The Hardy-Weinberg principle

The baseline of a population that isn’t evolving.

The idea

For a gene with two alleles, let p be the frequency of the dominant allele A and q the frequency of the recessive allele a, so p + q = 1. Hardy and Weinberg showed independently in 1908 that if a population is very large, mates at random, and experiences no mutation, no migration (gene flow), and no natural selection, then allele frequencies stay constant from generation to generation and the genotypes settle at p² (AA), 2pq (Aa), and q² (aa). Because heterozygotes hide inside the dominant phenotype, the recessive phenotype frequency, q², is the usual starting point for any calculation. A population whose genotype frequencies drift away from these values is telling you that at least one of the five assumptions is being broken — in other words, that it is evolving.

Work through an example

Cystic fibrosis, a recessive condition, affects about 1 in 2,500 people of European ancestry, so q² = 0.0004. Taking the square root, q = 0.02, and p = 1 − 0.02 = 0.98. The carrier frequency is 2pq = 2 × 0.98 × 0.02 = 0.0392, roughly 1 person in 25 — which is why a disease that is rare can still be carried by about 4% of the population.

What to watch for

If 16% of a population shows the recessive trait, q is not 0.16: that figure is q², so q = √0.16 = 0.4, p = 0.6, and heterozygotes make up 2 × 0.6 × 0.4 = 48%. Nor must the dominant phenotype be the common one: with q = 0.8, fully 64% of individuals are aa even though A is dominant. Dominance describes masking, not frequency.