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Biology 4415/ Evolution PRACTICE PROBLEMS IN POPULATION GENETICS
1. In a study of the Hopi, a Native American tribe of central Arizona, Woolf and Dukepoo^1 found 26 albino individuals in a total population of 6000. This form of albinism is controlled by a single gene with two alleles: albinism is recessive to normal skin coloration. a) Why can’t you calculate the allele frequencies from this information alone? b) Calculate the expected allele frequencies and genotype frequencies if the population were in Hardy-Weinberg equilibrium. How many of the Hopi are estimated to be carriers of the recessive albino allele? (^1) Woolf, C. M. and Dukepoo, F. C. 1959. Hopi Indians, interbreeding and albinoism. Science 164: 30-37.
2. A wildflower native to California, the dwarf lupin ( Lupinus nanus ) normally bears blue flowers. Occasionally, plants with pink flowers are observed in wild populations. Flower color is controlled at a single locus, with the pink allele completely recessive to the blue allele. Harding^2 censused several lupin populations in the California Coast Ranges. In one population of lupins at Spanish Flat, California, he found 25 pink flowers and 3291 blue flowers, for a total of 3316 flowers. a) Calculate the expected allele frequencies and genotype frequencies if the population were in Hardy-Weinberg equilibrium. b) Harding studied the fertility of lupins by counting number of seed pods produced per plant in a subsample of the Spanish Flat population. He found the following: mean # pods number of plants examined blue 19.33 39 pink 13.08 24 Assume that heterozygotes are as fit as homozygous blue lupins, and that seeds from both pink and blue lupins all suffer about the same mortality rate after germinating. Calculate the relative fitness of each genotype. (^2) Harding, J. 1970. Genetics of Lupinus. II. The selective disadvantage of the pink flower color mutant in Lupinus nanus. Evolution 24: 120-127.
4. A 1970 study^4 of 93 house mice ( Mus musculus ) in a single barn in Texas focused on a single locus (the gene for a certain enzyme) with two alleles, A and A’. The genotype frequencies found were: AA 0. AA’ 0. A’A’ 0. a) Calculate the allele frequencies. b) How does this population differ from the predictions of Hardy-Weinberg equilibrium? Show your work. c) In this specific case, what factor or factors are most likely to be causing deviations from Hardy-Weinberg equilibrium? How can you tell? (^4) I don’t remember where I got this problem...
5. The geneticist P. M. Sheppard^5 carried out a selection experiment on a laboratory population of the fruit fly Drosophila melanogaster. The stubble allele, which affects bristle shape of the fly, is dominant to the wild-type allele.Flies that are homozygous for stubble always die during embryonic development. a) Sheppard started out with 86% normal flies and 14% stubble flies. Calculate the allele frequencies. b) Assuming for now that wild-type and stubble flies do not differ in fitness, use the allele frequencies to calculate the mean fitness. Then predict the percentages of normal and stubble flies in the next generation. Show all work. c) Sheppard introduced an additional source of selection: he removed 60% of the wild-type flies before they could breed in each generation. Repeat part b taking this into account. (^5) Sheppard, P. M. 1959. Natural Selection and Heredity. Philosophical Library, New York.
7. P. D. N. Hebert^7 studied the frequencies of alleles for the gene that codes for the enzyme malate dehydrogenase ( Mdh ) in the “water flea,” Daphnia magna , living in ponds near Cambridge, England. There are three alleles of the Mdh gene, abbreviated S, M and F. Hebert found the following genotypes: genotype observed number SS 3 SM 8 SF 19 MM 15 MF 37 FF 32 total 114 a) Calculate the allele frequencies. b) Is the population in Hardy-Weinberg equilibrium? (^7) Hebert, P. D. N. 1974. Enzyme variability in natural populations of Daphnia magna. III. Genotypic frequencies in intermittent populations. Genetics 77: 335-341.
