title: The necessary and sufficient conditions of density-dependent evolutionary stable strategy (DDESS) in the two-phenotype model.
abstract: In this paper, we discuss the stability conditions of both the density-dependent pure and mixed strategy models of a polymorphic haploid population with only two pure strategies. Our results show that for the definition of density dependent evolutionary stable strategy DDESS and its stability. Cressman's frequency conditions are necessary and sufficient, and Cressman's density condition is not required.
authors.affiliation: Animal Ecological Laboratory, Institute of Zoology, Academia Sinica, Haidian, Beijing, P.R. China.
authors.forename: Y
authors.initials: Y
authors.lastname: Tao
authors.forename: Z
authors.initials: Z
authors.lastname: Wang
mesh_terms: D000818:Animals; D005075:Biological Evolution; D006238:Haploidy; D008433:Mathematics; D008957:Models, Genetic; D010641:Phenotype; D011156:Population Density