# Fisher's fundamental theorem of natural selection

Fisher's fundamental theorem of natural selection is an idea about genetic variance[1][2] in population genetics developed by the statistician and evolutionary biologist Ronald Fisher. The proper way of applying the abstract mathematics of the theorem to actual biology has been a matter of some debate.

It states:

"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."[3]

Or in more modern terminology:

"The rate of increase in the mean fitness of any organism, at any time, that is ascribable to natural selection acting through changes in gene frequencies, is exactly equal to its genetic variance in fitness at that time".[4]

## History

The theorem was first formulated in Fisher's 1930 book The Genetical Theory of Natural Selection.[3] Fisher likened it to the law of entropy in physics, stating that "It is not a little instructive that so similar a law should hold the supreme position among the biological sciences". The model of quasi-linkage equilibrium was introduced by Motoo Kimura in 1965 as an approximation in the case of weak selection and weak epistasis.[5][6]

Largely as a result of Fisher's feud with the American geneticist Sewall Wright about adaptive landscapes, the theorem was widely misunderstood to mean that the average fitness of a population would always increase, even though models showed this not to be the case.[7] In 1972, George R. Price showed that Fisher's theorem was indeed correct (and that Fisher's proof was also correct, given a typo or two), but did not find it to be of great significance. The sophistication that Price pointed out, and that had made understanding difficult, is that the theorem gives a formula for part of the change in gene frequency, and not for all of it. This is a part that can be said to be due to natural selection.[8]

Due to confounding factors, tests of the fundamental theorem are quite rare though Bolnick in 2007 did test this effect in a natural population.[9]

## References

1. ^ Crow, J.F. (2002). "Here's to Fisher, additive genetic variance, and the fundamental theorem of natural selection". Perspective. Evolution. 56 (7): 1313–1316. doi:10.1554/0014-3820(2002)056[1313:phstfa]2.0.co;2. PMID 12206233. S2CID 198157405.
2. ^ Lessard, Sabin (1997). "Fisher's Fundamental Theorem of Natural Selection Revisited". Theoretical Population Biology. 52 (2): 119–136. doi:10.1006/tpbi.1997.1324. PMID 9356328.
3. ^ a b Fisher, R.A. (1930). The Genetical Theory of Natural Selection. Oxford, UK: Clarendon Press.
4. ^ Edwards, A.W.F. (1994). "The fundamental theorem of natural selection". Biological Reviews. 69 (4): 443–474. doi:10.1111/j.1469-185x.1994.tb01247.x. PMID 7999947. S2CID 10052338.
5. ^ Kimura, Motoo (1965). "Attainment of quasi-linkage equilibrium when gene frequencies are changing by natural selection". Genetics. 52 (5): 875–890. doi:10.1093/genetics/52.5.875. PMC 1210959. PMID 17248281.
6. ^ Singh, Rama S.; Krimbas, Costas B. (28 March 2000). Evolutionary Genetics: From molecules to morphology. Cambridge University Press. p. 267. ISBN 978-0-521-57123-4.
7. ^ Provine, William B. (May 2001). The Origins of Theoretical Population Genetics: With a new afterword. University of Chicago Press. pp. 140–166. ISBN 978-0-226-68464-2.
8. ^ Price, G.R. (1972). "Fisher's "fundamental theorem" made clear". Annals of Human Genetics. 36 (2): 129–140. doi:10.1111/j.1469-1809.1972.tb00764.x. PMID 4656569. S2CID 20757537.
9. ^ Bolnick, D.I.; Nosil, P. (2007). "Natural selection in populations subject to a migration load". Evolution. 61 (9): 2229–2243. doi:10.1111/j.1558-5646.2007.00179.x. PMID 17767592.