In a Hardy Weinberg population suppose the allele Q is dominant over the allele q at what homozygous frequency

Question

In a Hardy Weinberg population; suppose the allele Q is dominant over the allele q at what homozygous frequency will the homozygous genotype (qq) become twice as frequent as the heterzygous genotype (Qq)?

Answer 1

Without any numbers to work with, the answer is essentially just a restatement of the question in algebraic form.  If q^2 is the frequency of the homozygous recessive genotype and 2pq is the frequency of the heterozygotes in the population, then the frequency that the homozygous recessive genotype is twice the frequency of the heterozygous genotype is when:

q^2 = 2  x  2pq = 4pq