Principle relating genetic variance to fitness
Fisher's fundamental theorem of natural selection is an idea aboutgenetic variance [ 1] [ 2] population genetics developed by thestatistician andevolutionary 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 infitness of anyorganism 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 ingene frequencies , is exactly equal to its genetic variance in fitness at that time".[ 5] The theorem was first formulated in Fisher's 1930 bookThe Genetical Theory of Natural Selection [ 4] law of entropy inphysics , stating that "It is not a little instructive that so similar a law should hold the supreme position among the biological sciences". The model ofquasi-linkage equilibrium was introduced byMotoo Kimura in 1965 as an approximation in the case ofweak selection and weakepistasis .[ 6] [ 7]
Largely as a result of Fisher's feud with the American geneticistSewall Wright aboutadaptive 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] 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]
^ 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.Bibcode :1997TPBio..52..119L .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 ^ 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 ISBN 978-0-521-57123-4 ^ Provine, William B. (May 2001).The Origins of Theoretical Population Genetics: With a new afterword 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 . 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.Bibcode :1989TPBio..36..167E .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.Bibcode :2015TPBio.104...59E .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 fromthe original "Abstract only" .stevefrank.org .Frank, Steve A. (1998).Foundation of Social Evolution 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.Bibcode :1992TEcoE...7...92F .doi :10.1016/0169-5347(92)90248-A .PMID 21235964 . Archived fromthe original "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 .