8. Avena fatua is a species of wild oat (a type of grass). Jain and Marshall studied wild oat population genetics in California.^8 One of the traits they examined was the pubescence (hairiness) of the leaf sheath, which is controlled by a single locus with two alleles, written L and l. They found that the frequencies of genotypes in one population were: LL 57.1% Ll 7.1% ll 35.8% a) Calculate the allele frequencies b) Predict what the genotype frequencies should be under Hardy-Weinberg equilibrium. If there is a difference between actual and predicted frequencies, explain briefly why the differences might exist. c) Calculate F. (^8) Jain, S. K. and Marshall, D. R. 1967. Variation in natural populations of Avena fatua and A. barbata. American Naturalist 101: 233-249.
10. True story: In 1912, the geneticist W. H. Goddard suggested that feeble-mindedness was caused by Mendelian inheritance at a single locus with two alleles. Persons homozygous for the recessive, feeble-minded allele (call it f ) were dopes, dummies, and dimwits—“incapable of managing their affairs with ordinary prudence”, as Goddard said. Heterozygotes ( Ff ) and homozygous dominants ( FF ) were of normal intelligence. This is not actually true —but pretend that it is, for the purposes of working this problem. (25 pts. total) a) According to the 1910 census, the population of the United Stetes was 91,972,266. Goddard estimated that 1% of the population was feeble-minded. Assume that the population of the US was in Hardy-Weinberg equilibrium. Calculate the allele frequencies, and then calculate the percentages of the population that would be heterozygous and homozygous dominant. (5 pts.) b) At one time or another, thirty states had laws mandating the compulsory surgical sterilization of the feebleminded. (As of 1996, Arkansas and nine other states still did have such a law on the books.)^9 There were organizations in the early 20th century that lobbied for their enactment nationwide. Imagine that, in some alternate-reality USA, a mandatory, nationwide law really was put into effect that forced the sterilization of all feebleminded individuals before they could reproduce. Assume that the authorities were so efficient that they were able to track down and sterilize 90% of the feebleminded—and that they never, ever sterilized anyone who wasn’t feebleminded. What would be the frequencies of genotypes, and of alleles, after one generation? (^9) Adler, R. R. 1996. Estate v. C.W .: A pragmatic approach to the involuntary sterilization of the mentally disabled. Nova Law Review 20:1323-1368.
11. Fundulus heteroclitus (common name: mummichog) is a small fish that lives in bays and estuaries along the east coast of North America, from Newfoundland to Florida. It’s been extensively used in evolutionary studies.^10 Northern populations of F. heteroclitus are virtually completely homozygous for an allele of a liver enzyme called Ldh-B (lactate dehydrogenase B), an allele which is just called Ldh-Ba. Southern populations are virtually completely homozygous for the other major allele of Ldh-B , referred to as Ldh-B b . Ldh-B has an effect on the survival of fish embryos when exposed to temperature stress. In an experimental test of this survival, Fundulus heteroclitus eggs from different populations were incubated at 30°C, under heat stress. 57% of the eggs from a southern population hatched successfully at 30°C. Only 22% of the eggs from a northern population hatched. Interestingly enough, 87% of the eggs that were heterozygous at the Ldh-B locus successfully hatched. a) Suppose you put 500 northern Fundulus fish and 500 southern fish in a large tank, allowed them to breed freely, and then incubated all the eggs at 30°C. Predict the frequencies of both alleles and genotypes after one generation. b) Predict the frequencies of both alleles and genotypes after a second generation. c) Suppose that, when you actually do this experiment, you discover that the actual heterozygote frequency is 0.55. Calculate F. (^10) Powers, D.A., M. Smith, I. Gonzalez-Villasenor, L. DiMichele, D. Crawford, G. Bernardi, and T. Lauerman. A multidisciplinary approach to the “selectionist/neutralist” controversy using the model teleost, Fundulus heteroclitus. Oxford Surveys in Evolutionary Biology 9 : 43-107.
