Results on asymptotic behaviour for discrete, two-patch metapopulations with density-dependent selection

A 4-dimensional system of nonlinear difference equations tracking allele frequencies and population sizes for a two-patch metapopulation model is studied. This system describes intergenerational changes brought about by density-dependent selection within patches and moderated by the effects of migra...

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Bibliographic Details
Published in:Journal of difference equations and applications 2005-04, Vol.11 (4-5), p.459-476
Main Authors: Selgrade, James F., Roberds ∥, James H.
Format: Article
Language:English
Subjects:
AMS 2000 Mathematics Subject Classification: 92D25
Attractor
Discrete population model
Equilibrium
Metapopulation
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Summary:A 4-dimensional system of nonlinear difference equations tracking allele frequencies and population sizes for a two-patch metapopulation model is studied. This system describes intergenerational changes brought about by density-dependent selection within patches and moderated by the effects of migration between patches. To determine conditions which result in similar behaviour at the level of local populations, we introduce the concept of symmetric equilibrium and relate it to properties of allelic and genotypic fitness. We present examples of metapopulation stability, instability and bistability, as well as an example showing that differentially greater migration into a stable patch results in metapopulation stability. Finally, we illustrate a Naimark-Sacker bifurcation giving a globally asymptotically stable invariant curve for the 4-dimensional model.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190412331335508