  Methods for population estimation and inference have evolved over the past
decade to allow for the incorporation of spatial information when using
capture-recapture study designs. Traditional approaches to specifying spatial
capture-recapture (SCR) models often rely on an individual-based detection
function that decays as a detection location is farther from an individual's
activity center. Traditional SCR models are intuitive because they incorporate
mechanisms of animal space use based on their assumptions about activity
centers. We modify the SCR model to accommodate a wide range of space use
patterns, including for those individuals that may exhibit traditional
elliptical utilization distributions. Our approach uses underlying Gaussian
processes to characterize the space use of individuals. This allows us to
account for multimodal and other complex space use patterns that may arise due
to movement. We refer to this class of models as geostatistical
capture-recapture (GCR) models. We adapt a recursive computing strategy to fit
GCR models to data in stages, some of which can be parallelized. This technique
facilitates implementation and leverages modern multicore and distributed
computing environments. We demonstrate the application of GCR models by
analyzing both simulated data and a data set involving capture histories of
snowshoe hares in central Colorado, USA.
