Hardy-Weinberg Theorem

Derivation of the Hardy-Weinberg Theorem:
three methods

In a monoecious species, for a single locus with two alleles A & a:
    Let frequency of A allele f(A) = p
    Let frequency of a allele f(a) = q
    Let allele frequenices in males & females be equal.
    What are the expected genotype frequencies?

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_fx q_m ) = 2pq

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

What are the areas of the four boxes in a Punnet Square?

By all three methods: f(AA) = p² f(Aa) = 2pq f(aa) = q²