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Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

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Abstract

The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    Ross Cressman

  2. Biology Center, Academy of Sciences of the Czech Republic, and Faculty of Biological Sciences, Branišovská 31, 370 05, České Budějovice, Czech Republic

    Vlastimil Křivan

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  1. Ross Cressman
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  2. Vlastimil Křivan
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Correspondence to Vlastimil Křivan.

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Cressman, R., Křivan, V. Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds. J. Math. Biol. 67, 329–358 (2013). https://doi.org/10.1007/s00285-012-0548-3

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  • DOI: https://doi.org/10.1007/s00285-012-0548-3

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