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What is allele frequency?

Allele frequency is the percentage of appearances of an allele in the genotypes of a given population (comparing to the other alleles of the studied gene).

For example, in the ABO blood system there are three alleles (IA, IB and i). Considering a group of three persons, one with genotype IAi, other IAIB and other ii, the frequency of the allele IA in this “population” is 2/6, the frequency of the allele IB is 1/6 and the frequency of the allele i is 3/6.

What is genetic equilibrium?

Genetic equilibrium is the result of the Hardy-Weinberg law, a principle that affirms that under specific conditions the frequencies of the alleles of a gene in a given population remain constant.

(The Hardy-Weinberg principle is not valid in the following conditions: for populations too small, in the occurrence of noncasual (driven) crossings, for populations with many infertile members and in case of action of evolutionary factors, like natural selection, mutations and migrations.)

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

Considering p the frequency of one of the alleles and q the frequency of the other allele of a given gene in a population, in this population individuals produce p gametes with the first allele for each q gamete containing the second allele. Therefore the probabilities of formation of homozygous genotype for the first allele is p2, of homozygous genotype for the second allele is q2 and of the heterozygous genotype is p.q + q.p, i.e., 2p.q.

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

In general the number of genotypical forms is not identical to the number of phenotypical forms since there are dominance and other interactions between genes that affect the manifestation of the phenotype.