The effect of landscape fragmentation on Turing-pattern formation

Zaker, N., Cobbold, C. A. and Lutscher, F. (2022) The effect of landscape fragmentation on Turing-pattern formation. Mathematical Biosciences and Engineering, 19(3), pp. 2506-2537. (doi: 10.3934/mbe.2022116)

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Diffusion-driven instability and Turing pattern formation are a well-known mechanism by which the local interaction of species, combined with random spatial movement, can generate stable patterns of population densities in the absence of spatial heterogeneity of the underlying medium. Some examples of such patterns exist in ecological interactions between predator and prey, but the conditions required for these patterns are not easily satisfied in ecological systems. At the same time, most ecological systems exist in heterogeneous landscapes, and landscape heterogeneity can affect species interactions and individual movement behavior. In this work, we explore whether and how landscape heterogeneity might facilitate Turing pattern formation in predator–prey interactions. We formulate reaction-diffusion equations for two interacting species on an infinite patchy landscape, consisting of two types of periodically alternating patches. Population dynamics and movement behavior differ between patch types, and individuals may have a preference for one of the two habitat types. We apply homogenization theory to derive an appropriately averaged model, to which we apply stability analysis for Turing patterns. We then study three scenarios in detail and find mechanisms by which diffusion-driven instabilities may arise even if the local interaction and movement rates do not indicate it.

Item Type:Articles
Additional Information:CC was supported by a Leverhulme Research Fellowship RF-2018- 577\9. FL gratefully acknowledges funding from the Natural Sciences and Engineering Research Council of Canada under a Discovery Grant (RGPIN-2016-04795) and a Discovery Accelerator Supplement (RGPAS-492878-2016).
Glasgow Author(s) Enlighten ID:Cobbold, Professor Christina and Zaker, Nazanin
Authors: Zaker, N., Cobbold, C. A., and Lutscher, F.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Biosciences and Engineering
Publisher:AIMS Press
ISSN (Online):1551-0018
Copyright Holders:Copyright © 2022 the Author(s), licensee AIMS Press
First Published:First published in Mathematical Biosciences and Engineering 19(3):2506-2537
Publisher Policy:Reproduced under a Creative Commons Licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
302369Insect abundance and climate variability: Novel insights from homogenisationChristina CobboldLeverhulme Trust (LEVERHUL)RF-2018-577\9M&S - Mathematics