Populations with individual variation in dispersal in heterogeneous environments: Dynamics and competition with simply diffusing populations

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We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reaction-diffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that “the slower diffuser wins”.

Original languageEnglish (US)
Pages (from-to)441-464
Number of pages24
JournalScience China Mathematics
Issue number3
StatePublished - Mar 1 2020



  • 35K40
  • 35K57
  • 92D40
  • 92D50
  • animal behavior
  • ecology and evolutionary biology
  • evolution of dispersal
  • individual variation in dispersal
  • population dynamics
  • reaction-diffusion

ASJC Scopus subject areas

  • Mathematics(all)

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