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In
population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and po ...
, fixation is the change in a
gene pool The gene pool is the set of all genes, or genetic information, in any population, usually of a particular species. Description A large gene pool indicates extensive genetic diversity, which is associated with robust populations that can surv ...
from a situation where there exists at least two variants of a particular
gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a b ...
(
allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. ::"The chrom ...
) in a given population to a situation where only one of the alleles remains. In the absence of
mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, m ...
or
heterozygote advantage A heterozygote advantage describes the case in which the heterozygous genotype has a higher relative fitness than either the homozygous dominant or homozygous recessive genotype. Loci exhibiting heterozygote advantage are a small minority of ...
, 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 Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecu ...
position in the DNA chain ( locus). In the process of substitution, a previously non-existent allele arises by
mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, m ...
and undergoes fixation by spreading through the population by random
genetic drift Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and there ...
or positive selection. Once the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
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 In biology, a taxon (back-formation from ''taxonomy''; plural taxa) is a group of one or more populations of an organism or organisms seen by taxonomists to form a unit. Although neither is required, a taxon is usually known by a particular nam ...
are said to have been fixed in each
species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriat ...
.


History

The earliest mention of gene fixation in published works was found in 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.


Probability

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 p in the population at that time. For example, if a population includes allele ''A'' with frequency equal to 20%, and allele ''a'' with frequency equal to 80%, there is an 80% chance that after an infinite number of generations ''a'' will be fixed at the locus (assuming genetic drift is the only operating evolutionary force). For a
diploid Ploidy () is the number of complete sets of chromosomes in a cell, and hence the number of possible alleles for autosomal and pseudoautosomal genes. Sets of chromosomes refer to the number of maternal and paternal chromosome copies, respectiv ...
population of size ''N'' and neutral
mutation rate In genetics, the mutation rate is the frequency of new mutations in a single gene or organism over time. Mutation rates are not constant and are not limited to a single type of mutation; there are many different types of mutations. Mutation rates ...
\mu, the initial frequency of a novel mutation is simply 1/(2''N''), and the number of new mutations per generation is 2N\mu. Since the fixation rate is the rate of novel neutral mutation multiplied by their probability of fixation, the overall fixation rate is 2N\mu \times \frac = \mu. Thus, the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations. For fixed population sizes, the probability of fixation for a new allele with selective advantage ''s'' can be approximated using the theory of branching processes. A population with nonoverlapping generations n = 0, 1, 2, 3, ... , and with X_n genes (or "individuals") at time n forms a Markov chain under the following assumptions. The introduction of an individual possessing an allele with a selective advantage corresponds to X_0 = 1. The number of offspring of any one individual must follow a fixed distribution and is independently determined. In this framework the generating functions p_n (x) for each X_n satisfy the recursion relation p_n (x) = p_1 ( p_(x) ) and can be used to compute the probabilities \pi_n = P(X_n = 0) of no descendants at time n. It can be shown that \pi_n = p_1 ( \pi_ ), and furthermore, that the \pi_n converge to a specific value \pi, which is the probability that the individual will have no descendants. The probability of fixation is then 1-\pi \approx 2 s / \sigma^2 since the indefinite survival of the beneficial allele will permit its increase in frequency to a point where selective forces will ensure fixation. Weakly deleterious mutations can fix in smaller populations through chance, and the probability of fixation will depend on rates of drift (~1/N_e) and selection (~s), where N_e is the
effective population size The effective population size (''N'e'') is a number that, in some simplified scenarios, corresponds to the number of breeding individuals in the population. More generally, ''N'e'' is the number of individuals that an idealised population w ...
. The ratio N_e s determines whether selection or drift dominates, and as long as this ratio is not too negative, there will be an appreciable chance that a mildly deleterious allele will fix. For example, in a diploid population of size N_e, a deleterious allele with selection coefficient -s has a probability fixation equal to (1-e^) /(1-e^). This estimate can be obtained directly from Kimura's 1962 work. Deleterious alleles with selection coefficients -s satisfying 2 N_e s \ll 1 are effectively neutral, and consequently have a probability of fixation approximately equal to 1/2N_e. Probability of fixation is also influenced by population size changes. For growing populations, selection coefficients are more effective. This means that beneficial alleles are more likely to become fixed, whereas deleterious alleles are more likely to be lost. In populations that are shrinking in size, selection coefficients are not as effective. Thus, there is a higher probability of beneficial alleles being lost and deleterious alleles being fixed. This is because if a beneficial mutation is rare, it can be lost purely due to chance of that individual not having offspring, no matter the selection coefficient. In growing populations, the average individual has a higher expected number of offspring, whereas in shrinking populations the average individual has a lower number of expected offspring. Thus, in growing populations it is more likely that the beneficial allele will be passed on to more individuals in the next generation. This continues until the allele flourishes in the population, and is eventually fixed. However, in a shrinking population it is more likely that the allele may not be passed on, simply because the parents produce no offspring. This would cause even a beneficial mutation to be lost.


