title: A criterion for the establishment of a stable polymorphism of higher order with an application to the evolution of polymorphism.
abstract: This note gives some further useful properties of the constant fitness selection model for multiple alleles which pertain to the effects of adding a new allele to n preexisting alleles in stable equilibrium. In particular the conditions are derived for the establishment of a stable equilibrium involving all n + 1 alleles. For 3 alleles (i.e. n = 2) I give a complete qualitative solution, including the case of the replacement of one diallelic polymorphism by another. As an application I discuss a possible mechanism for the evolution of polymorphism using Monte Carlo methods similar to Lewontin, Ginzburg and Tuljapurkar (1978).
mesh_terms: D000483:Alleles; D008957:Models, Genetic; D009010:Monte Carlo Method; D009154:Mutation; D011110:Polymorphism, Genetic