamental pieces of information for population ecology and species conservation, but they are difficult to estimate for rare and elusive species. Mark--resight models are popular for estimating population abundance because they are less invasive and expensive than traditional mark-recapture. However, density estimation using mark-resight is difficult because the area sampled must be explicitly defined, historically using ad hoc approaches. We developed a spatial mark--resight model for estimating population density that combines spatial resighting data and telemetry data. Incorporating telemetry data allows us to inform model parameters related to movement and individual location. Our model also allows <100% individual identification of marked individuals. We implemented the model in a Bayesian framework, using a custom-made Metropolis-within-Gibbs Markov chain Monte Carlo algorithm. As an example, we applied this model to a mark--resight study of raccoons (Procyon lotor) on South Core Banks, a barrier island in Cape Lookout National Seashore, North Carolina, USA. We estimated a population of 186.71 +/- 14.81 individuals, which translated to a density of 8.29 +/- 0.66 individuals/km2 (mean +/- SD). The model presented here will have widespread utility in future applications, especially for species that are not naturally marked.

Density estimation in a wolverine population using spatial capture–recapture models

ABSTRACT Classical closed-population capture—recapture models do not accommodate the spatial information inherent in encounter history data obtained from camera-trapping studies. As a result, individual heterogeneity in encounter probability is induced, and it is not possible to estimate density objectively because trap arrays do not have a well-defined sample area. We applied newly-developed, capture—recapture models that accommodate the spatial attribute inherent in capture—recapture data to a population of wolverines (Gulo gulo) in Southeast Alaska in 2008. We used camera-trapping data collected from 37 cameras in a 2,140-km2 area of forested and open habitats largely enclosed by ocean and glacial icefields. We detected 21 unique individuals 115 times. Wolverines exhibited a strong positive trap response, with an increased tendency to revisit previously visited traps. Under the trap-response model, we estimated wolverine density at 9.7 individuals/1,000 km2 (95% Bayesian CI: 5.9–15.0). Our model provides a formal statistical framework for estimating density from wolverine camera-trapping studies that accounts for a behavioral response due to baited traps. Further, our model-based estimator does not have strict requirements about the spatial configuration of traps or length of trapping sessions, providing considerable operational flexibility in the development of field studies.

Estimating Distribution of Hidden Objects with Drones: From Tennis Balls to Manatees

Unmanned aerial vehicles (UAV), or drones, have been used widely in military applications, but more recently civilian applications have emerged (e.g., wildlife population monitoring, traffic monitoring, law enforcement, oil and gas pipeline threat detection). UAV can have several advantages over manned aircraft for wildlife surveys, including reduced ecological footprint, increased safety, and the ability to collect high-resolution geo-referenced imagery that can document the presence of species without the use of a human observer. We illustrate how geo-referenced data collected with UAV technology in combination with recently developed statistical models can improve our ability to estimate the distribution of organisms. To demonstrate the efficacy of this methodology, we conducted an experiment in which tennis balls were used as surrogates of organisms to be surveyed. We used a UAV to collect images of an experimental field with a known number of tennis balls, each of which had a certain probability of being hidden. We then applied spatially explicit occupancy models to estimate the number of balls and created precise distribution maps. We conducted three consecutive surveys over the experimental field and estimated the total number of balls to be 328 (95%CI: 312, 348). The true number was 329 balls, but simple counts based on the UAV pictures would have led to a total maximum count of 284. The distribution of the balls in the field followed a simulated environmental gradient. We also were able to accurately estimate the relationship between the gradient and the distribution of balls. Our experiment demonstrates how this technology can be used to create precise distribution maps in which discrete regions of the study area are assigned a probability of presence of an object. Finally, we discuss the applicability and relevance of this experimental study to the case study of Florida manatee distribution at power plants.