What equation represents the relationship between allele frequencies in a population at Hardy-Weinberg equilibrium?

The Hardy-Weinberg equilibrium describes a model where allele and genotype frequencies in a population remain constant from generation to generation, in the absence of evolutionary influences such as mutation, selection, or genetic drift. The correct answer encompasses two key equations that are foundational to understanding this equilibrium.

First, the equation p + q = 1 describes the relationship between the frequencies of the two alleles (let's say allele A with frequency p and allele a with frequency q) in a diploid organism. This means that if you add the frequencies of all alleles in the population, they must equal 1, representing the entirety of the genetic contribution.

Second, the equation p^2 + 2pq + q^2 = 1 refers to the expected genotype frequencies generated from these allele frequencies under Hardy-Weinberg equilibrium. Here, p^2 represents the frequency of the homozygous dominant genotype (AA), 2pq represents the frequency of the heterozygous genotype (Aa), and q^2 represents the frequency of the homozygous recessive genotype (aa). The sum of these frequencies must also equal 1, reflecting that all individuals in the population belong to one of these genotype categories.

Together, these two equations form the complete