Evolutionarily Stable Allele Distributions

For the one-locusm-allele case we give a definition of an Evolutionarily Stable Allele Distribution (ESAD) for sexual populations, such that the associated game dynamics is a modified Fisher selection equation. For the ESAD we prove some basic statements which are parallel to those known in classical ESS theory. For an illustration, considering a two-allele dominant inheritance, we show that, if there is only a game-theoretical conflict within the populations (and no Fisher type selection) then the ESS of the asexual population and the ESAD of the sexual one provide the same phenotype distribution. We also give an example of a two-allele non-dominant inheritance where the phenotype distributions corresponding to ESS and ESAD differ, the mean fitnesses of the two populations at their evolutionarily stable states, however, are equal.