title: Continuous stability and evolutionary convergence.
abstract: A stochastic process of long-term evolution due to mutation and selection is defined over an asexually reproducing population, with selection according to a population game with a one-dimensional continuity of pure strategies. Limiting the analysis to mutations of small effect, it is shown that long-term dynamic stability in such a process is equivalent to continuous stability in the relevant population game. In the case of a one-dimensional strategy set (but not necessarily if the strategy set is multi-dimensional), this result is virtually independent of the distribution of mutations.
authors.affiliation: Department of Statistics, School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, Israel.
authors.forename: I
authors.initials: I
authors.lastname: Eshel
authors.forename: U
authors.initials: U
authors.lastname: Motro
authors.forename: E
authors.initials: E
authors.lastname: Sansone
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D008954:Models, Biological; D009154:Mutation; D012100:Reproduction, Asexual