10 20 30 40 50 60 70 80 90 100 Generations

Figure 6.5 The change in the genotype and allele frequency of a completely dominant allele (A) when natural selection acts against the AA and Aa genotypes exhibiting the dominant phenotype. Notice that the frequency of the A allele decreases slowly at first when the A allele is common in the population since the aa genotype is infrequent. The colored, dashed line in the bottom panel corresponds to the allele frequencies in the top panel. In this illustration waa = wAa = 0.8 while waa = 1.0. Genotype frequencies assume random mating.

quencies of the three genotypes over time starting from an initial allele frequency of p = 0.75. The frequency of the dominant homozygote (AA) declines due to its lower viability while the frequency of the recessive homozygote (aa) increases due to its higher viability. Even though the heterozygote has a lower relative fitness than the recessive homozygote, its frequencies initially increases since the frequency of the two alleles approaches equality. The frequency of the heterozygote temporarily peaks at the maximum value of 2pq = 0.5 at the same point that the frequency of the two homozygotes both equal 0.25. The heterozygote frequency then drops again as the frequency of the recessive homozygote continues to increase and the frequency of the dominant homozygote continues to decrease.

The bottom panel of Fig. 6.5 shows that the frequency of the dominant allele decreases toward zero under this type of natural selection. (Again, the one allele frequency trajectory that corresponds to the genotype frequencies in the top panel is given as a colored, dashed line.) At an initial dominant allele frequency ofp = 0.95, only 0.25% (or q2) of the genotypes are aa. This makes natural selection slow to change allele frequencies until the frequency of the recessive allele increases enough to make the higher fitness aa genotype more common in the population. The allele frequency trajectories that start at lower initial frequencies for the A allele change more rapidly and bear out this point. Does the recessive allele go to fixation when there is natural selection against the dominant homozygote and heterozygote? In this case yes, since both the dominant homozygote and the heterozygote have a lower fitness than the favored homozygote and therefore the dominant allele is not shielded from natural selection in the heterozygote.

General dominance

The previous two examples of natural selection against dominant and recessive phenotypes cover the extremes of dominance. The impact of dominant and recessive alleles on the outcome of natural selection on a diallelic locus can be made more general by employing a dominance coefficient, symbolized h. Complete dominance (the heterozygote and a homozygote having identical phenotypes) for one allele is represented by h = 0 and complete dominance for the other allele is represented by h = 1. When the heterozygote has a phenotype that is the average of the two homozygotes then h = 1/2, a situation sometimes called codominance. A dominance coefficient of h = 1/2 is more descriptively referred to as additive gene action since the phenotype of the heterozygote is the sum of the phenotypic effects of each allele. For example, if phenotypes are AA = 3 spots, Aa = 2 spots and aa = 1 spot, an A allele contributes 1.5 spots and an a allele contributes 0.5 spots in the heterozygote when gene action is additive. Look at Table 6.4 and verify the fitness of the heterozygote when h = 0, 1, and 1/2. This method to specify fitness has the advantage that the results of natural selection can be predicted for any degree of dominance. There is also a strong biological motivation, since alleles commonly show a wide range of dominance or gene action in actual populations, ranging between being completely dominant or completely recessive.

The outcome of selection for three cases of gene action are shown in Fig. 6.6. All three cases start at the same initial allele frequency and share the same selection coefficient. However, gene action varies from completely dominant to completely recessive with the additive case in between. The results of natural selection on a completely dominant allele (rapid change in allele frequency initially but never reaching fixation) and on a completely recessive allele (slow initial change in allele frequency then more rapid change and eventual fixation) are identical to the dynamics seen in earlier examples. The allele

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