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**An interpretation and proof of the fundamental theorem of natural selection.**
*(English)*
Zbl 0702.92012

This is indeed a very interesting paper. It touches one of the cornerstones of population genetics: Fisher’s fundamental theorem of natural selection. The author claims that Fisher’s intended statement is quite different from its common interpretation that the total (rate of) change in average fitness is positive. This interpretation may fail with discrete generations and non-random mating or with multilocus models. According to the author, Fisher only claimed that a so-called partial change in average fitness is positive and exactly (rather than approximately) related to the additive genetic variance. As long as allelic frequencies do not change in the mating process, that claim holds irrespective of random mating, discrete or continuous time, one locus or many loci (the extension to this case is shown in the paper).

It is preferable, however, to obtain approximations to the common interpretation of the Fisher’s theorem result. On that line, and with random mating, a complete analysis for two loci was done by T. Nagylaki [Genetics 83, 583-600 (1976)] and a statistical-type analysis for multiple loci was done by L. R. Ginzburg and the reviewer [Theor. Popul. Biol. 17, 298-320 (1980; Zbl 0449.92013)]. The reason is that, despite the greater generality of Fisher’s intended result, it does not seem to have, according to the author, the biological significance Fisher apparently saw in it.

It is preferable, however, to obtain approximations to the common interpretation of the Fisher’s theorem result. On that line, and with random mating, a complete analysis for two loci was done by T. Nagylaki [Genetics 83, 583-600 (1976)] and a statistical-type analysis for multiple loci was done by L. R. Ginzburg and the reviewer [Theor. Popul. Biol. 17, 298-320 (1980; Zbl 0449.92013)]. The reason is that, despite the greater generality of Fisher’s intended result, it does not seem to have, according to the author, the biological significance Fisher apparently saw in it.

Reviewer: C.A.Braumann

### MSC:

92D10 | Genetics and epigenetics |

### Keywords:

population genetics; Fisher’s fundamental theorem of natural selection; change in average fitness; multilocus models; additive genetic variance### Citations:

Zbl 0449.92013
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\textit{W. J. Ewens}, Theor. Popul. Biol. 36, No. 2, 167--180 (1989; Zbl 0702.92012)

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### References:

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