Annals of Applied Statistics

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

Richard B. Chandler and J. Andrew Royle

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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.

Article information

Ann. Appl. Stat., Volume 7, Number 2 (2013), 936-954.

First available in Project Euclid: 27 June 2013

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Zentralblatt MATH identifier

Abundance estimation camera traps data augmentation hierarchical models $N$-mixture model Neyman–Scott process Poisson cluster process point counts spatial capture–recapture spatial point process population density


Chandler, Richard B.; Royle, J. Andrew. Spatially explicit models for inference about density in unmarked or partially marked populations. Ann. Appl. Stat. 7 (2013), no. 2, 936--954. doi:10.1214/12-AOAS610.

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Supplemental materials

  • Supplementary material: Full conditional distributions, R code, and history plots. Supplement A1 is a description of the full conditional distributions. Supplement A2 includes R code for implementing the MCMC algorithms and simulating data. It also contains the northern parula data set and a description of the method used to obtain the informative prior used in the analysis of the Parula data. Supplement A3 is a panel of history plots for the Markov chains from the northern parula analysis.