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Figure 7.1 A fitness surface made by including mean fitness on a De Finetti plot of the three genotype frequencies for a diallelic locus. The colored lines indicate the possible trajectories of genotype frequencies as natural selection increases the mean fitness of the population. The fitness values are wAA =1.0, wAa =0.6, and waa = 0.2 so the highest mean fitness is found in the lower left apex when the population is fixed for the AA genotype. This highest fitness point can be reached by continually increasing mean fitness from any initial point on the surface. Gene action is additive because alleles have a constant impact fitness regardless of the allele they are paired with in a genotype. An A allele always contributes 0.5 and an a allele 0.1 toward the fitness of a genotype.

Frequency of Aa

Figure 7.1 A fitness surface made by including mean fitness on a De Finetti plot of the three genotype frequencies for a diallelic locus. The colored lines indicate the possible trajectories of genotype frequencies as natural selection increases the mean fitness of the population. The fitness values are wAA =1.0, wAa =0.6, and waa = 0.2 so the highest mean fitness is found in the lower left apex when the population is fixed for the AA genotype. This highest fitness point can be reached by continually increasing mean fitness from any initial point on the surface. Gene action is additive because alleles have a constant impact fitness regardless of the allele they are paired with in a genotype. An A allele always contributes 0.5 and an a allele 0.1 toward the fitness of a genotype.

Frequency of AA

Frequency of Aa left vertex or where the AA genotype is fixed in the population. Therefore, natural selection will change genotype frequencies such that the population climbs in mean fitness until reaching fixation for AA.

Natural selection on one locus with three alleles

With an understanding of fitness surfaces, let's now turn to the classic case of natural selection on three alleles at the human hemoglobin P gene (see Allison 1956; Modiano et al. 2001). The hemoglobin protein is found in red blood cells and is responsible for binding and then carrying oxygen from the lungs to the entire body. Adult hemoglobin is formed from four separate proteins, two a (or "alpha") proteins and two P (or "beta") proteins. The hemoglobin P gene encodes the P protein, which is often referred to as P-globin or Hb. The Hb A allele is the most common allele in human populations. Although several hundred Hb alleles have been identified in human populations, the Hb S allele is a common low-frequency allele. The S allele is characterized by a nucleotide change that results in substitution of the hydrophobic amino acid valine in place of the hydro-philic glutamic acid at the sixth amino acid position of the P-globin protein. Individuals homozygous for the S allele exhibit changes in red blood cell morphology ("sickling") and impaired oxygen transport that leads to chronic anemia (Ashley-Koch et al. 2000). The Hb C allele is also present at low frequencies in West African and southeast Asian populations. Individuals who are CC homozygotes have mild to moderate anemia and enlargement of the spleen that is often asymptomatic (e.g. Fairhurst & Casella 2004).

The fitness of Hb genotypes depends on the environment where people live. In areas of the world without the malarial parasite Plasmodium falciparum, genotypes that result in anemia and related conditions have lower fitness. However, in regions where malarial infection is common, certain Hb genotypes confer resistance to infection by P. falciparum that may partly or completely compensate for any disadvantage due to anemia. Two estimates of the relative fitnesses of the six Hb genotypes in Western Africa where malaria is common are shown in Table 7.1.

A seemingly obvious prediction from Table 7.1 is that natural selection in populations where malaria is common would increase the frequency of the CC genotype and eventually fix the C allele. But is this really what will happen? The answer comes from examining fitness surfaces for the six Hb genotypes. With three alleles there are six genotype frequencies, which is too many to represent in a De Finetti plot like Fig. 7.1. But since the allele frequencies must sum to one, we can represent the fitness surface on a ternary graph where each axis represents one of the three allele frequencies. Fitness surfaces drawn in this way are shown Fig. 7.2 for the two sets of fitness values given in Table 7.1. These three allele fitness surfaces are now rippled or hilly compared to the fitness surface in Fig. 7.1.

Understanding how genotype frequencies will change on a fitness surface requires calculating the change in allele frequencies due to selection for a series of points on the surface. The sign and magnitude of the change in allele frequency will be a function of the slope of the fitness surface at any point we examine. To do this for the fitness surfaces

Table 7.1 Relative fitness estimates for the six genotypes of the hemoglobin P gene estimated in Western Africa where malaria is common. Values from Cavallo-Sforza and Bodmer (1971) are based by deviation from Hardy-Weinberg expected genotype frequencies. Values from Hedrick (2004) are estimated from relative risk of mortality for individuals with AA, AC, AS, and CC genotypes and assume 20% overall mortality from malaria.

Table 7.1 Relative fitness estimates for the six genotypes of the hemoglobin P gene estimated in Western Africa where malaria is common. Values from Cavallo-Sforza and Bodmer (1971) are based by deviation from Hardy-Weinberg expected genotype frequencies. Values from Hedrick (2004) are estimated from relative risk of mortality for individuals with AA, AC, AS, and CC genotypes and assume 20% overall mortality from malaria.

Relative fitness (w)

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