Chapter 21, Problem 14P

The equation p² + 2pq + q^2> = 1 representing the Hardy-Weinberg proportions examines genes with only two alleles in a population.

a.

Derive a similar equation describing the equilibrium proportions of genotypes for a gene with three alleles. [Hint: Remember that the Hardy-Weinberg equation can be written as the binomial expansion (p + q)2 .]

b.

A single gene with three alleles (IA, IB, and i) is responsible for the ABO blood groups. Individuals with blood type A can be either IA IA or IA i; those with blood type B can be either IB IB or IB i; people with AB blood are IA IB, and type O individuals are ii. Among Armenians, the frequency of IA is 0.360, the frequency of IB is 0.104, and the frequency of i is 0.536. Calculate the frequencies of individuals in this population with the four possible blood types, assuming Hardy-Weinberg equilibrium.