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Spatial effects in discrete generation population models

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Abstract.

A framework is developed for constructing a large class of discrete generation, continuous space models of evolving single species populations and finding their bifurcating patterned spatial distributions. Our models involve, in separate stages, the spatial redistribution (through movement laws) and local regulation of the population; and the fundamental properties of these events in a homogeneous environment are found. Emphasis is placed on the interaction of migrating individuals with the existing population through conspecific attraction (or repulsion), as well as on random dispersion. The nature of the competition of these two effects in a linearized scenario is clarified. The bifurcation of stationary spatially patterned population distributions is studied, with special attention given to the role played by that competition.

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Authors and Affiliations

  1. Centre for Mathematical Biology, University of Oxford, Oxford, UK

    C. Carrillo

  2. Dept. of Mathematics, University of Utah, USA

    P. Fife

Authors
  1. C. Carrillo
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  2. P. Fife
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Correspondence to C. Carrillo.

Additional information

Acknowledgement We gratefully received valuable help through discussions with Hiroshi Matano, Davar Khosnevisan, and Nacho Barradas. Khosnevisan provided us with the background information for Sections 3.3.1 and 3.3.2. Matano provided us with a proof of Lemma 4.4 similar to the one given here. Barradas drew our attention to the relation (2.1).

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Carrillo, C., Fife, P. Spatial effects in discrete generation population models. J. Math. Biol. 50, 161–188 (2005). https://doi.org/10.1007/s00285-004-0284-4

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  • DOI: https://doi.org/10.1007/s00285-004-0284-4

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