Final answer:
The Hardy-Weinberg theorem describes the conditions and equations for a population's genetic makeup to remain constant. The key equation p² + 2pq + q² = 1, relies on conditions such as no mutations and random mating. Variables p and q represent allele frequencies, and deviations indicate possible evolutionary changes.
Step-by-step explanation:
The Hardy-Weinberg theorem is a fundamental principle in population genetics that provides the conditions under which allele and genotype frequencies remain constant from one generation to the next, known as Hardy-Weinberg equilibrium. These conditions include no mutations, no migration, large population size, random mating, and no natural selection. When these conditions are met, the equation p² + 2pq + q² = 1 describes the distribution of genotypes in the population, where p is the frequency of the dominant allele and q is the frequency of the recessive allele, with the constraint that p + q = 1. The variables used in this equation represent the frequencies of the genotypes: p² is the frequency of the homozygous dominant genotype (AA), 2pq is the frequency of the heterozygous genotype (Aa), and q² is the frequency of the homozygous recessive genotype (aa). Deviations from the predicted frequencies could indicate that evolution is occurring, allowing scientists to infer about different evolutionary forces acting on the population.