Hardy-Weinberg Equilibrium

In population genetics, the Hardy-Weinberg principle serves as the fundamental null hypothesis. It states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary forces. Mathematically represented as p² + 2pq + q² = 1, it models a random-mating population of infinite size with no mutation, selection, migration, or genetic drift. Real populations never fully satisfy these conditions, but by measuring deviations from this equilibrium using statistical tests (like the chi-square test), geneticists can detect and measure the strength of evolutionary forces. The formula proves that sexual reproduction alone does not change allele frequencies, establishing that evolution requires active evolutionary pressures.

At its heart, Hardy-Weinberg is simple probability. If alleles pair up at random, the chance of an AA child is just p × p = p², exactly like flipping two heads. That lets you work backwards: from the fraction of people affected by a recessive condition (q²) you recover how common the silent carriers are. If 1 in 10,000 is affected, then q = 0.01 and carriers (2pq) are about 1 in 50 — 200 times more common than the disease itself.

This cornerstone of genetics came from someone who thought little of it. In 1908 the geneticist Reginald Punnett — a cricketing friend of G. H. Hardy at Cambridge — could not explain why a dominant trait didn't slowly take over a population. Hardy scribbled the answer, then published it almost apologetically, being a pure mathematician who disdained applied maths. The physician Wilhelm Weinberg derived the same law that year in German; it was ignored for 35 years until Curt Stern gave both men equal credit in 1943.