[2] Whether a gene will ultimately be lost or fixed is dependent on selection coefficients and chance fluctuations in allelic proportions.
[3] 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.
In the paper, Kimura uses mathematical techniques to determine the probability of fixation of mutant genes in a population.
[4] 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
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).
[5] 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.
genes (or "individuals") at time n forms a Markov chain under the following assumptions.
The number of offspring of any one individual must follow a fixed distribution and is independently determined.
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 (~
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.
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.
However, in a shrinking population it is more likely that the allele may not be passed on, simply because the parents produce no offspring.
[6] 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.
[2] Average time to fixation Ne is the effective population size, the number of individuals in an idealised population under genetic drift required to produce an equivalent amount of genetic diversity.
[7] 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.
[8] It aims to trace back to a single ancestral copy called the most recent common ancestor.
[9] 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.
He found that when subjected to flooding, only seeds with alcohol dehydrogenase activity germinated.
[10] 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 caused by selective sweeps.
Genetic hitchhiking occurs when one allele is strongly selected for and driven to fixation.
[11] By looking at the Drosophila melanogaster population data, Lee et al. found a reduced amount of heterogeneity within 25 base pairs of focal substitutions.
Additionally, they found that substitutions in slowly evolving genes were associated with stronger genetic hitchhiking effects.