# Fisher's fundamental theorem of natural selection

(Redirected from Fisher's fundamental theorem)

R. A. Fisher's so-called fundamental theorem of natural selection, although it uses some mathematical notation, is not a theorem in the mathematical sense, but an idea in population genetics which was originally stated thus:

"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."[1]

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".[2]

## History

The theorem was first formulated by Ronald Fisher in his 1930 book The Genetical Theory of Natural Selection.[1] 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". 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[3] (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).[4]

## References

1. ^ a b Fisher, R.A. (1930) The Genetical Theory of Natural Selection, Clarendon Press, Oxford
2. ^ Edwards, A.W.F. (1994) The fundamental theorem of natural selection. Biological Reviews 69:443–474.
3. ^ Price, G.R. (1972). Fisher's "fundamental theorem" made clear. Annals of Human Genetics 36:129–140
4. ^ * Bolnick D. I. & Nosil, P. Natural Selection in Populations Subject to a Migration Load. Evolution, Advance access, doi:10.1111/j.1558–5646.2007.00179.x [1]
• Brooks, D. R. & Wiley, E. O. Evolution as Entropy, Towards a unified theory of Biology. The University of Chicago Press, 1986.
• Ewens, W. J. 1989 An interpretation and proof of the Fundamental Theorem of Natural Selection. Theor. Pop. Biol. 36, 167–180
• Frank, S.A. (1997) The Price Equation, Fisher's fundamental theorem, kin selection, and causal analysis. Evolution 51:1712–1729. Abstractpage for pdfs
• Frank, S.A. (1998) Foundation of Social Evolution. Princeton: Princeton University Press. Book's website ISBN 0-691-05934-9
• Frank, S.A. and Slatkin, M. (1992) Fisher's fundamental theorem of natural selection. Trends in Ecology and Evolution 7:92–95. abstractpdfs
• 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.
• Kjellström, G. Evolution as a statistical optimization algorithm. Evolutionary Theory 11:105–117, January, 1996.
• Maynard Smith, J. Evolutionary Genetics. Oxford University Press, 1998.
• Mayr, E. What Evolution is. Basic Books, New York, 2001.