7.03 Problem Set 6 Due before 5 PM on Monday, November 27 Hand in answers in recitation section or in the box outside of 68-120 1. a) Imagine a continent that has an indigenous population that has allelic variation of a gene that determines the ability of the body to store fat. Before modern times when food was scarce, a relatively rare allele (known as the “thrifty” allele) gives a heterozygous advantage of 2%. Individuals that are homozygous for the thrifty allele, because of health problems such as obesity and diabetes, have a fitness of 0.4. Calculate the expected frequency for the thrifty allele in this population. b) Explain why the rate of new mutations for the thrifty allele is not relevant for this calculation. c) Now consider the same continent in modern times in which the population can be thought of having two parts: 10% of the population comes from the indigenous people described above, and 90% of the population has immigrated from Europe where the thrifty allele is so rare that its frequency is effectively 0. Modern high calorie, high fat diet individuals who are homozygous for the thrifty allele are considered to have an inherited obesity related disease. Assuming random mating of the two populations, calculate the frequency of inherited obesity on the continent. d) What would the frequency of inherited obesity on the continent be if mating between individuals were completely assortative (i.e. no mixing between the immigrant and indigenous populations)?2. In this problem we will derive general expressions for two of the more practical results from human population genetics – X-linked recessive traits occur more often in males than females and individuals with rare recessive traits often have parents who are related to one another. a) Derive an expression, as a function of allele frequency (q), for the ratio of affected males to affected females for a X-linked recessive trait. b) Derive an expression, as a function of allele frequency (q), for the probability that an individual with a rare recessive trait will have parents who are first cousins relative to the probability of first cousin parents in the general population. Assume the a priori probability of parents who are first cousins is 0.005. You only need to derive a formula accurate for q < 10-2 – make any reasonable simplifying approximations that you
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