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Equation 20.20 is the general form of equation 20.18 for any value of s. The change in allelic frequency due to mutation can be found by using equation 20.4: q p q
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where and are the rate of forward and back mutation, respectively. When equilibrium exists, the change
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Tamarin: Principles of Genetics, Seventh Edition
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IV. Quantitative and Evolutionary Genetics
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20. Population Genetics: Process that Change Allelic Frequencies
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Population Genetics: Processes That Change Allelic Frequencies
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Table 20.4 All Possible One-Locus, Two-Allele
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Selection Models (Assuming All Selection Coef cients Are Constants)
Genotypic Fitness Type of Selection 1. Against recessive homozygotes 2. Against heterozygotes 3. Against one allele 4. Against homozygotes 1 A1 A1 1 1 1 s1 1 1 1 A1 A2 1 s s1 1 1 A2 A2 1 1 s2 s2 s
dominant allele. Similarly, the (1 s1, 1 s2, 1) model is eliminated for the same reason (allele A2 is acting like the dominant allele and A1 like the recessive allele). We now describe the outcome of each of the models in the table. In both models 1 and 3 (table 20.4), selection is against genotypes containing the A2 allele. Model 1, which we just derived in detail, is the model for a deleterious recessive allele. Almost any enzyme defect in a metabolic pathway ts this model, such as PKU, alkaptonuria, Tay-Sachs disease, and so on. In model 3, however, natural selection can detect the heterozygote, as is the case with deleterious alleles that are not completely recessive. An example would be the hemoglobin anomaly called thalassemia, a disorder common in some European and Asian populations, that produces a severe anemia in homozygotes and a milder anemia in heterozygotes. It should be clear that selection can more quickly eliminate a partially recessive allele than a completely recessive allele because the allele can no longer hide in the heterozygote. Dominant or semidominant alleles (model 3) are usually more quickly removed from a population because they are completely open to selection. It takes an in nite number of generations to remove a recessive lethal allele, but only one generation for natural selection to remove a completely dominant lethal allele (see model 3, where s1 s2 1). Examples of dominant deleterious traits in
people are Huntington disease, facioscapular muscular dystrophy, and chondrodystrophy. Model 2 is interesting because selection against the heterozygote leads to an unstable equilibrium at q 0.5. If one heterozygote is removed by selection, one each of the two alleles is eliminated. However, if p and q are not equal (and thus not equal to 0.5), then one A1 allele is not the same proportion of the A1 alleles as one A2 allele is of all the A2 alleles. In other words, in a population of fty individuals with q 0.1 and p 0.9, one A2 allele is 10% (1/10) of the A2 alleles, whereas one A1 allele is only 1.1% (1/90) of the A1 alleles. Removing one each of the two alleles causes a decrease in q. Therefore, a population following model 2 is at equilibrium at p q 0.5. However, this is an unstable equilibrium. Any perturbation that changes the allelic frequencies causes the rarer allele to be selected against and eventually removed from the population. An example is the maternal-fetal incompatibility at the Rh locus in human beings. The disease erythroblastosis occurs only in heterozygous fetuses (Rh Rh ) in Rh-negative (Rh Rh ) mothers. Heterozygotes are, therefore, selected against. In model 4, selection is against homozygotes. This model is called the heterozygote advantage, and we will derive its equilibrium condition because the results are important to evolutionary theory (table 20.5). At equilibrium q pq(s1 p s2q) W
(20.23)
For this expression to be zero, either p 0, q 0, or (s1 p s2q) 0
If p 0 or q 0, the result is trivial; the equilibrium exists only because of the absence of one of the alleles. The more meaningful equilibrium occurs when s1 p s2q 0. In that case s1 p and
s2q or s1(1
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