# Allele frequency

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**Allele frequency**, or **gene frequency**, is the relative frequency of an [allele](/source/Allele) (variant of a [gene](/source/Gene)) at a particular [locus](/source/Locus_(genetics)) in a [population](/source/Population_(biology)), expressed as a fraction or percentage.[1] Specifically, it is the fraction of all chromosomes in the population that carry that allele over the total population or sample size. [Evolution](/source/Evolution) is the change in allele frequencies that occurs over time within a population.

Given the following:

1. A particular locus on a chromosome and a given allele at that locus
1. A population of *N* individuals with [ploidy](/source/Ploidy) *n*, i.e. an individual carries *n* copies of each chromosome in their [somatic cells](/source/Somatic_cell) (e.g. two chromosomes in the cells of [diploid](/source/Diploid) species)
1. 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](/source/Genotype_frequency), although they are related, and allele frequencies can be calculated from genotype frequencies.[1]

In [population genetics](/source/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](/source/Allele_frequency_spectrum).

## Calculation of allele frequencies from genotype frequencies

The actual frequency calculations depend on the [ploidy](/source/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

- p = i/N.

### Diploids

If f(\mathbf{AA}), f(\mathbf{AB}), and f(\mathbf{BB}) 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.[2]

- p=f(\mathbf{AA})+ \frac{1}{2}f(\mathbf{AB})= \mbox{frequency of A}

- q=f(\mathbf{BB})+ \frac{1}{2}f(\mathbf{AB})= \mbox{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:

- p+q=f(\mathbf{AA})+f(\mathbf{BB})+f(\mathbf{AB})=1

- q=1-p and 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](/source/Allele#Genotype_frequencies))

Allele frequency can always be calculated from [genotype frequency](/source/Genotype_frequency), whereas the reverse requires that the [Hardy–Weinberg conditions](/source/Hardy%E2%80%93Weinberg_principle) 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](/source/Homozygous) genotypes (**AA** and **BB**), and one [heterozygous](/source/Heterozygous) genotype (**AB**). If we sample 10 individuals from the population, and we observe the genotype frequencies

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

then there are 6\times2 + 3 = 15 observed copies of the **A** allele and 1\times2 + 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.

## Dynamics

Population genetics describes the genetic composition of a population, including allele frequencies, and how allele frequencies are expected to change over time. The [Hardy–Weinberg law](/source/Hardy%E2%80%93Weinberg_law) describes the expected equilibrium [genotype frequencies](/source/Genotype_frequency) in a diploid population after random mating. Random mating alone does not change allele frequencies, and the Hardy–Weinberg equilibrium assumes an infinite population size and a selectively neutral locus.[1]

In natural populations [natural selection](/source/Natural_selection) ([adaptation](/source/Adaptation) mechanism), [gene flow](/source/Gene_flow), and [mutation](/source/Mutation) combine to change allele frequencies across generations. [Genetic drift](/source/Genetic_drift) causes changes in allele frequency from random sampling due to offspring number variance in a finite population size, with small populations experiencing larger per generation fluctuations in frequency than large populations. There is also a theory that second adaptation mechanism exists – [niche construction](/source/Niche_construction)[3] According to [extended evolutionary synthesis](/source/Extended_evolutionary_synthesis) adaptation occur due to natural selection, environmental induction, non-genetic inheritance, learning and cultural transmission.[4] An allele at a particular locus may also confer some fitness effect for an individual carrying that allele, on which natural selection acts. Beneficial alleles tend to increase in frequency, while deleterious alleles tend to decrease in frequency. Even when an allele is selectively neutral, selection acting on nearby genes may also change its allele frequency through [hitchhiking](/source/Genetic_hitchhiking) or [background selection](/source/Background_selection).

While heterozygosity at a given locus decreases over time as alleles become fixed or lost in the population, variation is maintained in the population through new mutations and gene flow due to migration between populations. For details, see [population genetics](/source/Population_genetics).

## See also

- [Allele frequency net database](/source/Allele_frequency_net_database)
- [Allele frequency spectrum](/source/Allele_frequency_spectrum)
- [Minor allele frequency](/source/Minor_allele_frequency) (MAF)
- [Single-nucleotide polymorphism](/source/Single-nucleotide_polymorphism)

## References

1. Gillespie, John H. (2004). *Population genetics: a concise guide*. 2. ed. Baltimore, Md.: The Johns Hopkins University Press. ISBN 978-0-8018-8008-7.

1. ["Population and Evolutionary Genetics"](https://web.archive.org/web/20240512174813/https://www.ndsu.edu/pubweb/~mcclean/plsc431/popgen/popgen2.htm). *ndsu.edu*. Archived from [the original](https://www.ndsu.edu/pubweb/~mcclean/plsc431/popgen/popgen2.htm) on 2024-05-12. Retrieved 2016-07-05.

1. Scott-Phillips, T. C.; Laland, K. N.; Shuker, D. M.; Dickins, T. E.; West, S. A. (2014). "The Niche Construction Perspective: A Critical Appraisal". *Evolution*. **68** (5): 1231–1243. [doi:10.1111/evo.12332](https://doi.org/10.1111/evo.12332). [PMC 4261998](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4261998). [PMID 24325256](https://pubmed.ncbi.nlm.nih.gov/24325256)

1. Laland, K. N.; Uller, T.; Feldman, M. W.; Sterelny, K.; Müller, G. B.; Moczek, A.; Jablonka, E.; Odling-Smee, J. (Aug 2015). "The extended evolutionary synthesis: its structure, assumptions and predictions.". *Proc Biol Sci*. **282** (1813). [doi:10.1098/rspb.2015.1019](https://doi.org/10.1098/rspb.2015.1019). [PMC 4632619](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4632619). [PMID 26246559](https://pubmed.ncbi.nlm.nih.gov/26246559)

## External links

- [ALFRED database](http://alfred.med.yale.edu/alfred/) [Archived](https://web.archive.org/web/20110120034110/http://alfred.med.yale.edu/alfred/) 2011-01-20 at the Wayback Machine
- [EHSTRAFD.org – Earth Human STR Allele Frequencies Database](https://web.archive.org/web/20090713043812/http://www.ehstrafd.org/)
- [VWA 17 Allele Frequency in Human Population (Poster)](https://web.archive.org/web/20110726020415/http://www.ehstrafd.org/download/vWA_17_A1.rar)
- [Allele Frequencies in Worldwide Populations](http://www.allelefrequencies.net)

Cheung, KH; Osier MV; Kidd JR; Pakstis AJ; Miller PL; Kidd KK (2000). "ALFRED: an allele frequency database for diverse populations and DNA polymorphisms". *Nucleic Acids Research*. **28** (1): 361–3. [doi:10.1093/nar/28.1.361](https://doi.org/10.1093/nar/28.1.361). [PMC 102486](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC102486). [PMID 10592274](https://pubmed.ncbi.nlm.nih.gov/10592274)

Middleton, D; Menchaca L; Rood H; Komerofsky R (2002). "New allele frequency database: www.allelefrequencies.net". *Tissue Antigens*. **61** (5): 403–7. [doi:10.1034/j.1399-0039.2003.00062.x](https://doi.org/10.1034/j.1399-0039.2003.00062.x). [PMID 12753660](https://pubmed.ncbi.nlm.nih.gov/12753660)

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Adapted from the Wikipedia article [Allele frequency](https://en.wikipedia.org/wiki/Allele_frequency) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Allele_frequency?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.