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homozygote genotype frequency from mating among heterozygotes after five generations is H/2(1 - (1/2)5) = H/2(1 - 1/32) = H/2(31/32). With the initial frequency of H = 0.5, H/2(31/32) = 0.2 42. Therefore, the frequencies of both homozygous genotypes are 0.25 + 0.242 = 0.492 after five generations. It is also apparent that the total increase in homozygotes (31/32) is exactly the same as the total decrease in heterozygotes (31/32), so that the allele frequencies in the population have remained constant. After five generations of assortative mating in this example, genotypes are much more likely to contain two identical alleles than they are to contain two unlike alleles. This conclusion is also reflected in the value of the fixation index for this example, F = (0.5 -0.016)/0.5 = 0.968. In general, positive assortative mating or inbreeding changes the way in which alleles are "packaged" into genotypes, increasing the frequencies of all homozygous genotypes by the same total amount that heterozygosity is decreased, but allele frequencies in a population do not change.

The fact that allele frequencies do not change over time can also be shown elegantly with some simple algebra. Using the notation in Fig. 2.12 and defining the frequency of the A allele as p and the a allele as q with subscripts to indicate generation, allele frequencies can be determined by the genotype counting method as p0 = D0 + 1/2H0 and q0 = R0 + 1/2H0. Figure 2.12 also provides the expressions for genotype frequencies from one generation to the next: D1 = D0 + 1/4H0, H1 = 1/2H0, and R1 = R0 + 1/4H0. We can then use these expressions to predict allele frequency in one generation:

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