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Density-dependent dispersal in integrodifference equations

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Abstract

Many species exhibit dispersal processes with positive density- dependence. We model this behavior using an integrodifference equation where the individual dispersal probability is a monotone increasing function of local density. We investigate how this dispersal probability affects the spreading speed of a single population and its ability to persist in fragmented habitats. We demonstrate that density-dependent dispersal probability can act as a mechanism for coexistence of otherwise non-coexisting competitors. We show that in time-varying habitats, an intermediate dispersal probability will evolve. Analytically, we find that the spreading speed for the integrodifference equation with density-dependent dispersal probability is not linearly determined. Furthermore, the next-generation operator is not compact and, in general, neither order-preserving nor monotonicity-preserving. We give two explicit examples of non-monotone, discontinuous traveling-wave profiles.

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  1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada

    Frithjof Lutscher

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Lutscher, F. Density-dependent dispersal in integrodifference equations. J. Math. Biol. 56, 499–524 (2008). https://doi.org/10.1007/s00285-007-0127-1

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  • DOI: https://doi.org/10.1007/s00285-007-0127-1

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