The Hardy-Weinberg principle (HWP) (also Hardy-Weinberg equilibrium or HWE) states that, under certain conditions, after one generation of random mating, the genotype frequencies at a single gene (or locus) will become fixed at a particular equilibrium value. It also specifies that those equilibrium frequencies can be represented as a simple function of the allele frequencies at that locus. In the simplest case of a single locus with two alleles A and a with allele frequencies of p and q, respectively, the HWP predicts that the genotypic frequencies for the AA homozygote to be p^{2}, the Aa heterozygote to be 2pq and the other aa homozygote to be q^{2}.
The Hardy-Weinberg principle is an expression of the notion of a population in "genetic equilibrium" and is a basic principle of population genetics. First formulated independently in 1908 by English mathematician G. H. Hardy and German physician Wilhelm Weinberg the original assumptions for Hardy-Weinberg equilibrium (HWE) were that populations are:
- diploid
- sexually reproducing
- randomly mating
Derivation of the Hardy-Weinberg principle
A more statistical description for the HWP, is that the alleles for the next generation for any given individual are chosen independently. Consider two alleles, A and a, with frequencies p and q, respectively, in the population then the different ways to form new genotypes can be derived using a Punnett square, where the size of each cell is proportional to the fraction of each genotypes in the next generation:
Females | |||
---|---|---|---|
A (p) | a (q) | ||
Males | A (p) | AA (p^{2}) | Aa (pq) |
a (q) | aA (qp) | aa (q^{2}) |
So the final three possible genotype frequencies, in the offspring, if the alleles are drawn independently become:
- p^{2} (AA)
- 2pq (Aa)
- q^{2} (aa)
- 2p_{i}p_{j} if i≠j and;
- p_{i}^{2} if i=j.