title: Density-dependent dispersal in integrodifference equations.
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.
authors.affiliation: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON K1N 6N5, Canada. flutsche@uottawa.ca
authors.forename: Frithjof
authors.initials: F
authors.lastname: Lutscher
mesh_terms: D025041:Animal Migration; D000818:Animals; D003163:Competitive Behavior; D017753:Ecosystem; D004641:Emigration and Immigration / Q000706:statistics & numerical data; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics; D011336:Probability