Social selection in human populations: protected polymorphism of deleterious alleles with incomplete penetrance

Population dynamics of two alleles, A1 and A2, at a locus under social selection have been studied by considering incomplete penetrance of the three genotypes. A social selection model is constructed by assuming that the fitness of an individual is determined by his or her own phenotype as well as parental phenotypes. For both multiplicative and additive fitness models, sufficient conditions for a protected polymorphism depend on the reduced fitness of affected individuals (gamma), the reduced fitness of all individuals resulting from affected parents (beta), and the penetrance probabilities, f1, f2, and f3, for the three genotypes, A1A1, A1A2, and A2A2. These conditions reduce to two biologically important cases: 1) f1 less than f2 greater than f3 and beta less than -gamma/(1 - gamma) and 2) f1 greater than f2 less than f3 and beta greater than - gamma/(1 - gamma), and the most common form of the equilibrium frequency of the allele A2 is given by (f1 - f2)/(f1 - 2f2 + f3).