Deviations from Hardy-Weinberg proportions for multiple alleles under viability selection

Departures of genotype frequencies from Hardy-Weinberg proportions (HWP) for a single autosomal locus due to viability selection in a random mating population have been studied only for the two-allele case. In this article, the analysis of deviations from HWP due to constant viability selection is extended to multiple alleles. The deviations for an autosomal locus with k alleles are measured by means of k fii fixation indices for homozygotes and k(k-1)/2 fij fixation indices for heterozygotes, and expressions are obtained for these indices (FIS statistics) under the multiallele viability model. Furthermore, expressions for fii and fij when the multiallele polymorphism is at stable equilibrium are also derived and it is demonstrated that the pattern of multiallele Hardy-Weinberg deviations at equilibrium is characterized by a global heterozygote excess and a deficiency of each of the homozygotes. This pattern may be useful for detecting whether a given multiallelic polymorphism is at stable equilibrium in the population due to viability selection. An analysis of Hardy-Weinberg deviations from published data for the three-allele polymorphism at the beta-globin locus in human populations from West Africa is presented for illustration.