Effect of environmental fluctuations on invasion fronts

Vicenç Méndez, Isaac Llopis, Daniel Campos, Werner Horsthemke

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)


We determine the density profile and velocity of invasion fronts in one-dimensional infinite habitats in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction-diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain analytical expressions for the front profile and velocity by constructing a variational principle. The effect of the noise differs, depending on whether it affects the density-independent growth rate, the intraspecific competition term or the Allee threshold. Fluctuations in the density-independent growth rate increase the invasion velocity and the population density of the invaded area. Fluctuations in the competition term also change the population density of the invaded area, but modify the invasion velocity only for certain initial conditions. Fluctuations in the Allee threshold can induce pulled or pushed invasion fronts as well as invasion failure. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction-diffusion equations with multiplicative noise. © 2011 Elsevier Ltd.
Original languageEnglish
Pages (from-to)31-38
JournalJournal of Theoretical Biology
Publication statusPublished - 21 Jul 2011


  • Allee effect
  • Environmental fluctuations
  • Invasion front


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