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 point process, where each point is the activity centre of an individual and density corresponds to the intensity surface. Estimates of density that assume a homogeneous model ( average density) are robust to unmodelled inhomogeneity, and the coverage of confidence intervals is good when the intensity surface does not change, even if it is quite uneven. However, coverage is poor when the intensity surface differs among realisations. Practical examples include populations with dynamic social aggregation, and the population in a region sampled using small detector arrays. Poor coverage results from overdispersion of the number of detected individuals; the number is Poisson when the intensity surface is static, but stochasticity leads to extra-Poisson variation. We investigated overdispersion from three point processes with a stochastic intensity surface (Thomas cluster process, random habitat mosaic and log-Gaussian Cox process). A previously proposed correction for overdispersion performed poorly. The problem is lessened by assuming population size to be fixed, but this assumption cannot be justified for common study designs. Rigorous correction for spatial overdispersion requires either prior knowledge of the generating process or replicated and representative sampling. When the generating process is known, variation in a new scalar measure of local density predicts overdispersion. Otherwise, overdispersion may be estimated empirically from the numbers detected on independent detector arrays.