Evolutionary dynamics and strong Allee effects

J. M. Cushing, Jarred T. Hudson

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.

Original languageEnglish (US)
Pages (from-to)941-958
Number of pages18
JournalJournal of biological dynamics
Volume6
Issue number2
DOIs
StatePublished - Mar 1 2012

Keywords

  • Allee effects
  • ESS
  • evolution
  • evolutionary game theory
  • population dynamics

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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