Fixation (population genetics)

In population genetics, fixation is the change in a gene pool from a situation where there exists at least two variants of a particular gene (allele) in a given population to a situation where only one of the alleles remains. That is, the allele becomes fixed. In the absence of mutation or heterozygote advantage, any allele must eventually be lost completely from the population or fixed (permanently established at 100% frequency in the population). Whether a gene will ultimately be lost or fixed is dependent on selection coefficients and chance fluctuations in allelic proportions. Fixation can refer to a gene in general or particular nucleotide position in the DNA chain (locus). In the process of substitution, a previously non-existent allele arises by mutation and undergoes fixation by spreading through the population by random genetic drift or positive selection. Once the frequency of the allele is at 100%, i.e. being the only gene variant present in any member, it is said to be "fixed" in the population. Similarly, genetic differences between taxa are said to have been fixed in each species. The earliest mention of gene fixation in published works was found in Motoo Kimura's 1962 paper "On Probability of Fixation of Mutant Genes in a Population". In the paper, Kimura uses mathematical techniques to determine the probability of fixation of mutant genes in a population. He showed that the probability of fixation depends on the initial frequency of the allele and the mean and variance of the gene frequency change per generation. Under conditions of genetic drift alone, every finite set of genes or alleles has a "coalescent point" at which all descendants converge to a single ancestor (i.e. they 'coalesce'). This fact can be used to derive the rate of gene fixation of a neutral allele (that is, one not under any form of selection) for a population of varying size (provided that it is finite and nonzero). Because the effect of natural selection is stipulated to be negligible, the probability at any given time that an allele will ultimately become fixed at its locus is simply its frequency in the population at that time.