Structure of Populations Under Mixed Random Mating and Selfing

A study has been made in respect of various properties such as genotypic composition, loss of heterozygosity and genotypic variability of populations with mixed breeding systems, namely, both random mating and selfing. The various gene pairs involved are assumed to be segregating independently and fertility and viability disturbances to be absent.

Assuming the initial population to be panmictic, a general expression has been derived from which it is possible to work out the frequency of any genotype, irrespective of the number of gene pairs involved, in the nth generation and, in the limiting case, in terms of the frequencies in the initial population. With an arbitrary initial population, the situation is more complex but it is observed that the genotype frequencies in the limiting case are independent of the initial frequencies and depend only on the gene frequencies and amount of self-fertilization. These limiting frequencies, would, therefore, appear to be the same as obtained for the panmictic initial population having the same gene frequencies.

Regarding the loss of heterozygosity in populations under mixed random mating and selfing, this loss cannot be predicted from the study of a single locus, when more than one locus is considered. The general expression for the loss in heterozygosity relative to the initial population in the nth generation due to mixed random mating and selfing has been obtained in the general case of several, independently segregating loci.

The expressions for the mean and the genotypic variance in the nth generation have also been obtained for the panmictic initial population. It is observed that the usual assumption that the variance due to several independently segregating loci is equal to the sum of variances due to each factor separately does not hold good in the present case and is true only when there is either one system of breeding in operation or when there is no dominance. It is, therefore, obvious that the trend of changes in the genotypic variance due to several loci cannot be predicted from the behaviour of a single locus because of the appearance of an additional term in the expression for the genotypic variance.