William Basener and John Sanford have responded here to my post concerning whether R.A. Fisher’s Fundamental Theorem of Natural Selection is critical to work on the theoretical population genetics of the interaction between mutation and natural selection. (This reply by Basener and Sanford is also reposted here.)
They had published a paper in Journal of Mathematical Biology in which they argued that the FTNS was the foundation of all subsequent work on the theoretical population genetics of natural selection, that the FTNS ignored mutations, and that it needed correcting. They then added terms for the effects of mutation to a limited version of the FTNS, one which was published by Crow and Kimura (1970). They reported numerical simulation results using that model, which showed natural selection to be unable to
prevent most deleterious mutations from fixing in the population.
My reply showed that the basic mathematical theory of the population genetics of deleterious mutations was not dependent on the Fundamental Theorem
of Natural Selection, but had been published before, by William Ernest Castle (1903), H.T.J. Norton (1915), R.A. Fisher (1922, 1929), J.B.S. Haldane (1927), and Sewall Wright (1928, 1929). The FTNS was an interesting result, but was not at all critical to subsequent work on mutations and selection.
In this rejoinder, I will deal with two issues: (1) Is the FTNS the foundation of the mathematical treatment of mutation and natural selection in populations, and (2) did R.A. Fisher draw from the FTNS the conclusion that natural selection led to ever-increasing mean fitnesses. I will show that the answer to both is “no”.