STABLE EQUILIBRIA AT TWO LOCI IN POPULATIONS WITH LARGE SELFING RATES

Alan Hastings ¹

¹ Department of Mathematics and Division of Environmental Studies, University of California, Davis, California 95616

The equilibrium structure of two-locus, two-allele models with very large selfing rates is found using perturbation techniques. For free recombination, r = , the following results hold. If the heterozygotes do not have at least an approximate 30% advantage in fitness relative to homozygotes, a stable equilibrium with all alleles present is possible only if all of the homozygote fitnesses differ at most by approximately the outcrossing rate, t, and all stable polymorphic equilibria have disequilibrium values, D, that are at most on the order of the outcrossing rate. Once the heterozygote fitnesses are above the threshold, there are stable equilibria possible with D near its maximum possible value. The results show that the observed disequilibria in highly selfed plant populations are not likely to result from selection leading to an equilibrium.