Fisher’s fundamental theorem

Now we show that there is a surprising relation between Fisher s fundamental theorem of natural selection and other theory developed by Fisher, the likelihood theory in statistics and Fisher information [21], As far as we know, the present chapter is the first publication in the literature pointing out the connections between these two problems formulated and studied by Fisher. 

This is known as Fisher s Fundamental Theorem of Natural Selection. In the absence of perturbations to the population or environment, fitness increases until the best genotypes are fixed and no variance in fitness remains. 

Fisher s Fundamental Theorem and the assumption of no perturbations suggest that there should be no variance in fitness. This assertion is difficult to test directly. Burt (1995) reviewed 13 estimates of the variance in fitness in six different species, and only two were significant. Because one cannot prove absence, the meaning of this result is unclear. Of course many examples of directional changes in populations suggest that variance in fitness is often present (Endler 1986). Experimenters have usually had to content themselves with measuring fitness components, and these very often display substantial genetic variance (Houle 1992, Mousseau Roff 1987, Roff Mousseau 1987). Two interpretations of this result are possible, and are most easily introduced with a simple model (Houle 1991). 

Fisher s fundamental theorem (1958) states that selection removes additive genetic variance, and thus should diminish narrow sense heritability. Because of Fisher s argument (which is mathematically correct), scientists have argued until recently that additive heritability was prima facie evidence that the trait was evolutionarily neutral (e.g. Tooby Cosmides 1990). Flowever, the ubiquity of additive genetic variation, even for traits subject to strong selective forces, has forced evolutionary biologists to try to account for the routine violations of Fisher s fundamental theorem. 

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