The same approach can be taken to obtain the expression for Aq.

sxx = 1 - wxx or wxx = 1 - sxx (6.33) Selection against a recessive phenotype where the subscript xx represents a genotype and the maximum relative fitness is one. Selection coefficients therefore represent the difference in viability between a given genotype and the genotype with the highest viability.

Examining the outcome of selection for each category of fitness values or selection coefficients will illustrate how viability selection is expected to change genotype and allele frequencies in populations. By iterating versions of equation 6.14 for all three genotypes as well as equations 6.21 and 6.22, we can visualize the action of natural selection. The behavior of allele frequencies under natural selection can be understood by examining plots of allele frequencies over time to see the direction and rate of allele frequency change. An important general feature of natural selection is the allele frequency reached when allele frequencies eventually stop changing, or the equilibrium allele frequency. The goal of this section is to understand both how and why genotype and allele frequencies change when acted on by a constant force of natural selection over time.

Although it is common to speak of an allele favored by natural selection, any change in allele frequencies is really caused by natural selection on genotypes due to their different-viability phenotypes. Alleles themselves do not have phenotypes nor fitness values in most types of natural selection (natural selection on gametes or haploid genomes are exceptions). The changing frequency of genotypes is what causes allele frequencies to change. Although two allele frequencies can be displayed with more economy than three genotype frequencies, it is critical not to forget that natural selection directly causes changes in genotype frequency and that change in allele frequencies is an indirect consequence.

The process of natural selection has the special quality that the genotype frequencies reached at equilibrium are always the same as long as the starting frequencies and relative fitness values are constant. Processes that always lead to the same outcome from a given set of initial conditions are called deterministic because the end state is completely determined by the initial state. Similar patterns of genotype frequencies in independent populations are therefore evidence that the process of natural selection is operating. In contrast, the stochastic process of genetic drift would result in random outcomes in each independent population. This also means that there is no need to view replicate outcomes of natural selection for the same set of initial conditions.

The results of natural selection acting against a completely recessive homozygous genotype (see Table 6.4) are shown in Fig. 6.4. The top panel shows the frequencies of the three genotypes over time starting from an initial allele frequency of p = q = 0.5. The frequency of the recessive homozygote (aa) declines because that genotype has lower viability. At the same time, the frequency of the dominant homozygote (AA) increases since it has a higher viability. Even though the heterozygote also has the maximum fitness, its frequency declines from a maximum of 0.5 as A alleles become more frequent and a alleles less frequent over time, reducing the value of 2pq. The bottom panel summarizes the results of natural selection in terms of allele frequencies over time for five initial allele frequencies. (The one allele frequency trajectory that corresponds to the genotype frequencies in the top panel is given as a colored, dashed line.)

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