Question: This problem introduces some aspects of a simple genetic model. Assume that genes in an organism occur in pairs and that each member of the pair can be either of the types a or A. The possible genotypes of an organism are then AA, Aa, and aa (Aa and a A are equivalent). When two organisms mate, each independently contributes one of its two genes; either one of the pair is transmitted with probability .5.
a. Suppose that the genotypes of the parents are AA and Aa. Find the possible genotypes of their offspring and the corresponding probabilities.
b. Suppose that the probabilities of the genotypes AA, Aa, and aa are p, 2q, and r, respectively, in the first generation. Find the probabilities in the second and third generations, and show that these are the same. This result is called the Hardy-Weinberg Law.
c. Compute the probabilities for the second and third generations as in part (b) but under the additional assumption that the probabilities that an individual of type AA, Aa, or aa survives to mate are u, v, and w, respectively.