Density Estimation by Spatially Explicit Capture–Recapture: Likelihood-Based Methods

Abstract

Population density is a key ecological variable, and it has recently been shown how captures on an array of traps over several closely-spaced time intervals may be modelled to provide estimates of population density (Borchers and Efford 2007). Specifics of the model depend on the properties of the traps (more generally ‘detectors’). We provide a concise description of the newly developed likelihood-based methods and extend them to include ‘proximity detectors’ that do not restrict the movements of animals after detection. This class of detector includes passive DNA sampling and camera traps. The probability model for spatial detection histories comprises a submodel for the distribution of home-range centres (e.g. 2-D Poisson) and a detection submodel (e.g. halfnormal function of distance between a range centre and a trap). The model may be fitted by maximising either the full likelihood or the likelihood conditional on the number of animals observed. A wide variety of other effects on detection probability may be included in the likelihood using covariates or mixture models, and differences in density between sites or between times may also be modelled. We apply the method to data on stoats Mustela erminea in a New Zealand beech forest identified by microsatellite DNA from hair samples. The method assumes that multiple individuals may be recorded at a detector on one occasion. Formal extension to ‘single-catch’ traps is difficult, but in our simulations the ‘multi-catch’ model yielded nearly unbiased estimates of density for moderate levels of trap saturation (≤ 86% traps occupied), even when animals were clustered or the traps spanned a gradient in density.