Problem Set 1
Up Problem Set 1 Problem Set 2 Problem Set 3 Problem Set 4 Problem Set 5

Solutions1

ANTH 450/550: Population and Quantitative Genetics

Problem Set 1

1. If (p + q) = 1, verify or disprove the following:

        a) 1 + q = 2 - p

        b) 1 - 2q = 2p - 1

        c) p - p2 = q - q2

        e) 1 - p / q = 2 - 1/p

2. Huntington's chorea is a genetic disease in humans caused by an autosomal dominant allele, with a frequency of 0.0004 in most populations. Based on this information, and assuming that a population is in Hardy-Weinberg equilibrium, what is the frequency of the choreic allele?

3. Two variants of a protein, S and T, can be detected in a certain local human population. Three recognizable phenotypes exist: S, T, and ST. A screen of the local population yielded 45 S phenotypes, 21T phenotypes, 30 ST phenotypes, and 4 individuals who could not be scored for either the S or T proteins. Test the hypothesis that the protiens S and T are determined by a pair of alleles at a single locus that is in Hardy-Weinberg equilibrium in the local population. Use the chi-square test. Do you accept or reject this hypothesis?

4. Now consider an alternative hypothesis. Suppose there are three alleles at a locus, S, T, and O such that allele O makes a protein that is undetectable by your assay. Hence the SS and SO genotypes make the S protein, the TT and TO genotypes make the T protein, and the OO genotype makes no detectable protein. Assume further that the population is randomly mating and that the frequencies of the three alleles are 0.50 for S, 0.30 for T, and O.20 for O.

Test this hypothesis with a chi-square test, giving the degrees of freedom (Remember: degrees of freedom for testing Hardy-Weinberg equilibrium is the number of theoretically observable phenotypic classes minus one, minus the number of parameters estimated from the data). What do the results tell you abot the impact of "silent alleles" on tests for Hardy-Weinberg?

5. The equation for the decay of linkage disequilibrium is given by

D = (1 - r) D

where r is the recombination rate and D is the initial level of disequilibrium. Starting with the equation

D = (P11 P22) - (P12 P21)

prove that the equation for D is true. Hint: Start with the equation for D in terms of P11 , P22, etc. and substitute in for the P terms.