Fisher's fundamental theorem of natural selection explained
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]
Further reading
- Book: Brooks . D.R. . Wiley . E.O. . 1986 . Evolution as Entropy: Towards a unified theory of biology . The University of Chicago Press . none .
- Ewens . W.J. . 1989 . An interpretation and proof of the Fundamental Theorem of Natural Selection . Theor. Popul. Biol. . 36 . 2 . 167–180. 10.1016/0040-5809(89)90028-2 . 2814903 . none .
- Ewens . W.J. . Lessard . S. . 2015 . On the interpretation and relevance of the Fundamental Theorem of Natural Selection . . 104 . 59–67 . 10.1016/j.tpb.2015.07.002. 26220589 . none .
- Frank . Steve A. . 1997 . The Price equation, Fisher's fundamental theorem, kin selection, and causal analysis . . 51 . 6 . 1712–1729 . https://web.archive.org/web/20040918165349/http://stevefrank.org/reprints-choice/97Evol-Causal-R.html . 2004-09-18 . dmy-all. 10.1111/j.1558-5646.1997.tb05096.x . 28565119 . 14820814 . none . Web site: Abstract only . stevefrank.org . none .
- Book: Frank, Steve A. . 1998 . Foundation of Social Evolution . Princeton, NJ . Princeton University Press . 0-691-05934-9 . none .
- Frank . Steve A. . Slatkin . M. . 1992 . Fisher's fundamental theorem of natural selection. . . 7 . 3 . 92–95 . https://web.archive.org/web/20040913124200/http://stevefrank.org/reprints-choice/92TREE-R.html . 2004-09-13 . dmy-all. 10.1016/0169-5347(92)90248-A . 21235964 . none . Web site: abstract only . stevefrank.org . none .
- 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. 10.1098/rspb.2000.1131 . 10902688 . 1690660 . none .
- Grafen . A . 2002 . A first formal link between the Price equation and an optimisation program . . 217 . 1 . 75–91 . 10.1006/jtbi.2002.3015 . 12183132 . 2002JThBi.217...75G . 10.1.1.380.8681 . none .
- Grafen . A. . 2003 . Fisher the evolutionary biologist . . 52 . 3 . 319–329 . 10.1111/1467-9884.00362 . 10.1.1.332.7319 . none .
- Kjellström . G. . Evolution as a statistical optimization algorithm . Evolutionary Theory . 11 . 105–117 . January 1996 . none .
- Book: Mayr, Ernst . 2001 . What Evolution Is . Basic Books . New York . none .
- 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 . 10.1073/pnas.88.6.2402 . 51240 . 2006177. 1991PNAS...88.2402N . free . none .
- Book: Smith, J. Maynard . Evolutionary Genetics . Oxford University Press . 1998 . none .
- van Veelen . Matthijs . Allen . Benjamin . Hoffman . Moshe . Simon . Burton . Veller . Carl . 2017 . Hamilton's rule . . 414 . 176–230 . 10.1016/j.jtbi.2016.08.019 . 27569292. 2017JThBi.414..176V . none .
External links
Notes and 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 . 12206233 . 10.1554/0014-3820(2002)056[1313:phstfa]2.0.co;2. 198157405 .
- Lessard . Sabin . 1997 . Fisher's Fundamental Theorem of Natural Selection Revisited. Theoretical Population Biology . 52 . 2 . 119–136 . 9356328 . 10.1006/tpbi.1997.1324 .
- 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 . en . 37 . 1 . 59–82 . 10.1016/j.shpsc.2005.12.004.
- Book: Fisher, R.A. . R.A. Fisher . 1930 . The Genetical Theory of Natural Selection . Clarendon Press . Oxford, UK. The Genetical Theory of Natural Selection .
- Edwards . A.W.F. . A.W.F. Edwards . 1994 . The fundamental theorem of natural selection . Biological Reviews . 69 . 4 . 443–474 . 10.1111/j.1469-185x.1994.tb01247.x . 7999947. 10052338 .
- Kimura . Motoo . Attainment of quasi-linkage equilibrium when gene frequencies are changing by natural selection . Genetics . 1965 . 52 . 5 . 875–890. 10.1093/genetics/52.5.875 . 17248281 . 1210959 .
- Book: Singh . Rama S. . Krimbas . Costas B. . Evolutionary Genetics: From molecules to morphology . 28 March 2000 . Cambridge University Press . 978-0-521-57123-4 . 267.
- Book: Provine, William B. . The Origins of Theoretical Population Genetics: With a new afterword . May 2001 . University of Chicago Press . 978-0-226-68464-2 . 140–166.
- Price . G.R. . George R. Price . 1972 . Fisher's "fundamental theorem" made clear . . 36 . 2 . 129–140 . 10.1111/j.1469-1809.1972.tb00764.x . 4656569. 20757537 .
- Bolnick . D.I. . Nosil . P. . 2007 . Natural selection in populations subject to a migration load . Evolution . 61 . 9 . 2229–2243 . 10.1111/j.1558-5646.2007.00179.x . 17767592.
