Allele frequency is a term of population genetics that is used in characterizing the genetic diversity of a species population, or equivalently the richness of its gene pool. Allele frequency is defined as follows: Population genetics is the study of the distribution of and change in allele frequencies under the influence of the five evolutionary forces: natural selection, genetic drift, mutation, migration and nonrandom mating. ... Genetics (from the Greek genno γεννώ= give birth) is the science of genes, heredity, and the variation of organisms. ... In biology, the most commonly used definition of species was first coined by Ernst Mayr. ... The gene pool of a species or a population is the complete set of unique alleles that would be found by inspecting the genetic material of every living member of that species or population. ...

Given a) a particular chromosome locus, b) a gene occupying that locus, c) a population of individuals carrying n loci in each of their somatic cells (e.g. two loci in the cells of diploid species, which contain two sets of chromosomes) and finally d) a variant or allele of the gene, then the allele frequency of that allele is the fraction or percentage of loci that the allele occupies within the population. Figure 1: Chromosome. ... The word locus (plural loci) is Latin for place. In biology and evolutionary computation, a locus is the position of a gene (or other significant sequence) on a chromosome. ... This stylistic schematic diagram shows a gene in relation to the double helix structure of DNA and to a chromosome (right). ... A somatic cell is a type of cell in an organism, such as the human body. ... Diploid (meaning double in Greek) cells have two copies (homologs) of each chromosome (both sex- and non-sex determining chromosomes), usually one from the mother and one from the father. ... An allele is any one of a number of viable DNA codings of the same gene (sometimes the term refers to a non-gene sequence) occupying a given locus (position) on a chromosome. ...

To take an example, if the frequency of an allele is 20% in a given population, then among population members, one in five chromosomes will carry that allele. Four out of five will be occupied by other variants of the gene, of which there may be one or many.

Note that for diploid genes, however, the proportion of individuals that carry this allele may be up to two in five. If the allele distributes randomly, then the binomial theorem will apply: 32% of the population will be heterozygous for the allele (i.e. carry one copy of that allele and one copy of another in each somatic cell) and 4% will be homozygous (carrying two copies of the allele). So all together 36% of diploid individuals would be expected to carry an allele that has a frequency of 20%. However, alleles distribute randomly only in the absence of selection and under other assumptions. When these conditions apply, a population is said to be in Hardy-Weinberg equilibrium. In ordinary language, the word random is used to express apparent lack of purpose or cause. ... In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... Heterozygote cells are diploid or polyploid and have different alleles at a locus (position) on homologous chromosomes. ... Homozygote cells are diploid or polyploid and have the same alleles at a locus (position) on homologous chromosomes. ... For computer science algorithms that find the kth smallest number in a list, see selection algorithm. ... Hardy–Weinberg principle for two alleles: the horizontal axis shows the two allele frequencies p and q, the vertical axis shows the genotype frequencies and the three possible genotypes are represented by the different glyphs The Hardy–Weinberg principle (HWP) (also Hardy–Weinberg equilibrium (HWE), or Hardy–Weinberg law) states...

The frequencies of all the alleles of a given gene often are graphed together as an allele frequency distribution histogram. Population genetics studies the different "forces" that might lead to changes in the distribution and frequencies of alleles -- in other words, to evolution. Besides selection, these forces include genetic drift, mutation and migration. This page deals with mathematical distributions. ... In statistics, a histogram is a graphical display of tabulated frequencies. ... Charles Darwin, father of the theory of evolution by natural selection. ... Genetic drift is a mechanism of evolution that acts in concert with natural selection to change the characteristics of species over time. ... Mutations are permanent, sometimes transmissible (if the change is to a germ cell) changes to the genetic material (usually DNA or RNA) of a cell. ... Migration occurs when living things move from one biome to another. ...

Compare genotype frequency.

Example

If there are ten individuals in a population and at a given locus there are two possible alleles, A and a, then if the genotypes of the individuals are: The genotype is the specific genetic makeup (the specific genome) of an individual, usually in the form of DNA. It codes for the phenotype of that individual. ...

AA, Aa, AA, aa, Aa, AA, AA, Aa, Aa, and AA

then the allele frequencies of allele A and allele a are:

p_A = (2+1+2+0+1+2+2+1+1+2)/20 = 0.7

p_a = (0+1+0+2+1+0+0+1+1+0)/20 = 0.3