Fisher's fundamental theorem of natural selection

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In population genetics, R. A. Fisher's fundamental theorem of natural selection was originally stated as:

"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."

History

The theorem was first formulated by R. A. Fisher 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. 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.

References

Edwards, A.W.F. (1994) The fundamental theorem of natural selection. Biological Reviews 69:443–474.
Fisher, R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford.
Frank, S.A. (1997) The Price Equation, Fisher's fundamental theorem, kin selection, and causal analysis. Evolution 51:1712-1729. [Abstract] - [page for pdfs]
Frank, S.A. (1998) Foundation of Social Evolution. Princeton: Princeton University Press. [Book's website] ISBN 0691059349
Frank, S.A. and Slatkin, M. (1992) Fisher's fundamental theorem of natural selection. Trends in Ecology and Evolution 7:92-95. [abstract] - [pdfs]
Grafen, A. (2000) Developments of the Price equation and natural selection under uncertainty. Proceedings of the Royal Society of London B, 267:1223–1227.
Grafen, A. (2002) A first formal link between the Price equation and an optimisation program. Journal of Theoretical Biology 217:75–91.
Grafen, A. (2003) Fisher the evolutionary biologist. Journal of the Royal Statistical Society: Series D (The Statistician), 52: 319–329.
Price, G.R. (1972). Fisher's "fundamental theorem" made clear. Annals of Human Genetics 36:129-140

External links

Grafen Fisher the evolutionary biologist http://users.ox.ac.uk/~grafen/cv/fisher.pdf
http://www.peregrine.dk/subjects/FISH.HTM

[ edit] Topics in population genetics
Key concepts: Hardy-Weinberg law \| linkage disequilibrium \| Fisher's fundamental theorem \| neutral theory
Selection: natural \| sexual \| artificial \| ecological
Genetic drift: small population size \| population bottleneck \| founder effect \| coalescence
Founders: R.A. Fisher \| J.B.S. Haldane \| Sewall Wright
Related topics: evolution \| microevolution \| evolutionary game theory \| fitness landscape \| genetic genealogy
List of evolutionary biology topics

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