Evolutionarily stable strategies and short-term selection in Mendelian populations re-visited

Emilia Sansone, Ilan Eshel

Research output: Contribution to journalArticlepeer-review

Abstract

This note concerns a one locus, two allele, random mating diploid population, subject to frequency-dependent viability selection. It is already known that in such a population, any evolutionarily stable strategies (ESS), if only accessible by the genotype-to-phenotype mapping, is the phenotypic image of a stable genetic equilibrium (Eshel, I. 1982. Evolutionarily stable strategies and viability selection in Mendelian populations. Theor. Popul. Biol. 22(2), 204-217; Cressman et al. 1996. Evolutionary stability in strategic models of single-locus frequency-dependent viability selection. J. Math. Biol. 34, 707-733). The opposite is not true. We find necessary and sufficient parametric conditions for global convergence to the ESS, but we also demonstrate conditions under which, although a unique, genetically accessible ESS exists, there is another, "non-phenotypic" genetically stable equilibrium.

Original languageEnglish
Pages (from-to)76-81
Number of pages6
JournalTheoretical Population Biology
Volume70
Issue number1
DOIs
StatePublished - Aug 2006

Keywords

  • Dynamic stability
  • ESS
  • Frequency dependent selection
  • Global stability

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