Editing Genetic drift (section)

===Time to fixation or loss===
Assuming genetic drift is the only evolutionary force acting on an allele, at any given time the probability that an allele will eventually become fixed in the population is simply its frequency in the population at that time.<ref>{{harvnb|Futuyma|1998|p=300}}</ref> For example, if the frequency ''p'' for allele '''A''' is 75% and the frequency ''q'' for allele '''B''' is 25%, then given unlimited time the probability '''A''' will ultimately become fixed in the population is 75% and the probability that '''B''' will become fixed is 25%.

The expected number of generations for fixation to occur is [[Proportionality (mathematics)|proportional]] to the population size, such that fixation is predicted to occur much more rapidly in smaller populations.<ref>{{cite journal | vauthors = Otto SP, Whitlock MC | title = The probability of fixation in populations of changing size | journal = Genetics | volume = 146 | issue = 2 | pages = 723–33 | date = June 1997 | pmid = 9178020 | pmc = 1208011 | url = http://www.genetics.org/content/146/2/723.full.pdf | publisher = Genetics Society of America| doi = 10.1093/genetics/146.2.723 | url-status = live | archive-date = 19 March 2015 | archive-url = https://web.archive.org/web/20150319042554/http://www.genetics.org/content/146/2/723.full.pdf | author-link1 = Sarah Otto }}</ref> Normally the effective population size, which is smaller than the total population, is used to determine these probabilities. The effective population (''N''<sub>''e''</sub>) takes into account factors such as the level of [[inbreeding]], the stage of the lifecycle in which the population is the smallest, and the fact that some neutral genes are genetically linked to others that are under selection.<ref name="Charlesworth09">{{cite journal | vauthors = Charlesworth B | title = Fundamental concepts in genetics: effective population size and patterns of molecular evolution and variation | journal = Nature Reviews. Genetics | volume = 10 | issue = 3 | pages = 195–205 | date = March 2009 | pmid = 19204717 | doi = 10.1038/nrg2526 | publisher = [[Nature Publishing Group]] | s2cid = 205484393 | author-link = Brian Charlesworth }}</ref> The effective population size may not be the same for every gene in the same population.<ref>{{cite journal | vauthors = Cutter AD, Choi JY | title = Natural selection shapes nucleotide polymorphism across the genome of the nematode Caenorhabditis briggsae | journal = Genome Research | volume = 20 | issue = 8 | pages = 1103–11 | date = August 2010 | pmid = 20508143 | pmc = 2909573 | doi = 10.1101/gr.104331.109 | publisher = [[Cold Spring Harbor Laboratory Press]] }}</ref>

One forward-looking formula used for approximating the expected time before a neutral allele becomes fixed through genetic drift, according to the Wright–Fisher model, is

: <math>
\bar{T}_\text{fixed} = \frac{-4N_e(1-p) \ln (1-p)}{p}
</math>

where ''T'' is the number of generations, ''N''<sub>''e''</sub> is the effective population size, and ''p'' is the initial frequency for the given allele. The result is the number of generations [[Expected value|expected]] to pass before fixation occurs for a given allele in a population with given size (''N''<sub>''e''</sub>) and allele frequency (''p'').<ref>{{harvnb|Hedrick|2005|p=315}}</ref>

The expected time for the neutral allele to be lost through genetic drift can be calculated as<ref name="Hartl_p112" />

: <math>
\bar{T}_\text{lost} = \frac{-4N_ep}{1-p} \ln p.
</math>

When a mutation appears only once in a population large enough for the initial frequency to be negligible, the formulas can be simplified to<ref>{{harvnb|Li|Graur|1991|p=33}}</ref>

: <math>
\bar{T}_\text{fixed} = 4N_e
</math>

for average number of generations expected before fixation of a neutral mutation, and

: <math>
\bar{T}_\text{lost} = 2 \left ( \frac{N_e}{N} \right ) \ln (2N)
</math>

for the average number of generations expected before the loss of a neutral mutation in a population of actual size N.<ref>{{harvnb|Kimura|Ohta|1971}}</ref>