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Title: Ideal free dispersal in integrodifference models.
In this paper, we use an integrodifference equation model and pairwise invasion analysis to find what dispersal strategies are evolutionarily stable strategies (ESS) when there is spatial heterogeneity in habitat suitability, and there may be seasonal changes in this spatial heterogeneity, so that there are both advantages and disadvantages of dispersing. We begin with the case where all spatial locations can support a viable population, and then consider the case where there are non-viable regions in the habitat that makes dispersal really necessary for sustaining a population. Our findings generally align with previous findings in the literature that were based on other modeling frameworks, namely that dispersal strategies associated with ideal free distributions are evolutionarily stable. In the case where only part of the habitat can sustain a population, a partial occupation ideal free distribution that occupies only the viable region is shown to be associated with a dispersal strategy that is evolutionarily stable. As in some previous works, the proofs of these results make use of properties of line sum symmetric functions, which are analogous to those of line sum symmetric matrices but applies to integral operators.
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Journal of mathematical biology
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National Science Foundation
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