Question

What is the mathematical expression for the genetic equilibrium for genes with two alleles? Is this statistical distribution the same as the statistical distribution of the respective phenotypes?

Answer 1

Considering p the frequency of one of the alleles and q the frequency of the other allele of a given gene in a population, this population of individuals produces p gametes with the first allele for each q gamete containing the second allele.

Therefore, the probability of the formation of the homozygous genotype for the first allele is p²; the probability of the formation of the homozygous genotype for the second allele is q²; and the probability of the formation of the heterozygous genotype is p.q + q.p, that is, 2p.q.

Since the sum of those probabilities is necessarily 1, the resulting mathematical expression is: p.p + 2p.q + q.q = 1.

In general, the number of genotypic forms is not identical to the number of phenotypic forms, since dominance and other interactions between genes affect the manifestation of the phenotype.