Chapter 22, Problem 13P

In a certain plant, leaf size is determined by four genes whose alleles assort independently and act additively. Thus, alleles A, B, C, and D each add 4 cm to leaf length and alleles A′, B′, C′, and D′ each add 2 cm to leaf length. Therefore, an AA BB CC DD plant has leaves 32 cm long and an A′A′ B′B′ C′C′ D′D′ plant has leaves 16 cm long.

a.	If true-breeding plants with leaves 32 cm long are crossed to true-breeding plants with leaves 16 cm long, the F will have leaves 24 cm long and the genotype AA′ BB′ CC′ DD′. List all possible leaf lengths and their expected frequencies in the F generation produced from these F plants. (Hint: Recall Problem 45e in Chapter 2.)
b.	Now assume that in a randomly mating population the following allele frequencies occur: frequency of A = 0.9 frequency of A’ = 0.1 frequency of B = 0.9 frequency of B’ = 0.1 frequency of C = 0.1 frequency of C’ = 0.9 frequency of D = 0.5 frequency of D’ = 0.5 Calculate separately the expected frequency in this population of the three possible genotypes for each of the four genes.
c.	What proportion of the plants in the population described in part (b) will have leaves that are 32 cm long?