Genetical ESS-models. II. Multi-strategy models and multiple alleles.

The problem of evolutionarily stable strategies (ESS) in sexual populations can be investigated by means of genetical ESS-models which link common sense, phenotypic ESS-models to an underlying genetical system. Thorough results are obtained for multi-strategy models in diploid, panmictic populations on the basis of multi-allelic, one-locus systems. A sexual population will be maintained at a phenotypic ESS if this can possibly be produced by the genotypes currently existing. If there is enough allelic variation, the corresponding gene pool may either be an ESS itself, or belong to an attracting, continuous set of states, which all determine the same evolutionarily stable population. The latter case allows new alleles to enter and spread in the gene pool without disturbing the phenotypic ESS. If a phenotypic ESS cannot be established, ESSs of the genetical model may be found which give rise to stable populations alternatively. Since these depend on the phenotypes determined by the currently existing genotypes, they may be destabilized by the occurrence of new mutations. In this sense, they are less durable than populations maintained at a phenotypic ESS and can be expected to evolve, in the long run, towards a phenotypic ESS.