Hardy–Weinberg Principle

Origins

After Mendelian genetics was rediscovered, some assumed that dominant traits would spread through a population until they reached a 3:1 ratio. In 1908 the British mathematician G. H. Hardy sent a short letter to Science showing with simple algebra that in a randomly mating population allele frequencies do not change by themselves, whether dominant or recessive. The same year the German physician Wilhelm Weinberg independently reached the same conclusion, and Castle (1903) had noted a similar result. After Curt Stern (1943) publicized Weinberg's contribution, the name "Hardy–Weinberg law" became standard.

Formula and conditions

If two alleles A and a have frequencies p and q (p + q = 1), then after one generation of random mating the genotypes AA, Aa and aa occur at frequencies p², 2pq and q², and stay there. For example, if a recessive trait (aa) affects 1 in 10,000 people, q = 0.01 and p = 0.99, so the carrier (Aa) frequency is about 2pq ≈ 0.0198, or roughly 1 in 50. The equilibrium requires (1) random mating, (2) a very large population with no drift, (3) no mutation, (4) no migration or gene flow and (5) no natural selection. Because real populations never fully meet these conditions, the principle is less a description of real populations than a reference point showing what happens when no evolutionary force acts.

Uses and significance

Hardy–Weinberg equilibrium serves as the null model in evolution research: deviations of observed genotype frequencies from expectations signal inbreeding, population structure, selection or migration. Fisher (1930) and Wright (1931) built modern population genetics by adding selection, drift and migration to this baseline. In medical genetics it is used to estimate carrier frequencies for recessive disorders, and in genome-wide association studies markers that deviate strongly from equilibrium are filtered out as likely genotyping errors (Wigginton et al., 2005). Forensic science also relies on it to compute random-match probabilities for DNA profiles.

FAQ

What is the Hardy–Weinberg principle in simple terms?

In a large population where no evolutionary force acts, the proportions of gene variants stay the same from generation to generation.

Why does it matter if real populations never meet its conditions?

Measuring how far a population departs from equilibrium reveals whether selection, migration, inbreeding or other forces are at work, so it serves as a baseline.

Sources reviewed: 2026-10-26

References

1. Hardy, G. H. (1908). Mendelian proportions in a mixed population. Science, 28(706), 49–50.
2. Weinberg, W. (1908). Über den Nachweis der Vererbung beim Menschen. Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg, 64, 368–382.
3. Castle, W. E. (1903). The laws of heredity of Galton and Mendel. Proceedings of the American Academy of Arts and Sciences, 39(8), 223–242.
4. Stern, C. (1943). The Hardy-Weinberg law. Science, 97(2510), 137–138.
5. Crow, J. F. (1988). Eighty years ago: The beginnings of population genetics. Genetics, 119(3), 473–476.
6. Edwards, A. W. F. (2008). G. H. Hardy (1908) and Hardy–Weinberg equilibrium. Genetics, 179(3), 1143–1150.
7. Wigginton, J. E., Cutler, D. J., & Abecasis, G. R. (2005). A note on exact tests of Hardy-Weinberg equilibrium. American Journal of Human Genetics, 76(5), 887–893.
8. Hartl, D. L., & Clark, A. G. (2007). Principles of Population Genetics (4th ed.). Sunderland, MA: Sinauer.
9. Hedrick, P. W. (2011). Genetics of Populations (4th ed.). Sudbury, MA: Jones and Bartlett.
10. Wright, S. (1931). Evolution in Mendelian populations. Genetics, 16(2), 97–159.
11. Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Clarendon Press.
12. Mayo, O. (2008). A century of Hardy–Weinberg equilibrium. Twin Research and Human Genetics, 11(3), 249–256.
13. Provine, W. B. (1971). The Origins of Theoretical Population Genetics. Chicago: University of Chicago Press.