The Hardy-Weinberg principle describes the genotype proportions produced by independently combining two parental gametes from the same allele pool. For alleles with allele frequencies , where , the Hardy-Weinberg proportions areThe two ordered heterozygote outcomes contribute . These proportions sum to , and their implied allele frequency is . Reshuffling copies therefore preserves their frequencies.
For stable Hardy-Weinberg equilibrium across generations, use a large population with random mating, equal allele frequencies in the parental pools, ordinary Mendelian segregation, and no natural selection, mutation, gene flow or genetic drift. Negligible genetic drift is an idealization of large population size. The one-generation random-mating equilibrium needs independent union of gametes; persistence additionally requires processes that change allele frequencies to be absent.
At , the predicted genotype proportions are . For 100 sampled individuals the expected values of the counts are , rather than the of a specified cross. The latter fixes both parental genotypes; Hardy-Weinberg proportions average over population mating.
An observed population need not have these proportions. For example, , no , and among 100 individuals still gives , but has no heterozygotes. Random mating predicts heterozygosity in the next generation under the stated model. A finite sample can also depart by chance, so a discrepancy is a starting point for investigating inbreeding, population stratification or genotyping error, rather than proof of one cause.
Hardy's 1908 note made the conceptual payoff explicit: a dominant phenotype does not by itself make its allele spread. Complete dominance describes expression; changes in frequency require a separate mechanism such as natural selection. See Hardy, Mendelian Proportions in a Mixed Population, Science 28 (1908), 49–50.
For ordered alleles independently drawn with probabilities , suppose disease penetrance is . Conditional on disease, the allele draws remain independent with probabilities . This follows by normalizing the product . Unordered homozygote probabilities are and heterozygote probabilities are . Unaffected controls do not generally share this factorization: their genotype weights contain .
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If parental genotype frequencies are and the two parental gametes are independently sampled from the same allele pool, Mendelian segregation gives allele frequency . Their independent union has the displayed Hardy-Weinberg proportions, irrespective of parental genotype proportions. Equal allele frequencies in the two sexes and no transmission or viability distortion are part of this conclusion.
From genotype counts in independent diploid individuals, the unbiased and maximum-likelihood estimator of the frequency of allele isIt is the sample proportion among the sampled alleles, so it is consistent and
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The Hardy-Weinberg principle is a foundational concept in population genetics that describes how allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary influences. This principle is based on several key assumptions: 1. **Large Population Size**: The population must be large enough to prevent random fluctuations in allele frequencies (genetic drift). 2. **No Mutations**: There should be no new mutations that introduce new alleles into the population.