STAT/BIOSTAT 550: Homework 2. Due April 11, 2014

2. At one of the loci of the rhesus blood group system, there are 2 alleles C and c.
a) In the simplest test, with only anti-C reagent, C is dominant to c. In a test of 1000 people, 160 are C-negative (genotype cc). Assuming Hardy-Weinberg Equilibrium, estimate the frequency of the c allele, and the variance of your estimator.
b) An anti-c reagent now becomes available, so that C and c are codominant. It is found that 400 individuals are CC and 440 are Cc. How does this change your estimate of the frequency of the c allele? And of the variance of the estimator?

3. (Example, due to Weir.)
Suppose a population consists of a mixture of two randomly-mating subpopulations of equal size. Consider a locus with three codominant alleles. In one subpopulation, the three alleles have frequencies p=0.6, q=0.3,and r=0.1, while in the other subpopulation they are p=0.4, q=0.1, r=0.5. Which genotypes have a smaller frequency than they would have in a single random-mating population with the same overall allele frequencies?

4. In a subdivided population, the proportion of individuals in subdivision i is a_i. In subdivision i, at a locus with two alleles A and B, the frequency of allele A is q_i, and within each subdivision the genotypes are in Hardy-Weinberg proportions.
Let q = sum_i a_i q_i and let V = sum_i a_i (q_i -q )².
Find the frequencies of the three genotype AA, AB and BB in terms of q and V.