Principle relating genetic variance to fitness
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, however, it is a true theorem.[ 3]
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."[ 4]
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".[ 5]
History
The theorem was first formulated in Fisher's 1930 book The Genetical Theory of Natural Selection .[ 4] 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 .[ 6] [ 7]
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.[ 8] 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.[ 9]
Due to confounding factors, tests of the fundamental theorem are quite rare though Bolnick in 2007 did test this effect in a natural population.[ 10]
References
^ 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 .
^ 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 .
^ Plutynski, Anya (2006). "What was Fisher's fundamental theorem of natural selection and what was it for?" . Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences . 37 (1): 59–82. doi :10.1016/j.shpsc.2005.12.004 .
^ a b Fisher, R.A. (1930). The Genetical Theory of Natural Selection . Oxford, UK: Clarendon Press.
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .
Further reading
Brooks, D.R.; Wiley, E.O. (1986). Evolution as Entropy: Towards a unified theory of biology . The University of Chicago Press.
Ewens, W.J. (1989). "An interpretation and proof of the Fundamental Theorem of Natural Selection". Theor. Popul. Biol . 36 (2): 167–180. doi :10.1016/0040-5809(89)90028-2 . PMID 2814903 .
Ewens, W.J.; Lessard, S. (2015). "On the interpretation and relevance of the Fundamental Theorem of Natural Selection". Theoretical Population Biology . 104 : 59–67. doi :10.1016/j.tpb.2015.07.002 . PMID 26220589 .
Frank, Steve A. (1997). "The Price equation, Fisher's fundamental theorem, kin selection, and causal analysis" . Evolution . 51 (6): 1712–1729. doi :10.1111/j.1558-5646.1997.tb05096.x . PMID 28565119 . S2CID 14820814 . Archived from the original on 18 September 2004. "Abstract only" . stevefrank.org .
Frank, Steve A. (1998). Foundation of Social Evolution . Princeton, NJ: Princeton University Press. ISBN 0-691-05934-9 .
Frank, Steve A.; Slatkin, M. (1992). "Fisher's fundamental theorem of natural selection" . Trends in Ecology and Evolution . 7 (3): 92–95. doi :10.1016/0169-5347(92)90248-A . PMID 21235964 . Archived from the original on 13 September 2004. "abstract only" . stevefrank.org .
Grafen, A. (2000). "Developments of the Price equation and natural selection under uncertainty" . Proceedings of the Royal Society of London B . 267 (1449): 1223–1227. doi :10.1098/rspb.2000.1131 . PMC 1690660 . PMID 10902688 .
Grafen, A (2002). "A first formal link between the Price equation and an optimisation program". Journal of Theoretical Biology . 217 (1): 75–91. Bibcode :2002JThBi.217...75G . CiteSeerX 10.1.1.380.8681 . doi :10.1006/jtbi.2002.3015 . PMID 12183132 .
Grafen, A. (2003). "Fisher the evolutionary biologist". Journal of the Royal Statistical Society, Series D . 52 (3): 319–329. CiteSeerX 10.1.1.332.7319 . doi :10.1111/1467-9884.00362 .
Kjellström, G. (January 1996). "Evolution as a statistical optimization algorithm". Evolutionary Theory . 11 : 105–117.
Mayr, Ernst (2001). What Evolution Is . New York: Basic Books.
Nagylaki, T. (1991). "Error bounds for the fundamental and secondary theorems of natural selection" . Proceedings of the National Academy of Sciences . 88 (6): 2402–2406. Bibcode :1991PNAS...88.2402N . doi :10.1073/pnas.88.6.2402 . PMC 51240 . PMID 2006177 .
Smith, J. Maynard (1998). Evolutionary Genetics . Oxford University Press.
van Veelen, Matthijs; Allen, Benjamin; Hoffman, Moshe; Simon, Burton; Veller, Carl (2017). "Hamilton's rule". Journal of Theoretical Biology . 414 : 176–230. Bibcode :2017JThBi.414..176V . doi :10.1016/j.jtbi.2016.08.019 . PMID 27569292 .
External links