Fisher's fundamental theorem of natural selection

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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.

Contents

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]

Related Research Articles

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<span class="mw-page-title-main">Ronald Fisher</span> British polymath (1890–1962)

Sir Ronald Aylmer Fisher was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who almost single-handedly created the foundations for modern statistical science" and "the single most important figure in 20th century statistics". In genetics, his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th-century revision of the theory of evolution known as the modern synthesis, being the one to most comprehensively combine the ideas of Gregor Mendel and Charles Darwin. For his contributions to biology, Richard Dawkins proclaimed Fisher as "the greatest of Darwin's successors". He is considered one of the founding fathers of Neo-Darwinism.

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The handicap principle is a disputed hypothesis proposed by the Israeli biologist Amotz Zahavi in 1975. It is meant to explain how sexual selection may lead to "honest" or reliable signalling between male and female animals which have an obvious motivation to bluff or deceive each other. The handicap principle suggests that secondary sexual characteristics are costly signals which must be reliable, as they cost the signaller resources that individuals with less of a particular trait could not afford. The handicap principle further proposes that animals of greater biological fitness signal this through handicapping behaviour, or morphology that effectively lowers overall fitness. The central idea is that sexually selected traits function like conspicuous consumption, signalling the ability to afford to squander a resource. Receivers then know that the signal indicates quality, because inferior-quality signallers are unable to produce such wastefully extravagant signals.

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The Genetical Theory of Natural Selection is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and stating with regard to mutations that "The vast majority of large mutations are deleterious; small mutations are both far more frequent and more likely to be useful", thus refuting orthogenesis. First published in 1930 by The Clarendon Press, it is one of the most important books of the modern synthesis, and helped define population genetics. It is commonly cited in biology books, outlining many concepts that are still considered important such as Fisherian runaway, Fisher's principle, reproductive value, Fisher's fundamental theorem of natural selection, Fisher's geometric model, the sexy son hypothesis, mimicry and the evolution of dominance. It was dictated to his wife in the evenings as he worked at Rothamsted Research in the day.

<span class="mw-page-title-main">George R. Price</span> American mathematician

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  1. Genetic drift allows a locally adapted subpopulation to move across an adaptive valley to the base of a higher adaptive peak.
  2. Natural selection will move the subpopulation up the higher peak.
  3. This new superiorly adapted subpopulation may then expand its range and outcompete or interbreed with other subpopulations, causing the spread of new adaptations and movement of the global population toward the new fitness peak.
<span class="mw-page-title-main">Genetic variance</span> Biological concept

Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection. In his 1930 book The Genetical Theory of Natural Selection, Fisher postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. Fisher tried to give a statistical formula about how the change of fitness in a population can be attributed to changes in the allele frequency. Fisher made no restrictive assumptions in his formula concerning fitness parameters, mate choices or the number of alleles and loci involved.

Mark A. Kirkpatrick is a theoretical population geneticist and evolutionary biologist. He currently holds the T. S. Painter Centennial Professorship in Genetics in the Department of Integrative Biology at the University of Texas at Austin. His research touches on a wide variety of topics, including the evolution of sex chromosomes, sexual selection, and speciation. Kirkpatrick is the co-author, along with Douglas J. Futuyma, of a popular undergraduate evolution textbook. He is a member of the United States National Academy of Sciences.

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. 1 2 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.

Further reading