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Figure 2 Graphical output of the computer program from gure 1, with axis labels drawn in. The frequency of the a allele, q, begins at 0.1 and asymptotes toward 0.6.
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s2 s1 s2
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(20.25)
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Several interesting conclusions follow. First, unlike the other models of selection, this model allows a population to maintain both alleles. We can demonstrate that this equilibrium is stable by graphing the q value against q. Such a graph appears in gure 20.12, in which q is the frequency of allele A2 and the tnesses of genotypes A1A1, A1A2, and A2A2 are assumed to be 0.8, 1, and 0.7, respectively. Note that if the equilibrium is perturbed by an increase or decrease in q, the population returns to the point of equilibrium. Second, the equilibrium is independent of the original allelic frequencies since it involves only the selection coef cients, s1 and s2. Last, the equilibrium for each allele (equations 20.24 and 20.25) is directly proportional to the selection coef cient against the other allele. As the selection against A1 increases (s1 increases), the equilibrium shifts toward a higher value of q (more A2 alleles; box 20.1).
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Plot of allelic frequency (q) versus change in allelic frequency ( q) for a polymorphism maintained by 0.2 and s2 0.3; heterozygote advantage. In this case, s1 ^ the equilibrium value, q , is 0.4. When perturbed, the population tends to return to this value unless the perturbation brings q to either 1.0 or 0.0, in which case the population is either xed for the a allele or has lost it. In both cases, no further change in allelic frequency will take place, barring mutation or migration.
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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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The McGraw Hill Companies, 2001
Solved Problems
S U M M A R Y
STUDY OBJECTIVE 1: To develop ways to analyze popula-
tion genetics problems
A ve-step protocol is presented to determine equilibrium allelic frequencies. STUDY OBJECTIVE 2: To analyze the effects of mutation,
Finite population size is a source of sampling error. It results in changes in allelic frequencies known as random genetic drift. The smaller the population, the more rapidly allelic frequencies change.The dynamics of random genetic drift were studied graphically. STUDY OBJECTIVE 3: To study the ways in which natural
migration, and population size on the Hardy-Weinberg equilibrium 571 577
The effects of relaxing some of the assumptions of the Hardy-Weinberg equilibrium are analyzed. Both mutation and migration transport alleles in and out of a population. Mutation provides the variability on which natural selection acts, but it usually does not directly affect the equilibrium because mutation rates are usually very low. If two randomly mating populations merge, or if two randomly mating demes are mistakenly treated as a single deme, the conglomerate will be de cient in heterozygotes.This deviation is called the Wahlund effect.
selection results in organisms adapted to their environments 577 584
Natural selection is de ned by differential reproductive success. Depending upon which phenotypes are most t, natural selection can act in several ways to change allelic and genotypic frequencies. Selection against the recessive homozygote acts to remove the allele from the population. Mutation brings the allele back into the population. Thus, a selection-mutation equilibrium maintains the unfavorable allele at a relatively low frequency. Heterozygote advantage maintains both alleles in a population.
S O L V E D
PROBLEM 1: At a particular locus, there are two alleles, B
P R O B L E M S
ability of its xation is 0.75 (see g. 20.8). Since it is convenient to measure time (number of generations) within populations of nite size in units of population size, we can see that an event that takes N generations will be one thousand generations in the small population, but one million generations in the large population.Thus, random genetic drift occurs in the larger population at about onethousandth the rate of the small population.
PROBLEM 3: In a laboratory colony of fruit ies, the t-
and b. The mutation rate of B to b is 3.5 10 4, whereas the mutation rate of b to B is 6 10 8. What is the equilibrium frequency of the b allele, assuming no other factor is operating in this population to disturb the HardyWeinberg equilibrium Answer: We let q f(b), 3.5 10 4, and 6 8 10 . We then simply substitute and into equation 20.6:
( ) (3.5 10 0.9998
3.5 10 4 4 6 10 8 )
PROBLEM 2: Given a population of about one million cicadas with a frequency of the a allele at the A locus of 0.75, what is the probability that the a allele will be lost due to random genetic drift How much longer will the possible loss of the allele take than the loss of the allele would take in a population of one thousand
Answer: Regardless of the size of a nite population, random genetic drift takes place. The probability of the loss of an allele with a frequency of 0.75 is 0.25; the prob-
nesses of the genotypes of an electrophoretic locus (malate dehydrogenase) are determined. Three genotypes, FF, FS, and SS, have tnesses of 0.85, 1.0, and 0.6, respectively. What is the equilibrium frequency of the slow allele (S) Answer: If the tnesses of the three genotypes FF, FS, and SS are as given, then the locus is exhibiting heterozygote advantage with selection coef cients of the two homozygotes of s1 0.15 (1 0.85) and s2 0.4 (1 0.6). If q is the frequency of the slow allele, then, using equation 20.24,
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