# Hardy–Weinberg equilibrium

**Hardy–Weinberg equilibrium** The balance in the relative numbers of alleles (see allele frequency) that is maintained within a large population over a period of time assuming that: (1) mating is random; (2) there is no natural selection; (3) there is no migration; (4) there is no mutation. In such a stable population, for a gene with two alleles, *A* (dominant) and *a* (recessive), if the frequency of *A* is *p* and the frequency of *a* is *q*, then the frequencies of the three possible genotypes (*AA*, *Aa*, and *aa*) can be expressed by the *Hardy–Weinberg equation*: *p*^{2} + 2*pq* + *q*^{2} = 1,

where *p*^{2} = frequency of *AA* (homozygous dominant) individuals, 2*pq* = frequency of *Aa* (heterozygous) individuals, and *q*^{2} = frequency of *aa* (homozygous recessive) individuals. The equation can be used to calculate allele frequencies if the numbers of homozygous recessive individuals in the population is known. The equation and the equilibrium are named after British mathematician G. H. Hardy (1877–1947) and German physician W. Weinberg (1862–1937).

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**Hardy–Weinberg equilibrium**