Journal of Mathematical Biology

, Volume 56, Issue 4, pp 499–524

Density-dependent dispersal in integrodifference equations


DOI: 10.1007/s00285-007-0127-1

Cite this article as:
Lutscher, F. J. Math. Biol. (2008) 56: 499. doi:10.1007/s00285-007-0127-1


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.


Integrodifference equations Spreading speeds Density-dependent dispersal Habitat fragmentation Competition Evolution of dispersal 

Mathematics Subject Classification (2000)

92D40 37N25 39A11 45M99 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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