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; and (5) the population is very large. 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:
where p2=frequency of AA (homozygous dominant) individuals, 2pq=frequency of Aa (heterozygous) individuals, and q2= 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; this is useful, e.g., for estimating the frequency of heterozygote carriers of a defective allele responsible for a genetic disease in a population. Moreover, the equation can be used to test if evolution is occurring at any particular genetic locus; if it is not, and the above conditions apply, then the calculated allele frequency will agree with that observed in a population for subsequent generations. A disparity in the calculated and observed frequencies might indicate that evolution is occurring. The equation and the equilibrium are named after British mathematician G. H. Hardy (1877–1947) and German physician W. Weinberg (1862–1937).