Box 1. The Hardy–Weinberg law

The Hardy–Weinberg (HW) law relates the frequencies of genes to those of genotypes in a randomly mating population. It is an application of the binomial expansion (p+q)²=p²+2pq+q², where p and q are the proportions of alleles A and a, and p², 2pq and q² are the proportions of genotypes AA, Aa and aa. If the parents mate at random, which is the equivalent to combining genes at random from a large pool to which each parent has contributed equally, the zygotes are in HW proportions. The larger the population, the closer the numbers agree with these binomial expectations. With differential mortality among the genotypes, the population will no longer be in HW proportions. In fact, departures from HW proportions are often taken as evidence for selection. With more than two alleles, the extension is straightforward; the binomial expansion becomes multinomial.