Hardy–Weinberg Heterozygote Frequency

Hardy and Weinberg independently showed in 1908 that allele frequencies in a large, randomly mating population do not change on their own. Genotype frequencies settle in one generation into $p^2$, $2pq$ and $q^2$, and stay there forever unless something acts on them. The heterozygote term is the interesting one, because it is the part that carries hidden variation.

The result has a ceiling that surprises people: heterozygosity peaks at 50%, reached exactly when both alleles are at 0.5, and falls away symmetrically on either side. An allele at 0.3 and an allele at 0.7 give identical heterozygosity of 42%. A rare allele at 1% sits almost entirely in heterozygotes — 1.98% of the population carries it against only 0.01% homozygous — which is why recessive deleterious alleles persist so stubbornly and why selecting against the visible homozygote removes them so slowly.

The equilibrium's real use is as a null hypothesis. It assumes no selection, no mutation, no migration, no drift and random mating, and a plant population almost never satisfies the last of those. Selfing species depart from it enormously — a wheat or bean population has far fewer heterozygotes than the equation predicts, which is the signal that reveals the mating system. Comparing observed heterozygosity against this expectation gives $F$, the fixation index, and $F$ is how population geneticists measure inbreeding without knowing a single pedigree.