Abstract
Spatially explicit capture-recapture (SECR) models treat detection probability as a function of the distance between each animal and its notional activity centre. Open-population variants of these models (open SECR) are increasingly used to estimate the vital rates (survival and recruitment) of spatial populations subject to turnover between sampling times. If activity centres also move between sampling times then modelling the movement can reduce bias in estimates of vital rates. The usual movement model in open SECR is a random walk with step length governed by a probability kernel. Space is discretized in open SECR for computational convenience, and in some implementations this includes truncation of the probability kernel. Computations for the movement submodel are nevertheless very time-consuming owing to the repeated convolution steps and the need to manage boundary effects. A novel 'sparse' discretized kernel is proposed that greatly reduces fitting time. The sparse kernel was tested by simulation and applied to two datasets. Differences between models fitted using the sparse and full kernels were minor and unlikely to matter in practice. The sparse kernel extends the practical limits of the movement modelling in open SECR to greater dispersal distances and greater spatial resolution. Supplementary materials accompanying this paper appear online.