Mating and offspring frequencies under partial outcrossing in a structured population

This paper gives a model of a structured population with respect to an autosomal locus with two alleles. The population reproduces in discrete and non-overlapping generations. The population is assumed to be in equilibrium in that exactly the same distribution of genotypic proportions is reproduced in each generation. The population is subdivided into `localities’ which are characterized by the local gene frequencies. Within each locality the genotypic proportions may depart from Hardy-Weinberg proportions and the same fixation index applies to all localities. The system departs from reality by assuming that the frequency of the first allele follows the beta distribution. However, this enables a convenient way to derive the mating frequencies of parents so that equilibrium is maintained. Wright’s F-statistics are applied to characterize the population as a whole. The system is extended to permit an arbitrary level of outbreeding.