17.2.5—Hardy-Weinberg principle

The Hardy–Weinberg model links allele frequencies to genotype frequencies for a gene with two alleles. Let p be the frequency of one allele and q the frequency of the other; frequencies are proportions of the population, so p + q = 1.

• p² is the expected frequency of one homozygous genotype.
• 2pq is the expected frequency of the heterozygous genotype.
• q² is the expected frequency of the other homozygous genotype.
• The three genotype frequencies sum to 1 because they represent all possible genotypes at this two-allele locus.

Use the model in this order:

1. Identify whether the data give an allele frequency or a genotype frequency; write the matching part of the equation.
2. If a homozygous recessive frequency q² is given, find q by taking its square root.
3. Use p = 1 − q (or q = 1 − p).
4. Calculate p², 2pq and q² as required, keeping all frequencies as proportions between 0 and 1.
5. Check that the three genotype frequencies add to 1 before interpreting them.

The prediction assumes a large population, random mating, no natural selection, no mutation and no migration into or out of the population. If these assumptions are not reasonable, an observed departure from the expected frequencies may indicate that one or more assumptions is violated, but the calculation alone does not identify which cause is responsible.

Hardy–Weinberg is a conditional model, not a statement that real populations must have these frequencies. It predicts expected genotype frequencies from allele frequencies under its assumptions; it does not by itself prove evolutionary change, identify a specific selection mechanism or replace experimental evidence.