Stable equilibria in multilocus genetic systems: a statistical investigation.

Abstract

A data base of gametic distributions at a stable equilibrium for genetic systems with up to five diallelic loci was created by numerically iterating equations for the dynamics of gametic frequencies in multilocus systems under selection. For a given number of loci, iterations were conducted for 4000 random sets of genotypic fitnesses, 6 values of recombination, and 10 different initial distributions. The data base was used to investigate the following properties of stable equilibria maintaining a polymorphism in a given number of loci that are expected a priori, i.e., without any constraints on fitnesses of genotypes: probability for a fitness set to yield a such equilibrium; probability for a random trajectory to converge to a such equilibrium; genetic load at a such equilibrium. The expected number of simultaneously stable equilibria, and the fraction of genome maintained polymorphic were also investigated as well as some parameters expected at an equilibrium maintaining all loci polymorphic. One of the most important findings is that multilocus genetic systems have a potential for maintaining a polymorphism in a large number of loci under selection without an input of new genetic variation.