Fixation Probabilities and Times

Sarah P Otto, University of British Columbia, Vancouver, British Columbia, Canada
Michael C Whitlock, University of British Columbia, Vancouver, British Columbia, Canada

Published online: March 2008

DOI: 10.1002/9780470015902.a0005464.pub2

The fixation probability of an allele is the probability that it will eventually be the ancestor of all the alleles within a population at that locus. The time to fixation is the number of generations that it takes for the allele to progress from its initial frequency to fixation.

Keywords: branching process; diffusion; fixation; probability of fixation; time to fixation

Figure 1. Mean time to fixation for additive alleles in a diploid population (from eqn (5)). The average time to fixation, conditioned on the fact that the allele does fix, is a decreasing function of |s|. As the strength of selection increases, both beneficial and deleterious alleles, if they fix, will fix faster. Alleles will also fix faster, on average, in populations of smaller effective size. Note that the mean time to fixation for neutral alleles (s=0) is 4Ne (for Ne=10 000, this time is 40 000 generations).
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 References
    Barton NH (1993) The probability of fixation of a favoured allele in a subdivided population. Genetical Research 62: 149–158.
    Barton NH (1995) Linkage and the limits to natural selection. Genetics 140: 821–841.
    Caballero A and Hill WG (1992) Effects of partial inbreeding on fixation rates and variation of mutant genes. Genetics 131: 493–507.
    book Crow JF and Kimura M (1970) An Introduction to Population Genetics Theory. New York, NY: Harper & Row.
    Ewens WJ (1967) The probability of survival of a new mutant in a fluctuating environment. Heredity 22: 438–443.
    book Ewens WJ (1979) Mathematical Population Genetics. Berlin: Springer.
    Haldane JBS (1927) A mathematical theory of natural and artificial selection, part V: selection and mutation. Proceedings of the Cambridge Philosophical Society 23: 838–844.
    Hill WG and Robertson A (1966) The effect of linkage on the limits to artificial selection. Genetical Research 8: 269–294.
    Kimura M (1957) Some problems of stochastic processes in genetics. Annals of Mathematical Statistics 28: 882–901.
    Kimura M (1962) On the probability of fixation of mutant genes in a population. Genetics 47: 713–719.
    book Kimura M (1983) The Neutral Theory of Molecular Evolution. Cambridge, UK: Cambridge University Press.
    Kimura M and Ohta T (1969) The average number of generations until fixation of a mutant gene in a finite population. Genetics 61: 763–771.
    Lynch M, Conery J and Bürger R (1995) Mutational meltdowns in sexual populations. Evolution 49: 1067–1080.
    Maruyama T and Kimura M (1974) A note on the speed of gene-frequency changes in reverse directions in a finite population. Evolution 28: 161–163.
    Orr HA and Coyne JA (1992) The genetics of adaptation: a reassessment. American Naturalist 140: 725–742.
    Otto SP and Whitlock MC (1997) The probability of fixation in populations of changing size. Genetics 146: 723–733.
    Whitlock MC (2003) Fixation probability and time in subdivided populations. Genetics 164: 767–779.
 Further Reading
    Fisher RA (1922) On the dominance ratio. Proceedings of the Royal Society of Edinburgh 42: 321–341.
    Fisher RA (1930) The distribution of gene ratios for rare mutations. Proceedings of the Royal Society of Edinburgh 50: 204–219.
    Gerrish PJ and Lenski RE (1998) The fate of competing beneficial mutations in an asexual population. Genetica 103: 127–144.
    book Li WH (1997) Molecular Evolution. Sunderland, MA: Sinauer Associates.
    Lynch M, Conery J and Bürger R (1995) Mutation accumulation and the extinction of small populations. American Naturalist 146: 489–518.
    Nurminsky DI (2001) Genes in sweeping competition. Cellular and Molecular Life Sciences 58: 125–134.
    Orr HA (1998) The population genetics of adaptation: the distribution of factors fixed during adaptive evolution. Evolution 52: 935–949.
    Poon A and Otto SP (2000) Compensating for our load of mutations: freezing the meltdown of small populations. Evolution 54: 1467–1479.
    Whitlock MC (2000) Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection. Evolution 54: 1855–1861.
    Wright S (1931) Evolution in Mendelian populations. Genetics 16: 97–159.

Related Sub-Topics:

Population Structure and Genetics | Evolution Rates
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Article Title: Fixation Probabilities and Times
 
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Otto, Sarah P, and Whitlock, Michael C(Mar 2008) Fixation Probabilities and Times. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0005464.pub2]