Selection in Complex Genetic Systems III. an Effect of Allele Multiplicity with Two Loci

Abstract

A two-locus model with three alleles at one locus and two at the other is studied. The viability system is such that all double heterozygotes have fitness unity, all single heterozygotes have fitness w < 1 and all double homozygotes have fitness w². The following are the major findings: 1. There are more stable equilibria for tight linkage than in the corresponding three-locus model, even though the number of chromosomes is lower. 2. The equilibria stable for tight linkage do not belong to a unique high complementarity class, as is the case for two alleles at each locus. Instead the strength of selection determines the structure of the equilibrium. 3. The increase in number of alleles seems to reduce the possible extent of assocation between the loci. 4. The measure of this association is not well defined, although we have suggested a statistically standard way of getting over this. 5. A mutation introduced while a population is in linkage disequilibrium may, per medium only of the change in number of alleles, destroy the linkage disequilibrium.