Hardy–Weinberg equilibrium

Hardy–Weinberg equilibrium describes an idealized population that is not evolving, so its allele and genotype frequencies stay the same across generations. The principle was worked out independently in the early 1900s by the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg. For a gene with two alleles at frequencies p and q, p + q = 1, and the expected genotype frequencies are p² for one homozygote, 2pq for heterozygotes and q² for the other homozygote, which together add up to 1.

The equilibrium holds only if the population is very large, mating is random, and there is no mutation, no migration and no natural selection. No real population meets all of these conditions, and that is what makes the principle useful: it serves as a null model. If the genotype counts observed in a population differ clearly from those predicted, some evolutionary force, such as genetic drift, gene flow or selection, is probably at work.

The equations also let geneticists estimate hidden carriers. If one person in 2,500 has a recessive condition, q² is 0.0004, so q is 0.02, and roughly 1 person in 25 is a heterozygous carrier.