What Is A Fixed Allele

Change in a genetic pool

In population genetics, fixation is the change in a cistron pool from a state of affairs where there exists at least two variants of a particular cistron (allele) in a given population to a situation where just one of the alleles remains.^[1] In the absence of mutation or heterozygote advantage, any allele must somewhen exist lost completely from the population or fixed (permanently established at 100% frequency in the population).^[ii] Whether a factor will ultimately be lost or stock-still is dependent on pick coefficients and chance fluctuations in allelic proportions.^[3] Fixation can refer to a gene in full general or item nucleotide position in the DNA chain (locus).

In the process of commutation, a previously non-real 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 whatsoever fellow member, it is said to exist "fixed" in the population.^[1]

Similarly, genetic differences between taxa are said to accept been fixed in each species.

History [edit]

The earliest mention of factor fixation in published works was found in Kimura's 1962 paper "On Probability of Fixation of Mutant Genes in a Population". In the newspaper, Kimura uses mathematical techniques to decide 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 hateful and variance of the gene frequency change per generation.^[iv]

Probability [edit]

Under conditions of genetic drift solitary, every finite set of genes or alleles has a "coalescent indicate" at which all descendants converge to a single ancestor (i.east. they 'coalesce'). This fact can be used to derive the rate of cistron fixation of a neutral allele (that is, one not under any form of selection) for a population of varying size (provided that information technology is finite and nonzero). Considering the effect of natural pick is stipulated to be negligible, the probability at any given fourth dimension that an allele will ultimately become fixed at its locus is only its frequency $p$ in the population at that time. For case, 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 space number of generations a will be fixed at the locus (assuming genetic drift is the but operating evolutionary strength).

For a diploid population of size N and neutral mutation rate $\mu$ , the initial frequency of a novel mutation is only one/(2N), 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 $2N\mu \times {\frac {1}{2N}}=\mu$ . Thus, the rate of fixation for a mutation not subject to selection is simply the charge per unit of introduction of such mutations.^[5]

For fixed population sizes, the probability of fixation for a new allele with selective advantage southward tin 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 $X_{0}=ane$ . The number of offspring of any 1 individual must follow a stock-still distribution and is independently determined. In this framework the generating functions $p_{n}(x)$ for each $X_{due north}$ satisfy the recursion relation $p_{n}(x)=p_{1}(p_{northward-ane}(x))$ and tin can be used to compute the probabilities $\pi _{northward}=P(X_{n}=0)$ of no descendants at time n. It tin exist shown that $\pi _{n}=p_{1}(\pi _{due north-one})$ , 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 $one-\pi \approx 2s/\sigma ^{2}$ since the indefinite survival of the beneficial allele will allow its increase in frequency to a indicate 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 ratio $N_{e}s$ determines whether selection or drift dominates, and as long as this ratio is not as well negative, there will be an appreciable chance that a mildly deleterious allele will fix. For example, in a diploid population of size $N_{due east}$ , a deleterious allele with selection coefficient $-s$ has a probability fixation equal to $(1-due east^{-2s})/(one-e^{-4N_{e}s})$ . This estimate tin can be obtained directly from Kimura'southward 1962 work.^[four] Deleterious alleles with selection coefficients $-s$ satisfying $2N_{e}due south\ll i$ 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, option coefficients are more constructive. This means that benign alleles are more likely to become fixed, whereas deleterious alleles are more than likely to exist lost. In populations that are shrinking in size, pick coefficients are not as effective. Thus, there is a higher probability of beneficial alleles being lost and deleterious alleles beingness fixed. This is because if a benign mutation is rare, it can exist lost purely due to take a 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 boilerplate individual has a lower number of expected offspring. Thus, in growing populations information technology is more than likely that the benign allele will be passed on to more individuals in the adjacent 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 considering the parents produce no offspring. This would cause even a beneficial mutation to be lost.^{[half dozen]}

Time [edit]

Additionally, enquiry has been done into the boilerplate time it takes for a neutral mutation to become stock-still. Kimura and Ohta (1969) showed that a new mutation that eventually fixes will spend an average of 4N_e generations equally a polymorphism in the population.^[2] Average time to fixation N_east is the effective population size, the number of individuals in an idealised population under genetic migrate required to produce an equivalent amount of genetic diversity. Commonly the population statistic used to define effective population size is heterozygosity, but others can exist used.^[7]

