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Evolutionarily stable strategy in a sex- and frequency-dependent selection model.

T Yi1, S Lessard, M Lemire

  • 1Département de Mathématiques et de Statistique, Université de Montréal, Québec, Canada.

Journal of Theoretical Biology
|July 11, 2000
PubMed
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This study explores a sex-dependent game model where genotypes determine strategy pairs. We demonstrate that Evolutionarily Stable Strategy (ESS) equilibria, if they exist, are locally asymptotically stable.

Area of Science:

  • Evolutionary Game Theory
  • Population Genetics
  • Mathematical Biology

Background:

  • Understanding the genetic basis of behavior is crucial in evolutionary biology.
  • Matrix game models are used to study strategic interactions within populations.
  • Sex-dependent traits add complexity to evolutionary models.

Purpose of the Study:

  • To investigate a sex-dependent matrix game haploid model.
  • To establish conditions for Evolutionarily Stable Strategy (ESS) in this model.
  • To analyze the stability of ESS equilibria.

Main Methods:

  • Developed a haploid model with sex-dependent phenotypes determined by a single locus.
  • Defined strategy pairs based on genotypes.
  • Applied the definition of ESS: a strategy pair that cannot be invaded by mutant alleles.

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Main Results:

  • Established a direct link between genotypes and strategy pairs.
  • Provided a condition for a strategy pair to be an ESS: resistance to invasion by mutant alleles.
  • Proved that any existing ESS equilibrium is locally asymptotically stable.

Conclusions:

  • The investigated sex-dependent model provides insights into the evolution of strategies.
  • Local asymptotic stability is a key property of ESS in this haploid system.
  • This framework can be extended to more complex genetic architectures and game dynamics.