Balancing selection at closely linked, overdominant loci in a finite population

High levels of allelic diversity and strong linkage disequilibrium are found in the major histocompatibility (MHC) system in humans and other vertebrates. This article proposes several descriptive statistics that quantify the extent and pattern of strong linkage disequilibrium between pairs of highly polymorphic loci. It also develops an approximate analytic theory incorporating the effects of balancing selection, mutation, recombination, and genetic drift at two closely linked loci and compares the theoretical predictions with published surveys of the MHC class II loci, DQA1 and DQB1, in humans and nonhuman primates. The descriptive statistics proposed include the fraction of complementary haplotypes (haplotypes with D' = 1), the fraction of excess haplotypes, and the numbers of alleles at each locus in complementary haplotypes with one or more alleles at the other locus. The model assumes the infinite alleles model of mutation and the symmetric overdominance model of selection. Analytic approximations in some cases are obtained in the strong selection, weak mutation (SSWM) limit introduced by J. Gillespie. The predictions of the approximate analysis are confirmed by simulation. Both the analytic theory and simulations show that relatively few haplotypes will be found when selection is strong and recombination is weak relative to genetic drift. The model can reproduce many of the observed patterns at DQA1 and DQB1 provided that the recombination rate is assumed to be very small.