Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes

Cobbold, C. A. , Lutscher, F. and Sherratt, J. A. (2015) Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes. Ecological Complexity, 24, pp. 69-81. (doi: 10.1016/j.ecocom.2015.10.001)

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Abstract

Spatial variation in population densities across a landscape is a feature of many ecological systems, from self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of populations. However the ways in which abiotic and biotic factors interact to determine the existence and nature of spatial patterns in population density remain poorly understood. Here we present a new approach to studying this question by analysing a predator–prey patch-model in a heterogenous landscape. We use analytical and numerical methods originally developed for studying nearest- neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a rich and highly complex array of coexisting stable patterns, located within an enormous number of unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable basins of attraction, making them significant in applications. We are able to identify mechanisms for these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby landscape heterogeneity can modulate the spatial scales at which these processes operate to structure the populations.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cobbold, Professor Christina
Authors: Cobbold, C. A., Lutscher, F., and Sherratt, J. A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
College of Medical Veterinary and Life Sciences > Institute of Biodiversity Animal Health and Comparative Medicine
Journal Name:Ecological Complexity
Publisher:Elsevier
ISSN:1476-945X
ISSN (Online):1476-9840
Copyright Holders:Copyright © 2015 Elsevier Ltd.
First Published:First published in Ecological Complexity 24:69-81
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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