期刊
JOURNAL OF MATHEMATICAL BIOLOGY
卷 56, 期 4, 页码 499-524出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-007-0127-1
关键词
integrodifference equations; spreading speeds; density-dependent dispersal; habitat fragmentation; competition; evolution of dispersal
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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