Hardy-Weinberg Principle

The Hardy-Weinberg principle states that in a large, randomly mating population with no selection, mutation or migration, the frequencies of alleles and genotypes stay constant from generation to generation. It was derived independently in 1908 by the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg.

For a gene with two alleles at frequencies p and q, where p + q = 1, the expected genotype frequencies are p² for one homozygote, 2pq for heterozygotes and q² for the other homozygote. Even if an allele is rare, most copies of it are carried in heterozygotes. For example, if one person in 2,500 has cystic fibrosis (q² = 0.0004), then q = 0.02 and about 3.9 percent of people, around 1 in 25, are carriers.

The model assumes random mating, a very large population, no mutation, no migration and no natural selection. It also needs equal survival of all genotypes. When these assumptions fail, the frequencies change, so the principle serves as a null model: departures from the expected proportions are evidence of selection, inbreeding, genetic drift or population structure.

Geneticists use it to estimate carrier frequencies, to check genotype data for errors and to test for associations between genes and disease. It showed that Mendelian inheritance does not by itself cause a dominant allele to spread, which answered an early objection to Mendel's laws. It is the starting point of population genetics and the study of allele frequency change in evolution.

• Allele Frequency — what the principle describes
• Genetic Drift — a cause of departure from it
• Population Genetics — the field it founded