Reaction-diffusion-advection models for the effects and evolution of dispersal

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44 Scopus citations

Abstract

This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.

Original languageEnglish (US)
Pages (from-to)1701-1745
Number of pages45
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number5
DOIs
StatePublished - May 1 2014

Keywords

  • Bifurcation
  • Dispersal
  • Ecology
  • Evolution
  • Persistence theory
  • Population dynamics
  • Reaction-diffusion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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