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

Authors
Journal
Theoretical Population Biology
0040-5809
Publisher
Elsevier
Publication Date
Volume
70
Issue
1
Identifiers
DOI: 10.1016/j.tpb.2005.09.002
Keywords
  • Ess
  • Dynamic Stability
  • Frequency Dependent Selection
  • Global Stability
Disciplines
  • Biology

Abstract

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.

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