Spatially explicit models for inference about density in unmarked or partially marked populations

Recently developed spatial capture-recapture (SCR) models represent a major advance over traditional capture-recapture (CR) models because they yield explicit estimates of animal density instead of population size within an unknown area. Furthermore, unlike nonspatial CR methods, SCR models account for heterogeneity in capture probability arising from the juxtaposition of animal activity centers and sample locations. Although the utility of SCR methods is gaining recognition, the requirement that all individuals can be uniquely identified excludes their use in many contexts. In this paper, we develop models for situations in which individual recognition is not possible, thereby allowing SCR concepts to be applied in studies of unmarked or partially marked populations. The data required for our model are spatially referenced counts made on one or more sample occasions at a collection of closely spaced sample units such that individuals can be encountered at multiple locations. Our approach includes a spatial point process for the animal activity centers and uses the spatial correlation in counts as information about the number and location of the activity centers. Camera-traps, hair snares, track plates, sound recordings, and even point counts can yield spatially correlated count data, and thus our model is widely applicable. A simulation study demonstrated that while the posterior mean exhibits frequentist bias on the order of 5-10% in small samples, the posterior mode is an accurate point estimator as long as adequate spatial correlation is present. Marking a subset of the population substantially increases posterior precision and is recommended whenever possible. We applied our model to avian point count data collected on an unmarked population of the northern parula (Parula americana) and obtained a density estimate (posterior mode) of 0.38 (95% CI: 0.19-1.64) birds/ha. Our paper challenges sampling and analytical conventions in ecology by demonstrating that neither spatial independence nor individual recognition is needed to estimate population density - rather, spatial dependence can be informative about individual distribution and density.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS610 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiresolution Models for Nonstationary Spatial Covariance Functions

This is the pre-print version of the article found in Statistical Modelling (http://smj.sagepub.com/).Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of a multiresolution (wavelet) basis functions and random coefficients. The key is to allow for a limited some number of correlations among coefficients and also to use a wavelet basis that is smooth. When approximately 6 % nonzero correlations are enforced, this representation gives a good approximation to a family of Matern covariance functions. This sparseness is important not only for model parsimony but also has implications for the efficient analysis of large spatial data sets. The covariance model is successfully applied to ozone model output and results in a nonstationary but smooth estimate.This work was supported by National Science Foundation grants DMS-93122686 and DMS-9815344.This work was supported by National Science Foundation grants DMS-93122686 and DMS-9815344

Acoustic space occupancy: Combining ecoacoustics and lidar to model biodiversity variation and detection bias across heterogeneous landscapes

There is global interest in quantifying changing biodiversity in human-modified landscapes. Ecoacoustics may offer a promising pathway for supporting multi-taxa monitoring, but its scalability has been hampered by the sonic complexity of biodiverse ecosystems and the imperfect detectability of animal-generated sounds. The acoustic signature of a habitat, or soundscape, contains information about multiple taxa and may circumvent species identification, but robust statistical technology for characterizing community-level attributes is lacking. Here, we present the Acoustic Space Occupancy Model, a flexible hierarchical framework designed to account for detection artifacts from acoustic surveys in order to model biologically relevant variation in acoustic space use among community assemblages. We illustrate its utility in a biologically and structurally diverse Amazon frontier forest landscape, a valuable test case for modeling biodiversity variation and acoustic attenuation from vegetation density. We use complementary airborne lidar data to capture aspects of 3D forest structure hypothesized to influence community composition and acoustic signal detection. Our novel analytic framework permitted us to model both the assembly and detectability of soundscapes using lidar-derived estimates of forest structure. Our empirical predictions were consistent with physical models of frequency-dependent attenuation, and we estimated that the probability of observing animal activity in the frequency channel most vulnerable to acoustic attenuation varied by over 60%, depending on vegetation density. There were also large differences in the biotic use of acoustic space predicted for intact and degraded forest habitats, with notable differences in the soundscape channels predominantly occupied by insects. This study advances the utility of ecoacoustics by providing a robust modeling framework for addressing detection bias from remote audio surveys while preserving the rich dimensionality of soundscape data, which may be critical for inferring biological patterns pertinent to multiple taxonomic groups in the tropics. Our methodology paves the way for greater integration of remotely sensed observations with high-throughput biodiversity data to help bring routine, multi-taxa monitoring to scale in dynamic and diverse landscapes

