Pseudo-random mating systems for 3-allele loci

A random mating population attains equilibrium by the Hardy-Weinberg law. By demonstrating some simple examples for 2-allele loci, Li (1988) showed that a nonrandom mating population of certain mating patterns may also attain equilibrium. He called such a type of population a pseudo-random mating population. Tai (1990), then, gave a generalized representation of these pseudo-random mating systems. In this paper the clear patterns of pseudo-random mating behavior for a 3-allele locus are derived. Both autosomal and sex-linked systems are discussed. The study of these mating patterns provides a way to understand the complicated mating system of a population, which usually is only with difficulty realized through sampled individuals from that population.