Approximating the ideal free distribution via reaction-diffusion-advection equations |
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Authors: | Robert Stephen Cantrell Chris Cosner Yuan Lou |
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Affiliation: | a Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA b Department of Mathematics, Ohio State University, Columbus, OH 43210, USA |
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Abstract: | We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions. |
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Keywords: | 35K57 92D25 |
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