Effect of spatial overdispersion on confidence intervals for population density estimated by spatial capture–recapture

Spatially explicit capture–recapture models are used widely to estimate the density of animal populations. The population is represented by an inhomogeneous Poisson process, where each point is the activity center of an individual and density corresponds to the intensity surface. Estimates of average density are robust to unmodeled inhomogeneity, but the coverage of confidence intervals is poor when the intensity surface is stochastic. Poor coverage is due to overdispersion of the number of detected individuals n with respect to the fitted Poisson distribution. We investigated overdispersion from stochastic generating models (log-Gaussian Cox process and Thomas cluster process). Variation in a scalar measure of local density – the detection-weighted mean density – predicts overdispersion when the generating process is known. A previously proposed correction for overdispersion was successful only in limited cases: rigorous correction for spatial overdispersion requires prior knowledge of the generating process. The problem is lessened by assuming population size to be fixed, but this assumption cannot be justified for common study designs.