Dynamics of a single species evolutionary model with Allee effects

Yun Kang, Oyita Udiani

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


We investigate the evolutionary outcomes of a single species population subject to Allee effects within the framework of a continuous strategy evolutionary game theory (EGT) model. Our model assumes a single trait creates a phenotypic trade-off between carrying capacity (i.e., competition) and predator evasion ability following a Gaussian distribution. This assumption contributes to one of our interesting findings that evolution prevents extinction even when population exhibits strong Allee effects. However, the extinction equilibrium can be an ESS under some special distributions of anti-predation phenotypes. The ratio of variation in competition and anti-predation phenotypes plays an important role in determining global dynamics of our EGT model: (a) evolution may suppress strong Allee effects for large values of this ratio; (b) evolution may preserve strong Allee effects for small values of this ratio by generating a low density evolutionary stable strategy (ESS) equilibrium which can serve as a potential Allee threshold; and (c) intermediate values of this ratio can result in multiple ESS equilibria.

Original languageEnglish (US)
Pages (from-to)492-515
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Oct 1 2014


  • ESS maximum principle
  • Evolutionary game theory
  • Evolutionary stable strategy (ESS)
  • Strong/weak Allee effects

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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