Let frequency of A allele f(A) = p
    Let frequency of a allele f(a) = q
    Let allele frequencies in males & females be equal (q_m = q_f).
 
    What are the expected genotype frequencies after one generation of random union of gametes?

I. What are the probabilities of obtaining various gametic combinations?
                  prob. of A from male & A from female:     p_m x p_f = p²
                  prob. of a from male & a from female:      q_m x q_f  = q²
                  prob. of A from male & a from female,
                           or  a from male & A from female:     (p_m x q_f ) + (p_f x q_m ) = 2pq

II. What is the result of the binomial expansion of p & q in males & females ?

                  (p_m + q_m) (p_f + q_f) = p² + 2pq + q²

III. What are the areas of the four boxes of a Punnet Square ?

Recall that in Mendelian genetics, the Punnet Square [left] shows the results of a single cross between two Aa individuals, in which case the square is divided into four equal quarters, each representing 1/4 of the offspring.

In a population of individuals with allele frequencies p & q [right], the two axes are divided as the relative proportions of p & q in males and female gametes. Then, the areas of AA, Aa, and aa are AA = p², (pq + pq) = 2pq, and aa = q².

By any of the three methods:    f(AA) = p²         f(Aa) = 2pq        f(aa) = q²