From birds to bacteria: generalised velocity jump processes with resting\n states

2014/07/30 by Jake P. Taylor‐King, Taylor-King, Jake P., E. Emiel van Loon +6 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Diffusion and Search Dynamics #Evolution and Genetic Dynamics #FOS: Biological sciences #Quantitative Methods (q-bio.QM) #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.1407.8177

openalex publication_date 2014/07/30 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

There are various cases of animal movement where behaviour broadly switches\nbetween two modes of operation, corresponding to a long distance movement state\nand a resting or local movement state. Here a mathematical description of this\nprocess is formulated, adapted from Friedrich et. al. (2006). The approach\nallows the specification any running or waiting time distribution along with\nany angular and speed distributions. The resulting system of partial\nintegro-differential equations are tumultuous and therefore it is necessary to\nboth simplify and derive summary statistics. An expression for the mean squared\ndisplacement is derived which shows good agreement with experimental data from\nthe bacterium Escherichia coli and the gull Larus fuscus. Finally a large time\ndiffusive approximation is considered via a Cattaneo approximation (Hillen,\n2004). This leads to the novel result that the effective diffusion constant is\ndependent on the mean and variance of the running time distribution but only on\nthe mean of the waiting time distribution.\n

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