Fixation rates can hands be modeled as well to see how long it takes for a factor to get fixed with varying population sizes and generations. For case, at The Biology Project Genetic Drift Simulation you tin model genetic drift and encounter how quickly the factor 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.^[8] It aims to trace back to a single bequeathed copy called the nigh contempo mutual ancestor.^[9]

Examples in research [edit]

In 1969, Schwartz at Indiana Academy was able to artificially induce gene fixation into maize, by subjecting samples to suboptimal weather. Schwartz located a mutation in a gene called Adh1, which when homozygous causes maize to be unable to produce alcohol dehydrogenase. Schwartz and so 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 establish that when subjected to flooding, just seeds with alcohol dehydrogenase activeness germinated. This ultimately acquired gene fixation of the Adh1 wild type allele. The Adh1 mutation was lost in the experimented population.^[x]

In 2014, Lee, Langley, and Begun conducted another inquiry written report related to gene fixation. They focused on Drosophila melanogaster population data and the effects of genetic hitchhiking caused past selective sweeps. Genetic hitchhiking occurs when i allele is strongly selected for and driven to fixation. This causes the surrounding areas to likewise be driven to fixation, even though they are not beingness selected for.^[xi] Past looking at the Drosophila melanogaster population information, Lee et al. establish a reduced amount of heterogeneity within 25 base pairs of focal substitutions. They accredit this to modest hitchhiking effects. They also constitute that neighboring fixations that changed amino acid polarities while maintaining the overall polarity of a poly peptide were under stronger selection pressures. Additionally, they establish that substitutions in slowly evolving genes were associated with stronger genetic hitchhiking furnishings.^[12]

References [edit]

^ ^a ^b Arie Zackay (2007). Random Genetic Drift & Cistron Fixation (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2013-08-29 .
^ ^a ^b Kimura, Motoo; Ohta, Tomoko (26 July 1968). "The average number of generations until fixation of a mutant gene in a finite population". Genetics. 61 (3): 763–771. PMC1212239. PMID 17248440.
^ Kimura, Motoo (1983). The Neutral Theory of Molecular Evolution. The Edinburgh Building, Cambridge: Cambridge University Press. ISBN978-0-521-23109-1 . Retrieved 16 Nov 2014.
^ ^a ^b Kimura, Motoo (29 January 1962). "On the probability of fixation of mutant genes in a population". Genetics. 47: 713–719. PMC1210364. PMID 14456043.
^ David H.A. Fitch (1997). Deviations from the naught hypotheses: Finite populations sizes and genetic migrate, mutation and cistron flow.
^ Otto, Sarah; Whitlock, Michael (7 March 1997). "The probability of fixation in populations of irresolute size" (PDF). Genetics. 146 (2): 723–733. PMC1208011. PMID 9178020. Retrieved 14 September 2014.
^ Caballero, Armando (9 March 1994). "Developments in the prediction of effective population size". Heredity. 73 (half dozen): 657–679. doi:10.1038/hdy.1994.174. PMID 7814264.
^ Griffiths, RC; Tavare, Simon (1998). "The Age of a Mutation in a General Coalescent Tree". Communications in Statistics. Stochastic Models. xiv (1&2): 273–295. doi:x.1080/15326349808807471.
^ Walsh, Bruce (22 March 2001). "Estimating the Time to the Most Recent Mutual Antecedent for the Y chromosome or Mitochondrial Deoxyribonucleic acid for a Pair of Individuals". Genetics. 158 (2): 897–912. PMC1461668. PMID 11404350.
^ Schwartz, Drew (1969). "An Example of Gene Fixation Resulting from Selective Reward in Suboptimal Weather". The American Naturalist. 103 (933): 479–481. doi:10.1086/282615. JSTOR 2459409. S2CID 85366302.
^ Rice, William (12 February 1987). "Genetic Hitchhiking and the Development of Reduced Genetic Activity of the Y Sexual activity Chromosome". Genetics. 116 (1): 161–167. PMC1203114. PMID 3596229.
^ Lee, Yuh; Langley, Charles; Begun, David (2014). "Differential Strengths of Positive Option Revealed past Hitchhiking Effects at Small Physical Scales in Drosophila melanogaster". Molecular Biological science and Evolution. 31 (4): 804–816. doi:10.1093/molbev/mst270. PMC4043186. PMID 24361994. Retrieved sixteen Nov 2014.