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5. Conceptual and Research Methods
- The University of Alabama Press
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Genetic Drift and Phenotypic Variability It was noted above that small populations experience the effects of genetic drift in more dramatic fashion. To model this, I consider gene 1 from population 1 listed in Table 4.3. If mating is random and the sex ratio is equal, then the probability of choosing any single allele is equal to the frequency of that allele. Assuming a small population size of 50 individuals (with 100 total alleles), the probability of selecting an ‘A’ allele is 98 percent and an ‘a’ or ‘a′’ allele is 1 percent , respectively. The probability of selecting two ‘a’ or ‘a′’ alleles (one from a father and one from a mother) is 4 percent, an unlikely event. Conversely, the probability of not picking either an ‘a’or ‘a′’ allele is equal to the probability of selecting two ‘A’ alleles, which is 96 percent. Therefore, for each generation there is a 96 percent chance of the ‘a’ and ‘a′’ becoming lost, resulting in the complete lack of genetic variability for this gene. If only one person survives to the next generation (a population bottleneck caused by an epidemic, for example ), then there is a high probability that the ‘a’ and ‘a′’ alleles will not be represented in this person. If population size does not decline, then the probability of faithful representation of all alleles increases. If the preceding were repeated for each of four loci, then, all else being equal, all populations would eventually resemble populations 1–3 in Table 4.2. That is, genetic drift works to reduce genetic variability and increase homozygosity within a population. Human Tooth Size 75 Changes in population size lead to similar changes in the expected effects of genetic drift. And, because the probability of allele ¤xation is equal to the initial allele frequency (Hartl and Clark 1987), the smaller the population size, the greater the potential effect of any given allele. For example, if there is only one copy of the ‘a’ allele in a population of size 50, there is a 1 percent chance of that allele becoming ¤xed, an unlikely occurrence. However, if the size of this population decreased to 5 individuals (and the ‘a’ allele happened to be carried by one of these individuals—the randomness factor), then the potential effect of this rare allele is much greater. The probability of allele ¤xation has increased to 10 percent. Also recognize that if we considered 100 different populations, each with initial allele frequencies of ‘A’ equals 98 percent and ‘a’ and ‘a′’ equal 1 percent, respectively, then we expect one population to become ¤xed for ‘a’, another to become ¤xed for ‘a′’, and 98 to become ¤xed for ‘A’. In all 100 populations, drift is working to ¤x one of these alleles, thus reducing heterozygosity. This explains why subdivided populations (Apalachee and Guale) are expected to diverge (have different allele frequencies) under a pure drift model. Genetic drift can be summarized as follows: (1) Genetic drift reduces variation within a population. The underlying mechanism for variance reduction is the ¤xation or loss of alleles at a locus. (2) Genetic drift increases variation between subdivided populations. The underlying mechanism is the stochastic nature of the allele sampling process, thus leading to expected divergent allele frequencies in subdivided populations. (3) Smaller populations experience greater drift effects because heterozygosity is lost more quickly as alleles deviate and approach ¤xation or loss. (4) Decreasing population size results in a loss of genetic variability as a result. Gene Flow and Phenotypic Variability To model gene ®ow, I once again consider the two populations in Table 4.3. In Table 4.4, I consider the effects of gene ®ow on allele frequencies resulting from individuals from population 2 (e.g., Yamassee, Guale, Timucua) migrating into population 1 (e.g., Apalachee). In the ¤rst generation, the allele frequencies for the ‘A’, ‘a’ and ‘a′’ alleles are 98, 1, and 1 percent, respectively (from Table 4.3, population 1). In the second generation, ten randomly selected migrants from population 2 migrate into population 1, resulting in the change of alleles frequencies presented for generation 2. In the second generation the allele frequencies for the ‘A’,‘a’and‘a′’alleles are 87, 6.5, and 6.5 percent, respectively. The rate of change 76 Chapter 4 for each allele is −11 percent, +5.5 percent, and +5.5 percent, respectively. Variation has increased within population 1 (Apalachee) because the proportion of heterozygous genotypes has increased, and the variation between...