Hardy–Weinberg Equilibrium
From one allele or genotype frequency, find all the others — for example the share of carriers of a recessive disease. Or test whether observed genotype counts fit equilibrium with a χ² test.
What is Hardy–Weinberg Equilibrium?
For a gene with two alleles, A (frequency p) and a (frequency q), random mating produces the genotypes AA, Aa and aa in the proportions p² : 2pq : q². In a population that is not evolving, these frequencies stay the same generation after generation.
Recessive conditions show up only in aa individuals, but most copies of the allele hide in healthy carriers (Aa). The equation reveals how common carriers are from how often the condition appears.
Live Graph
p = 0.98Conditions for Equilibrium
| Assumption | If violated… |
|---|---|
| No mutation | new alleles appear |
| Random mating | genotype ratios shift (e.g. inbreeding) |
| No natural selection | favoured alleles increase |
| Very large population | genetic drift changes frequencies |
| No migration (gene flow) | alleles enter or leave |
Worked Techniques
Only aa individuals are visibly different, so q² is usually what you can count. Take the square root to get q.
About 1 in 25 people carry the allele — a hundred times more than show the condition.
Compare observed counts with the expected p²N, 2pqN and q²N. With one degree of freedom, χ² above 3.84 means p < 0.05: the population is likely not in equilibrium.
Sources & Verification
- G. H. Hardy, “Mendelian proportions in a mixed population”, Science 28(706), 49–50 (1908).
- R. R. Sokal & F. J. Rohlf, Biometry, 4th ed., W. H. Freeman, 2012 — Ch. 17 (Analysis of Frequencies).