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."

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 genic variance in fitness at that time". (A.W.F. Edwards 1994)

[edit] 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.

Another thing making the fundamental theorem dubious is that the mean fitness is determined as a mean over the set of genes in a large population, assuming that a gene may be a unit of selection having a fitness of its own. Of course, it is true that genes are enriched in a population, but this enrichment is ruled by the selection of individuals.

So, if selection is supposed to take place on the individual level, based on phenotypes, a quite different result may be obtained. For instance, let s(x) be the probability that the individual having the array of phenotypes x will be selected to produce offspring to the next generation. Further, suppose that the probability density function, p. d. f., of phenotypes in the population is N(m – x), where m is the mean of the distribution, then the mean fitness – as determined over the set of individuals – may be determined as

P(m) = integral { s(x) N(m – x) dx }.

In the special case when N(m – x) is a Gaussian p. d. f., the theorem of Gaussian adaptation may be shown, leading to a different view of evolutionary properties.


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Topics in population genetics
v • d • e
Key concepts: Hardy-Weinberg law | genetic linkage | linkage disequilibrium | Fisher's fundamental theorem | neutral theory
Selection: natural | sexual | artificial | ecological
Effects of selection on genomic variation: genetic hitchhiking | background selection
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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