Two-sided assortative mating for a single locus

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Abstract
Most models previously considered for assortative mating were such that no change in gene frequencies occurred, or that 1-sided assortative mating was occurring. Two-sided assortative mating is more realistic for human populations, and a model of 2-sided assortative mating is analyzed for 2 autosomal alleles with dominance, an important case for human genetics. The concept of a relative probability of mating between 2 phenotypes is used, and this variable can take into account factors such as different propensities for assortment in the various phenotypes and so forth. The gene frequency may vary from generation to generation and conditions for the establishment of a stable polymorphism are given. A special case of 2-sided assortative mating with 2 autosomal alleles and a constant correlation between mates was previously considered where the value expressed by the heterozygote is numerically exactly half-way between the values exhibited by the 2 homozygotes. A special form of assortative mating was studied where the probability of occurrence of matings between the same homozygotes was increased in each generation by the same constant factor as the probability of occurrence of matings between different homozygotes was decreased. The probability of occurrence of matings involving heterozygotes remains the same as if mating were random. For this particular model the frequency of the genotypes in those who mate in generation t is the same as for the general population in generation t, but the genotypic frequencies change from generation to generation, reaching an equilibrium value. Stark considered a similar model to Stanton''s, the major difference occurring in the construction of the mating frequencies, which in this case occurs according to the canonical decomposition of the 2-way table of mating frequencies. Stark shows the correspondence between the results for this model and those given by Malecot. The results for all these models depend on the particular values assigned to the genotypes. Also, these models could be extended for the case of 2 autosomal alleles with dominance.