Hardy–Weinberg Principle

The Hardy–Weinberg principle describes the theoretical condition under which a population's allele and genotype frequencies remain exactly constant from one generation to the next — in other words, a population that is genetically at equilibrium and therefore, by definition, not evolving. For a gene with two alleles, if 'A' has frequency p and 'a' has frequency q, then p + q = 1, and under random mating the genotype frequencies in the next generation are given by expanding (p + q)^2, i.e. $p^2 + 2pq + q^2 = 1$, where p^2 is the frequency of AA, 2pq is the frequency of Aa, and q^2 is the frequency of aa. Working through the textbook's beetle example: if p (allele A) = 0.3 and q (allele a) = 0.7, then p^2 = 0.09 (9% AA), 2pq = 2(0.3)(0.7) = 0.42 (42% Aa), and q^2 = 0.49 (49% aa) — and because these values sum to 1, the population is said to be in Hardy–Weinberg equilibrium; under random mating with no disturbing force acting, these same genotype proportions will reappear unchanged in the next generation. This equilibrium, however, only holds if five conditions are simultaneously met: no mutation (no new alleles created, none lost, no gene duplication), random mating (every individual has an equal chance to mate, with no preference for particular genotypes), no gene flow (no individuals or gametes entering or leaving the population), infinitely/very large population size (so chance sampling effects are negligible), and no natural selection (every genotype is equally fit to survive and reproduce). If even …