title: From Birds to Bacteria: Generalised Velocity Jump Processes with Resting States.
abstract: 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. (Phys Rev E, 74:041103, 2006b). 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 (Hillen in Discrete Continuous Dyn Syst Ser B, 5:299-318, 2003). 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.
authors.affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK, jake.taylor-king@sjc.ox.ac.uk.
authors.forename: Jake P
authors.initials: JP
authors.lastname: Taylor-King
authors.forename: E Emiel
authors.initials: EE
authors.lastname: van Loon
authors.forename: Gabriel
authors.initials: G
authors.lastname: Rosser
authors.forename: S Jon
authors.initials: SJ
authors.lastname: Chapman
mesh_terms: D025041:Animal Migration / Q000502:physiology; D000818:Animals; D018407:Bacterial Physiological Phenomena; D001717:Birds / Q000502:physiology*; D046091:Charadriiformes / Q000502:physiology; D003198:Computer Simulation; D004926:Escherichia coli / Q000502:physiology; D055641:Mathematical Concepts; D008954:Models, Biological; D009068:Movement / Q000502:physiology