HardyWeinbergmodel

The Hardy-Weinberg model, or Hardy-Weinberg equilibrium, is a foundational concept in population genetics that describes how allele and genotype frequencies behave in a large, randomly mating population with no evolutionary forces acting. For a gene with two alleles, A and a, let p be the frequency of A and q the frequency of a, with p + q = 1. In the next generation, the expected genotype frequencies are AA with frequency p^2, Aa with frequency 2pq, and aa with frequency q^2. The overall genotype distribution thus follows the binomial expansion (p + q)^2 = p^2 + 2pq + q^2 = 1.

The model rests on several key assumptions: no mutation, no migration, no natural selection, an infinitely large population to prevent genetic drift, and random mating. When these conditions hold, allele frequencies remain constant across generations and the genotype frequencies settle at p^2, 2pq, and q^2, regardless of the starting genotype distribution.

Hardy-Weinberg equilibrium serves as a null model for evolution. Deviations from the expected proportions suggest that one or more evolutionary forces—such as selection, migration, mutation, genetic drift, or nonrandom mating—are at work. The model also provides a practical framework for estimating allele frequencies from genotype data and for testing whether a population is evolving at a particular locus. Extensions of the model address multiple alleles, nonrandom mating, linked genes, and sex-linked inheritance.