Population Influences on Tornado Reports in the United States

The number of tornadoes reported in the United States is believed to be less than the actual incidence of tornadoes, especially prior to the 1990s, because tornadoes may be undetectable by human witnesses in sparsely populated areas. We use a hierarchical Bayesian model to simultaneously correct for population-based sampling bias and estimate tornado density using historical tornado report data. The expected result is that F2-F5 compared to F0-F1 tornado reports would vary less with population density. The results agree with this hypothesis for the following population centers: Atlanta, GA; Champaign, IL; Des Moines, IA. However, the results indicated just the opposite in Oklahoma. We speculate the result is explained by misclassification of tornadoes that were worthy of F2-F5 Fujita scale rating but were classified as F0-F1 tornadoes, thereby artificially decreasing the number of F2-F5 and increasing the number of F0-F1 reports in rural Oklahoma.Wikle and Zhou acknowledge the support of NSF grant DMS 0139903. Anderson acknowledges the support of NSF grant ATM-9911417

Community distance sampling models allowing for imperfect detection and temporary emigration

Recent developments of community abundance models (CAMs) enable us to analyze communities subject to imperfect detection. However, existing CAMs assume spatial closure, that is, that individuals are always present in the sampling plots, which is often violated in field surveys. Violation of this assumption, such as in the presence of spatial temporary emigration, can lead to the underestimates of detection probability and overestimates of population densities and diversity metrics. Here, we propose a model that simultaneously accommodates both temporary emigration and imperfect detection by integrating CAMs and a form of hierarchical distance sampling for open populations. Expected values of species richness are obtained via the summation of occupancy (or incidence) probabilities, based on species-level densities, across all species of the community. Simulations were used to examine the effects of spatial temporary emigration on the estimation of biological communities. We also applied the proposed model to empirical data and constructed area-based rarefaction curves accounting for temporary emigration. Simulation experiments showed that temporary emigration can decrease the local species richness (a diversity) based on densities and increase the species turnover (b diversity). Raw species counts can overestimate or underestimate a diversity in the presence of temporary emigration, but the specific biases depend on the values of detection and emigration probabilities. Our newly proposed model yielded unbiased estimates of a, b, and c diversity in the presence of temporary emigration. The application to empirical data suggested that accounting for temporary emigration lowered area-based rarefaction curves because availability probabilities of individual species were estimated to be <1. Temporary emigration prevails in field surveys and has broad significance for understanding the ecology and function of biological communities and separation of imperfect detection and temporary emigration resolves long-standing issues in the use of count data. We therefore suggest that the consideration of temporary emigration would contribute to understanding the nature and role of biological communities.Y. Yamaura was supported by JSPS KAKENHI (Grant Numbers JP26292074 and JP16KK0176

Optimal sampling design for spatial capture-recapture

Spatial capture-recapture (SCR) has emerged as the industry standard for estimating population density by leveraging information from spatial locations of repeat encounters of individuals. The precision of density estimates depends fundamentally on the number and spatial configuration of traps. Despite this knowledge, existing sampling design recommendations are heuristic and their performance remains untested for most practical applications. To address this issue, we propose a genetic algorithm that minimizes any sensible, criteria-based objective function to produce near-optimal sampling designs. To motivate the idea of optimality, we compare the performance of designs optimized using three model-based criteria related to the probability of capture. We use simulation to show that these designs out-perform those based on existing recommendations in terms of bias, precision, and accuracy in the estimation of population size. Our approach, available as a function in the R package oSCR, allows conservation practitioners and researchers to generate customized and improved sampling designs for wildlife monitoring.Publisher PDFPeer reviewe