1Practice Problems 51. Calculate H for each of the following genes from the allele frequencies:(a) f(A1) = 0.5 f(A2)= 0.5(b) f(B1) = 0.99 f(B2) = 0.01(c) f(C1) = 0.2 f(C2) = 0.2 f(C3) = 0.2 f(C4) = 0.2 f(C5) = 0.2(d) f(D1) = 0.90 f(D2) = 0.04 f(D3) = 0.03 f(D4) = 0.02 f(D5) = 0.01Do you see any general patterns in these numbers?2. The c coat color gene was sequenced from 335 individuals from a population ofunicorns. Four different alleles were found, called c1, c2, c3, and c4. Four genotypeswere found, with numbers as follows:c1/c1309c1/c4 24c1/c2 1c1/c3 1(a) Calculate the frequencies of each allele, to four decimal places/(b) Calculate the expected heterozygosity to four decimal places:(c) Is this population of unicorns inbred, outbred, or random mating?3. Suppose that you measure the nucleotide diversity in the open reading frame of thehuman cytochrome oxidase subunit 3 gene, using restriction enzymes. The diversityturns out to be 0.001.(a) Consider the third base pair in the second codon of the open reading frame. What isthe probability that it is identical in your cytochrome oxidase 3 gene and mine?(b) Consider the first base pair in the open reading frame: what is the probability that itis identical in our genes?4. On a scale where the selection coefficient of a mutant allele can range from –1 to +1,what would be the selection coefficient of each of the following mutant alleles? Answerscould be -1, > -1 and < 0, 0, > 0 and < 1, or 1.(a) A mutation in the first codon position of a processed pseudogene in the mouse? (b) In bacteria, an erythromycin-resistance mutation in culture medium containing theantibiotic.(c) In bacteria, an erythromycin-resistance mutation in culture medium with noantibiotic.5. For each of the following populations, indicate whether you would predict that theobserved heterozygosity be equal to (=), greater than (>), or less than (<) the expectedheterozygosity:2(a) a random mating population of one million human beings(b) the gorillas in the Columbus, Ohio zoo6. How much expected heterozygosity would you expect to see under the neutralhypothesis, if you looked for electrophoretic variants for α-globin in a large sample ofrabbits from a population, assuming that the rabbit population is in mutation-driftequilibrium? Calculate the expected heterozygosity, assuming that the mutation rate is5 X 10-5 mutations per gene per generation and the effective population size is (a) 103,(b) 105, and (c) 107. (Note that you can't use the approximate formula in this case.) (d)Assuming that this mutation rate is approximately correct for electrophoretic variants ofα-globin, and that α-globin is a fairly typical protein, which of the preceding effectivepopulation sizes do you think is closer to correct for this population of rabbits? Hint:look at the expected heterozygosities.7. A genetic engineer introduces a modified globin gene in an unfertilized mouse egg,replacing the normal allele by transformation. The egg is fertilized in vitro andimplanted in a foster mother who rears it to maturity. Then the modified(heterozygous) mouse is illegally released from captivity by animal rights activists whobelieve that it is suffering. Actually it is very healthy: the modified globin gene has thesame fitness as the wild type. The mouse joins a wild population of 50 individuals.(a) The modified mouse has 20 offspring by wild fathers and then dies, what is theprobability that the engineered globin gene will be lost in the first generation? Notethat you can use basic Mendelian genetics to answer this question, as opposed towhat we learned about population genetics.(b) What is the probability that the engineered globin allele will be lost from thepopulation sometime, without ever being fixed?8. Which of the following is the most accurate explanation of why functionallyimportant sequences such as promoters can be recognized by their sequenceconservation? Explain why you did, or did not, choose each one.(a) They have a lower mutation rate than other sequences.(b) They have more synonymous substitutions than other sequences.(c) They are transcribed more often than other sequences.(d) They have a higher ratio of detrimental to neutral mutations than do