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Directionally Correlated Movement Can Drive Qualitative Changes in Emergent Population Distribution Patterns

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  • Jonathan R. Potts

    (School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK)

Abstract

A fundamental goal of ecology is to understand the spatial distribution of species. For moving animals, their location is crucially dependent on the movement mechanisms they employ to navigate the landscape. Animals across many taxa are known to exhibit directional correlation in their movement. This work explores the effect of such directional correlation on spatial pattern formation in a model of between-population taxis (i.e., movement of each population in response to the presence of the others). A telegrapher-taxis formalism is used, which generalises a previously studied diffusion-taxis system by incorporating a parameter T , measuring the characteristic time for directional persistence. The results give general criteria for determining when changes in T will drive qualitative changes in the predictions of linear pattern formation analysis for N ≥ 2 populations. As a specific example, the N = 2 case is explored in detail, showing that directional correlation can cause one population to ‘chase’ the other across the landscape while maintaining a non-constant spatial distribution. Overall, this study demonstrates the importance of accounting for directional correlation in movement for understanding both quantitative and qualitative aspects of species distributions.

Suggested Citation

  • Jonathan R. Potts, 2019. "Directionally Correlated Movement Can Drive Qualitative Changes in Emergent Population Distribution Patterns," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:640-:d:249521
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    References listed on IDEAS

    as
    1. Alka A Potdar & Junhwan Jeon & Alissa M Weaver & Vito Quaranta & Peter T Cummings, 2010. "Human Mammary Epithelial Cells Exhibit a Bimodal Correlated Random Walk Pattern," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-10, March.
    2. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
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