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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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E X E R C I S E S
MUTATION
A N D
P R O B L E M S *
conglomerate population. If the migration rate was 0.1, calculate the frequency of t in the original, native population.
1. Consider a locus with alleles A and a in a large, randomly mating population under the in uence of mutation. a. If the mutation rate of A to a is 6 10 5, and the back-mutation rate to A is 7 10 7, what is the equilibrium frequency of a b. If q 0.9 in generation n, what would it be one generation later, under only the in uence of mutation 2. Derive an expression for mutation equilibrium when no back mutation is occurring. 3. Consider a population in which p 0.9 and q 0.1. If the forward mutation rate, A a, is 5 10 5 and the reverse mutation rate, a A, is 2 10 5, calcu^ late the equilibrium frequency, q , of the a allele. 4. If the forward mutation rate, A a, is ve times the reverse mutation rate, what is the equilibrium frequency of the a allele
MIGRATION
SMALL POPULATION SIZE
10. In a population of ve hundred individuals with a frequency of allele A of 0.7, what is the ultimate fate of the A allele What is the probability that the population will eventually lose the A allele How many are N/5 generations 4N generations
NATURAL SELECTION
5. The following data refer to the R allele in the Rh blood system: frequency in western Europeans 0.62 frequency in eastern Europeans 0.45 frequency in Mongols 0.03 What is the total proportion of alleles that have entered the eastern European population Given the data from problem 1 of chapter 19, what factors could have caused the population to leave Hardy-Weinberg equilibrium (See also SMALL POPULATION SIZE and NATURAL SELECTION) In a population of nine hundred butter ies, the frequency ( p) of the fast allele of the enzyme phosphoenol pyruvate is 0.6, and the frequency of the slow form (q) is 0.4. Ninety butter ies migrate to this population, and the migrants have a slow-allele frequency of 0.8. Calculate the allelic frequencies of the new population. If the frequency of the N allele is 0.25 in a native population, 0.32 in a conglomerate population, and 0.4 in a migrant population, what percentage of the N alleles in the conglomerate population were derived from the migrant population In a particular population, the frequency of allele t was 0.25 in a migrant population and 0.45 in the
11. Differentiate among stabilizing, directional, and disruptive selection. 12. Derive a model of selection in which the tness of the heterozygote is half the tness of one of the homozygotes and twice the tness of the other. Give expressions for the following: a. Mean population tness b. Equilibrium allelic frequency (stable ) 13. Derive an expression for the equilibrium allelic frequencies under a model in which selection acts against heterozygotes. Is the equilibrium stable 14. Table 20.6 describes selection at the A locus in a given diploid species in which p f(A) and q f(a). a. Describe the type of selection occurring here. Why does the total equal one before selection but W, after b. Derive an equation for q after one generation of selection (qn 1). ^ c. This system will reach equilibrium, with p s2). If selection is twice as strong s2/(s1 against aa as against AA, what are the equilibrium allelic frequencies If s1 0.1 and s2 0.3, what percentage of heterozygotes is at equilibrium 15. Given a locus with alleles A and a in a sexually reproducing, diploid population in Hardy-Weinberg equilibrium, set up a model and the initial formula for the frequency of the dominant allele after one generation ( pn 1) if selection acts against the dominant phenotype. What are the equilibrium conditions 16. There is a locus with alleles A and a in a large, randomly mating, diploid, sexually reproducing population. Allele A mutates to a at a rate of , and no back mutation takes place. However, the aa homozygote is selected against with a tness of 1 s. Give a formula for the equilibrium condition. If 5 10 5
* Answers to selected Exercises and Problems are on page A-22.
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