Theoretical Proportion of Heterozygosity in Populations with Various Proportions of Self‐and Cross‐Fertilization¹

Analysis of some nonrandom mating models

“…Similar results were also discussed by Haldane and Moshinsky (1939) for equilibrium populations. Garber (1951) dealt with the approach to equilibrium with varying percentages of cross-and self-fertilization in the case of one autosomal locus for a panmictic initial population, whereas Ali and Hadley (1955) discussed the effect of such a system on the amount of heterozygosity, Bennett and BineL (1956) considered the association between Mendelian factors for two pairs of genes at equilib rium with mixed selfing and random mating. They concluded that when equilibrium is reached the genes are associated at random but the two factors which are segregating independently are not associated at random.…”

Population Studies in Predominantly Self-Pollinated Species, Iii. A Matrix Model for Mixed Selfing and Random Outcrossing

“…Genetic analyses of predominantly self-fertilizing populations would be aided if a theoretical model were available for computing the genotypic frequencies expected in any generation, given initial genotypic frequencies and the amount of selfing versus outcrossing. The models that are available either have employed algebraic recursions relating genotypic frequencies in successive generations 6 or have approached the problem indirectly in terms of the inbreeding coefficient.7 These methods have the disadvantage that they either do not provide formulas for direct computation of genotypic frequencies during passage to the limit, or equilibrium state, or are not readily extended to multilocus situations. We shall therefore develop a model, using the method of generation matrices,8 which permits direct calculation of the genotypic array for any generation, given the initial genotypic frequencies and the proportion of selfing and random outcrossing.…”

Analysis of some nonrandom mating models

“…whereas Ali and Hadley (1955) discussed the effect of such a system on the amount of heterozygosity, Bennett and BineL (1956) considered the association between Mendelian factors for two pairs of genes at equilib rium with mixed selfing and random mating. They concluded that when equilibrium is reached the genes are associated at random but the two factors which are segregating independently are not associated at random.…”