Allele frequency

Given the following:

1. A particular locus on a chromosome and a given allele at that locus
2. A population of N individuals with ploidy n, i.e. an individual carries n copies of each chromosome in their somatic cells (e.g. two chromosomes in the cells of diploid species)
3. The allele exists in i chromosomes in the population

then the allele frequency is the fraction of all the occurrences i of that allele and the total number of chromosome copies across the population, i/(nN).

The allele frequency is distinct from the genotype frequency, although they are related, and allele frequencies can be calculated from genotype frequencies.

In population genetics, allele frequencies are used to describe the amount of variation at a particular locus or across multiple loci. When considering the ensemble of allele frequencies for many distinct loci, their distribution is called the allele frequency spectrum.

Calculation of allele frequencies from genotype frequencies

The actual frequency calculations depend on the ploidy of the species for autosomal genes.

Monoploids

The frequency (p) of an allele A is the fraction of the number of copies (i) of the A allele and the population or sample size (N), so

${\displaystyle p=i/N.}$

Diploids

If ${\displaystyle f(\mathbf{A}\mathbf{A})}$, ${\displaystyle f(\mathbf{A}\mathbf{B})}$, and ${\displaystyle f(\mathbf{B}\mathbf{B})}$ are the frequencies of the three genotypes at a locus with two alleles, then the frequency p of the A-allele and the frequency q of the B-allele in the population are obtained by counting alleles.

${\displaystyle p=f(\mathbf{A}\mathbf{A})+\frac{1}{2}f(\mathbf{A}\mathbf{B})=\text{frequency of A}}$

${\displaystyle q=f(\mathbf{B}\mathbf{B})+\frac{1}{2}f(\mathbf{A}\mathbf{B})=\text{frequency of B}}$

Because p and q are the frequencies of the only two alleles present at that locus, they must sum to 1. To check this:

${\displaystyle p+q=f(\mathbf{A}\mathbf{A})+f(\mathbf{B}\mathbf{B})+f(\mathbf{A}\mathbf{B})=1}$

${\displaystyle q=1-p}$ and ${\displaystyle p=1-q}$

If there are more than two different allelic forms, the frequency for each allele is simply the frequency of its homozygote plus half the sum of the frequencies for all the heterozygotes in which it appears.

(For 3 alleles see Allele § Genotype frequencies)

Allele frequency can always be calculated from genotype frequency, whereas the reverse requires that the Hardy–Weinberg conditions of random mating apply.

Example

Consider a locus that carries two alleles, A and B. In a diploid population there are three possible genotypes, two homozygous genotypes (AA and BB), and one heterozygous genotype (AB). If we sample 10 individuals from the population, and we observe the genotype frequencies

1. freq (AA) = 6
2. freq (AB) = 3
3. freq (BB) = 1

then there are ${\displaystyle 6\times 2+3=15}$ observed copies of the A allele and ${\displaystyle 1\times 2+3=5}$ of the B allele, out of 20 total chromosome copies. The frequency p of the A allele is p = 15/20 = 0.75, and the frequency q of the B allele is q = 5/20 = 0.25.