Random diffusion models for animal movement

Abstract

Models of animal movement are necessary both as unambiguous descriptions of particular movement patterns and as starting points for the interpretation of observations on location. Radio-tracking, with frequent sampling so that successive observations are dependent, is an important special case to which only a single narrow class of models has been applied. The standard approach uses a bivariate Ornstein–Uhlenbeck diffusion process, for which the stationary distribution is always normal, limiting its flexibility for modelling stationary home range or territorial behaviour. I describe a new class of random diffusion models for animal movement, flexible enough to incorporate many realistic features, but simple enough to be estimated statistically and to be interpreted behaviourally. The models incorporate a finite number of different behavioural or physiological states for an animal, and a set of diffusion rules describing the movement of the animal while in particular states. Mathematically, the models are diffusions in finite random temporal environments. The class of models generalizes the standard Ornstein–Uhlenbeck model (which can be thought of as the 1-state case), and can represent features such as multimodal and asymmetric home ranges and utilization distributions. I give a range of examples of particular models within this class, including an application to the modelling of the movements of wood mice, for which radio-tracking can give information on behaviour, as well as location.