Imagine you are a geneticist interested in studying a newly discovered species of very colorful birds. You have found that a single gene is responsible for their beautiful colors and that yellow birds are homozygous for the yellow allele, blue birds are homozygous for the blue allele and green birds are heterozygous for these alleles. You focused your efforts on studying one specific population and counted 9% yellow, 49% blue and 42% green birds. What are the allele frequencies in this population?\

Hardy–Weinberg equilibrium, states that allele and genotype frequencies in a population will remain constant from generation to generation. Equilibrium is reached in the absence of selection, mutation, genetic drift and other forces and allele frequencies p and q are constant between generations. In the simplest case of a single locus with two alleles denoted A and a with frequencies f(A) = p and f(a) = q, the expected genotype frequencies under random mating are f(AA) = p² for the AA homozygotes, f(aa) = q² for the aa homozygotes, and f(Aa) = 2pq for the heterozygotes.

p²+2*p*q+q²= 1 p+q= 1 q= 1-p

yellow (p²)= 9%= 0.09 p= √0.09= 0.3

green (2*p*q)= 42%= 0.42

blue (q²)=49%= 0.49 q=1-0.3= 0.7 or q= √0.49= 0.7