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The evolution of strategy variation: will an ESS evolve?

Steven Hecht Orzack1, W G S Hines

  • 1Fresh Pond Research Institute, 173 Harvey Street, Cambridge, Massachusetts 02140, USA. orzack@freshpond.org

Evolution; International Journal of Organic Evolution
|July 30, 2005
PubMed
Summary

Evolutionarily stable strategy (ESS) models often have ambiguous predictions for mixed strategies. Finite populations are less likely to evolve a single ESS than previously thought, with probabilities depending on population size and competition.

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Area of Science:

  • Evolutionary game theory
  • Population genetics

Background:

  • Evolutionarily stable strategy (ESS) models predict individual strategies that resist mutant invasion.
  • Some models yield ambiguous predictions for mixed strategies, termed 'degenerate' predictions, where only a population-level stable state is predicted, allowing for monomorphism or polymorphism.

Purpose of the Study:

  • To investigate the impact of finite population size on degenerate ESS models.
  • To determine the probability of evolving a monomorphic ESS versus a polymorphism in finite populations.

Main Methods:

  • Incorporation of population finiteness into degenerate models.
  • Monte Carlo simulations to assess the probability of evolving an ESS.

Main Results:

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  • Finite population effects on monomorphism evolution are of equal order, preventing clear predominance.
  • The probability of evolving an ESS is generally lower than previously reported.
  • ESS evolution probability is contingent on population size, competition type, and initial strategy distribution.

    • Conclusions:

    • Degenerate ESS models in finite populations yield lower probabilities for ESS evolution.
    • Natural selection strength can increase as population size decreases, challenging established assumptions.
    • Findings highlight the importance of population size and structure in evolutionary dynamics.