as a function of genotype frequencies in the previous generation using substitution for D1 and H1:

which simplifies to:

and then recognizing that the right hand side is equal to the frequency of A in generation 0:

Thus, allele frequencies remain constant under complete assortative mating. As practice, you should carry out the algebra for the frequency of the a allele.

Under complete self-fertilization heterozygosity declines very rapidly. There can also be partial self-fertilization in a population (termed mixed mating), where some matings are self-fertilization and others are between two individuals (called outcrossing). In addition, many organisms are not capable of self-fertilization but instead engage in biparental inbreeding to some degree. In general, these forms of inbreeding will reduce heterozygosity compared to random mating, although they will not drive heterozygosity toward zero as in the case of complete selfing. The rate of decline in heterozygosity can be determined for many possible types of mating systems and a few examples are shown in Fig. 2.13. Regardless of the specifics of the form of consanguineous mating that occurs, it remains true that inbreeding causes alleles to be packaged more frequently as homozygotes (heterozygosity declines) and inbreeding does not alter allele frequencies in a population.

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