Movement toward better environments and the evolution of rapid diffusion

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89 Scopus citations


We study a reaction-diffusion-advection model for two ecologically equivalent competitors with different dispersal strategies inhabiting a spatially heterogeneous environment. The competitors represent different phenotypes of the same species. One is assumed to disperse by simple diffusion, the other by diffusion together with directed movement toward more favorable environments. We show that under suitable conditions on the underlying spatial domain, the competitor that moves toward more favorable environments may have a competitive advantage even if it diffuses more rapidly than the other competitor. This is in contrast with the case in which both competitors disperse by pure diffusion, where the competitor that diffuses more slowly always has the advantage. We determine competitive advantage by examining the invasibility, i.e. stability or instability, of steady states with only one competitor present. The mathematical approach is a perturbation analysis of principal eigenvalues.

Original languageEnglish (US)
Pages (from-to)199-214
Number of pages16
JournalMathematical Biosciences
Issue number2
StatePublished - Dec 2006


  • Competition
  • Eigenvalue perturbation
  • Evolution of dispersal
  • Heterogeneous environments
  • Lotka-Volterra
  • Principal eigenvalues
  • Reaction-diffusion-advection

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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