Population Genetics and Genetic Disorders

Hardy-Weinberg and selection

The Hardy-Weinberg principle states that allele and genotype frequencies in a large, randomly mating population stay constant from generation to generation when no evolutionary forces act on the locus. For a locus with two alleles, A and a, with frequencies p and q, the relation p + q = 1 must hold. At equilibrium the genotype frequencies are p^2 for AA, 2pq for Aa, and q^2 for aa, so p^2 + 2pq + q^2 = 1. Because the heterozygote frequency is 2pq, once one allele frequency is known the other follows from q = 1 - p, and the heterozygote frequency can be computed directly. The recessive genotype frequency gives the allele frequency directly: if the frequency of aa is q^2, then q is its square root, and p = 1 - q.

When genotypes are counted rather than given as frequencies, allele frequencies are calculated from allele copies. Each diploid individual carries two alleles, so a homozygote contributes two copies of its allele and a heterozygote contributes one copy of each. The frequency of an allele is its count divided by the total number of alleles, which is twice the number of individuals.

Selection changes allele frequencies, so the population is no longer in equilibrium once selection acts. Directional selection favours one extreme phenotype. Stabilising selection favours the intermediate phenotype and removes the extremes. Disruptive selection favours both extremes and selects against the intermediate, and over time it can split a population into two forms. Genetic drift, by contrast, is random with respect to fitness and does not systematically favour any phenotype.

The response to selection is quantified by the breeder's equation, R = h^2 S, where R is the response (the change in the progeny mean), S is the selection differential (the mean of the selected parents minus the population mean), and h^2 is narrow-sense heritability. Rearranging gives h^2 = R/S. For example, if the population mean is 10, the selected parents have a mean of 14, and the progeny mean is 11, then S = 4, R = 1, and h^2 = 0.25.