Jake P. Taylor-King
University of Oxford

Generalised Velocity Jump Processes: formulation, tracking data, and Levy walks

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long-distance movement state and a resting or local movement state. Here, a mathematical description of this process is formulated, adapted from Friedrich et al. The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of integro-partial differential equations is tumultuous, and therefore, it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived, which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally, a large time diffusive approximation is considered via a Cattaneo approximation. This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.