The evolution of dispersal rates in a heterogeneous time-periodic environment

V. Hutson, K. Mischaikow, P. Poláčik

Research output: Contribution to journalArticle

109 Scopus citations

Abstract

A reaction-diffusion model for the evolution of dispersal rates is considered in which there is both spatial heterogeneity and temporal periodicity. The model is restricted to two phenotypes because of technical difficulties, but a wide range of mathematical techniques and computational effort are needed to obtain useful answers. We find that the question of selection is a great deal richer than in the autonomous case, where the phenotype with the lowest diffusion is selected for. In the current model either the lower or higher diffuser rate may be selected, or there may be coexistence of phenotypes. The paper raises several open questions and suggests in particular that a mutation-selection multi-phenotypic model would repay study.

Original languageEnglish (US)
Pages (from-to)501-533
Number of pages33
JournalJournal of Mathematical Biology
Volume43
Issue number6
DOIs
StatePublished - Dec 2001

Keywords

  • Evolution of dispersal
  • Migration modification
  • Periodic-parabolic eigenvalue
  • Reaction-diffusion

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