Fisher's fundamental theorem of natural selection
Encyclopedia
In population genetics
, R. A. Fisher
's fundamental theorem
of natural selection
was originally stated as:
Or, in more modern terminology:
in his 1930 book The Genetical Theory of Natural Selection
. Fisher held that "It is not a little instructive that so similar a law should hold the supreme position among the biological sciences". However, for forty years it was misunderstood, it being read as saying that the average fitness of a population would always increase, and models showed this not to be the case. The misunderstanding can be seen largely as a result of Fisher's feud with the American geneticist Sewall Wright
primarily about adaptive landscapes.
The American George R. Price
showed in 1972 that Fisher's theorem was correct as stated, and that the proof was also correct, given a typo or two (see Price equation
). Price showed the result was true, 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.
More recent work (reviewed in Grafen 2003) builds on Price's understanding in two ways. One aims to improve the theorem by completing it, i.e. by finding a formula for the whole of the change in gene frequency. The other argues that the partial change is indeed of great conceptual significance, and aims to extend similar partial change results into more and more general population genetic models.
Due to confounding factors, tests of the fundamental theorem are quite rare. For an example of this effect in a natural population, see (Bolnick, 2007).
Population genetics
Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, R. A. Fisher
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
's fundamental theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
of natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
was originally stated as:
- "The rate of increase in fitnessFitness (biology)Fitness is a central idea in evolutionary theory. It can be defined either with respect to a genotype or to a phenotype in a given environment...
of any organism at any time is equal to its genetic variance in fitness at that time."
Or, in more modern terminology:
- "The rate of increase in the mean fitness of any organism at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genetic variance in fitness at that time".
History
The theorem was first formulated by R. A. FisherRonald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
in his 1930 book The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection is a book by R.A. Fisher first published in 1930 by Clarendon. It is one of the most important books of the modern evolutionary synthesis and is commonly cited in biology books.-Editions:...
. Fisher held that "It is not a little instructive that so similar a law should hold the supreme position among the biological sciences". However, for forty years it was misunderstood, it being read as saying that the average fitness of a population would always increase, and models showed this not to be the case. The misunderstanding can be seen largely as a result of Fisher's feud with the American geneticist Sewall Wright
Sewall Wright
Sewall Green Wright was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. With R. A. Fisher and J.B.S. Haldane, he was a founder of theoretical population genetics. He is the discoverer of the inbreeding coefficient and of...
primarily about adaptive landscapes.
The American George R. Price
George R. Price
George Robert Price was an American population geneticist. Originally a physical chemist and later a science journalist, he moved to London in 1967, where he worked in theoretical biology at the Galton Laboratory, making three important contributions: first, rederiving W.D...
showed in 1972 that Fisher's theorem was correct as stated, and that the proof was also correct, given a typo or two (see Price equation
Price equation
The Price equation is a covariance equation which is a mathematical description of evolution and natural selection. The Price equation was derived by George R. Price, working in London to re-derive W.D. Hamilton's work on kin selection...
). Price showed the result was true, 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.
More recent work (reviewed in Grafen 2003) builds on Price's understanding in two ways. One aims to improve the theorem by completing it, i.e. by finding a formula for the whole of the change in gene frequency. The other argues that the partial change is indeed of great conceptual significance, and aims to extend similar partial change results into more and more general population genetic models.
Due to confounding factors, tests of the fundamental theorem are quite rare. For an example of this effect in a natural population, see (Bolnick, 2007).
External links
- Grafen Fisher the evolutionary biologist http://users.ox.ac.uk/~grafen/cv/fisher.pdf
- http://www.peregrine.dk/subjects/FISH.HTM
- Error bounds for the fundamental and secondary theorems of natural selection