A Spatial Capture–Recapture Model with Hawkes-Inspired Detection Rates to account for Animal Movement

Abstract Standard spatial capture–recapture (SCR) models assume independence between detections of the same individual conditional on its activity center, but in many circumstances this is unrealistic. We develop a model for continuous-time camera trap surveys that explicitly model dependence induced by animal movement. We formulate capture rates as a weighted mixture of two bivariate Gaussians. One of these is a fixed home range while the other is centered where the individual was last detected. After a capture, our model increases the capture rate at nearby traps in a Hawkes-like manner. We also decrease rates at far away traps so that individuals are not automatically “trap-happy.” This is in contrast to standard models whose rates vary in space but not time. Thus, our model gives additional inference about temporal and spatial clustering of detections. We present both frequentist and data augmentation approaches to fitting our model, demonstrate by simulation that our model gives reliable estimates, and fit our model to a dataset of leopard ( Panthera pardus ) sightings. Compared to SCR, we obtain a lower population estimate and a higher home range size estimate alongside additional inference about animal movement. Supplementary materials accompanying this paper appear on-line.