Gurney, William and Veitch, A.R. (2000) *Self-organisation, scale and stability in a spatial predator-prey interaction.* Bulletin of Mathematical Biology, 62 (1). pp. 61-86. ISSN 0092-8240

## Abstract

Simple predator-prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig-McArthur model with immobile prey can be stabilized by self-organized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the self-organized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic.

Item type: | Article |
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ID code: | 41755 |

Keywords: | Simple predator-prey models, self-organisation, spatial predator-prey interaction, spatial Rosenzweig-McArthur model , Probabilities. Mathematical statistics, Agricultural and Biological Sciences(all), Neuroscience(all), Biochemistry, Genetics and Molecular Biology(all), Environmental Science(all), Immunology, Computational Theory and Mathematics, Mathematics(all), Pharmacology |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 26 Oct 2012 12:59 |

Last modified: | 05 Sep 2014 18:38 |

URI: | http://strathprints.strath.ac.uk/id/eprint/41755 |

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