Calculating Allele and Genotype Frequencies

Hardy-Weinberg gives two linked equations. The allele equation, p + q = 1, says every copy of the gene in the population is either the dominant allele (p) or the recessive allele (q). The genotype equation, p² + 2pq + q² = 1, says every individual is homozygous dominant (p²), heterozygous (2pq), or homozygous recessive (q²). The bridge between them matters: only the recessive phenotype identifies itself cleanly, because both AA and Aa individuals look the same. So q² is the one frequency you can read directly off a population by counting recessive-looking individuals, then square-root it to get q, then subtract from 1 to get p.

Work it through: if 16 of 400 individuals show the recessive trait, q² = 16/400 = 0.04, so q = 0.2 and p = 0.8. With p and q known, you can predict genotype counts. If q = 0.3 in a population of 1000, p = 0.7, and the expected number of heterozygotes is 2pq x n = 2(0.7)(0.3)(1000) = 420. To test whether a real population matches these predictions, compare observed counts to expected ones: for 60 AA, 20 Aa, 20 aa (n=100), count alleles directly (2(60)+20 = 140 A alleles, 2(20)+20 = 60 a alleles out of 200 total, so p=0.7, q=0.3), then check if expected p², 2pq, q² counts (49, 42, 9) match the observed 60, 20, 20. They don't, so this population is not in equilibrium.

This calculation is the quantitative backbone of the whole unit: it gives you a numerical baseline for what evolution looks like when it's NOT happening, so any mismatch between observed and expected genotype counts is evidence that selection, drift, migration, nonrandom mating, or mutation is acting on the population.