Time

Additionally, research has been done into the average time it takes for a neutral mutation to become fixed. Kimura and Ohta (1969) showed that a new mutation that eventually fixes will spend an average of 4Ne generations as a polymorphism in the population. Average time to fixation Ne is the
effective population size The effective population size (''N'e'') is a number that, in some simplified scenarios, corresponds to the number of breeding individuals in the population. More generally, ''N'e'' is the number of individuals that an idealised population w ...
, the number of individuals in an idealised population under
genetic drift Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and there ...
required to produce an equivalent amount of genetic diversity. Usually the population statistic used to define effective population size is heterozygosity, but others can be used. Fixation rates can easily be modeled as well to see how long it takes for a gene to become fixed with varying population sizes and generations. For example, a
The Biology Project Genetic Drift Simulation
you can model
genetic drift Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and there ...
and see how quickly the gene for worm color goes to fixation in terms of generations for different population sizes. Additionally, fixation rates can be modeled using coalescent trees. A coalescent tree traces the descent of alleles of a gene in a population. It aims to trace back to a single ancestral copy called the most recent common ancestor.


Examples in research

In 1969, Schwartz at Indiana University was able to artificially induce gene fixation into maize, by subjecting samples to suboptimal conditions. Schwartz located a mutation in a gene called Adh1, which when homozygous causes maize to be unable to produce alcohol dehydrogenase. Schwartz then subjected seeds, with both normal alcohol dehydrogenase activity and no activity, to flooding conditions and observed whether the seeds were able to germinate or not. He found that when subjected to flooding, only seeds with alcohol dehydrogenase activity germinated. This ultimately caused gene fixation of the Adh1 wild type allele. The Adh1 mutation was lost in the experimented population. In 2014, Lee, Langley, and Begun conducted another research study related to gene fixation. They focused on ''Drosophila melanogaster'' population data and the effects of
genetic hitchhiking Genetic may refer to: * Genetics, in biology, the science of genes, heredity, and the variation of organisms **Genetic, used as an adjective, refers to genes *** Genetic disorder, any disorder caused by a genetic mutation, whether inherited or de ...
caused by selective sweeps. Genetic hitchhiking occurs when one allele is strongly selected for and driven to fixation. This causes the surrounding areas to also be driven to fixation, even though they are not being selected for. By looking at the ''Drosophila melanogaster'' population data, Lee et al. found a reduced amount of heterogeneity within 25 base pairs of focal substitutions. They accredit this to small-scale hitchhiking effects. They also found that neighboring fixations that changed amino acid polarities while maintaining the overall polarity of a protein were under stronger selection pressures. Additionally, they found that substitutions in slowly evolving genes were associated with stronger genetic hitchhiking effects.


References


Further reading

* Gillespie, J.H. (1994) ''The Causes of Molecular Evolution''. Oxford University Press. * Hartl, D.L. and Clark, A.G. (2006) ''Principles of Population Genetics'' (4th edition). Sinauer Associates. * {{cite journal , last1 = Kimura , first1 = M , year = 1962 , title = On the Probability of Fixation of Mutant Genes in a Population , pmid=14456043 , journal = Genetics , volume = 47 , pages = 713–719 , pmc=1210364 Population genetics