p² + 2pq + q² = 1 | p + q = 1
The Hardy-Weinberg principle is the null model of population genetics. In the absence of evolution (no mutation, selection, migration, genetic drift, or non-random mating), allele frequencies stay constant: p + q = 1 and genotype frequencies follow p² + 2pq + q² = 1. This allows estimating carrier frequencies: if 1/2500 people have cystic fibrosis (q² = 0.0004), then q = 0.02, p = 0.98, and 2pq = 3.9% are carriers (~1 in 25). Deviations from H-W indicate evolutionary forces at work. Chi-square tests compare observed vs expected genotype counts to test for equilibrium. The principle is essential in genetic counseling, forensic DNA analysis, and conservation genetics.