Approximating the ideal free distribution via reaction-diffusion-advection equations

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60 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3687-3703
Number of pages17
JournalJournal of Differential Equations
Issue number12
StatePublished - Dec 15 2008


  • Ideal free distribution
  • Reaction-diffusion-advection

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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