Multiscale modelling of animal movement with persistent dynamics

Abstract

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale spatial distributions. Due to this dichotomy, it is challenging to describe mathematically how animals' distributions arise from their short-term movement patterns, and to combine data sets collected at different scales. We propose a multiscale model of animal movement and space use based on the underdamped Langevin process, widely used in statistical physics. The model is convenient to describe animal movement for three reasons: it is specified in continuous time (such that its parameters are not dependent on an arbitrary time scale), its speed and direction are autocorrelated (similarly to real animal trajectories), and it has a closed form stationary distribution that we can view as a model of long-term space use. We use the common form of a resource selection function for the stationary distribution, to model the environmental drivers behind the animal's movement decisions. We further increase flexibility by allowing movement parameters to be time-varying, and find conditions under which the stationary distribution is preserved. We derive an explicit mathematical link to step selection functions, commonly used in wildlife studies, providing new theoretical results about their scale-dependence. We formulate the underdamped Langevin model as a state-space model and present a computationally efficient method of inference based on the Kalman filter and a marginal likelihood approach for mixed effect extensions.