Evolutionarily stable strategies and short-term selection in Mendelian populations re-visited.
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.
Sansone
Emilia
E
Department of Mathematics and its Applications, University of Naples, Naples, Italy. esansone@unina.it
Eshel
Ilan
I
D000818:Animals; D005075:Biological Evolution; D005828:Genetics, Population; D005838:Genotype; D015233:Models, Statistical; D010641:Phenotype; D011157:Population Dynamics