Coincidence of ESAD and ESS in dominant-recessive hereditary systems.
The paper deals with the following question: when do the phenotypic evolutionarily stable state (ESS) and the evolutionarily stable allele distribution (ESAD) coincide? It is supposed that for a sexual population, in dominant-recessive inheritance system, n allele at one autosomal locus determine n possible pure individual phenotypes and each pure phenotype is obtained as the phenotype of a homozygote. Under these conditions, earlier results of the authors imply that, if a phenotype distribution is an ESS then the allele distribution generating it is an ESAD. In this paper, apart from a certain degenerate pay-off matrices, the inverse statement is also proved: if a distribution is an ESAD then the corresponding phenotypic distribution is an ESS.
Garay
József
J
Ecological Modelling Research Group, Department of Plant Taxonomy and Ecology, Hungarian Academy of Science, L. Eötvös University, Ludovika tér 2, Budapest H-1038, Hungary. garayj@ludens.elte.hu
Varga
Zoltán
Z
D000483:Alleles; D000818:Animals; D005075:Biological Evolution; D005799:Genes, Dominant; D005808:Genes, Recessive; D005828:Genetics, Population; D008957:Models, Genetic; D010641:Phenotype; D012098:Reproduction / Q000235:genetics; D012100:Reproduction, Asexual / Q000235:genetics