Does all of evolutionary theory rest on Fisher’s Fundamental Theorem?

The blogs of creationists and ID advocates have been buzzing with the news that a new paper by William Basener and John Sanford, in Journal of Mathematical Biology, shows that natural selection will not lead to the increase of fitness. Some of the blog reports will be found here, here, here, here, here, and here. Sal Cordova has been quoting the paper at length in a comment here.

Basener and Sanford argue that the Fundamental Theorem of Natural Selection, put forward by R.A. Fisher in his book The Genetical Theory of Natural Selection in 1930, was the main foundation of the Modern Evolutionary Synthesis of the 1930s and 1940s. And that when mutation is added to the evolutionary forces modeled by that theorem, it can be shown that fitnesses typically decline rather than increase. They argue that Fisher expected increase of fitness to be typical (they call this Fisher’s Theorem”).

I’m going to argue here that this is a wrong reading of the history of theoretical population genetics and of the history of the Modern Synthesis. In a separate post, in a few days at Panda’s Thumb, I will argue that Basener and Sanford’s computer simulation has a fatal flaw that makes its behavior quite atypical of evolutionary processes.

Was the mathematics of natural selection, and the mathematics of mutation, ignored in theoretical population genetics until Fisher’s 1930 book? Well, actually, no. Here is the major work on this before 1930:

1. In 1903, three years after the rediscovery of Mendel’s work, the mammalian geneticist William Ernest Castle showed in Proceedings of the American Academy of Arts and Sciences a numerical calculation of the elimination of a lethal recessive allele from population.

2. In 1915, in an Appendix to a book Mimicry in Butterflies by the well-known geneticist R. C. Punnett, H. T. J. Norton showed numerical calculations for a case of natural selection, showing that selection was effective in favoring an advantageous allele. Norton’s mathematical equations were not given until later, in 1928. Jennings (1916) and Wentworth and Remick (1917), in papers in Genetics, did further work on the elimination of recessive lethal alleles.

3. In 1922, R. A. Fisher published a major paper in the Proceedings of the Royal Society of Edinburgh, showing the algebra of natural selection for dominant alleles and for alleles of intermediate dominance, as well as the effects of mutation and of genetic drift (which he called the “Hagedoorn effect”). His treatment of genetic drift was pioneering, but made a technical mistake later corrected by Sewall Wright in 1929.

4. J. B. S. Haldane, starting in 1924, published a numbered series of papers under the general title “A mathematical theory of natural and artificial selection”, the first in Transactions of the Cambridge Philosophical Society and all the rest except the 10th in Proceedings of the Cambridge Philosophical Society. These treated many cases of natural selection and different mating systems.

5. In his 1927 paper in that series, whose subtitle is “Selection and mutation”, Haldane gives the probability of fixation of a new favored mutant when it is present in just a single copy in the presence of genetic drift. For infinite populations where genetic drift is absent, he derived the equilibrium frequency of a mutant allele when its increase is countered by natural selection.

6. In a paper in 1928 in American Naturalist, R. A. Fisher put forth an argument that natural selection would alter the degree of dominance of a deleterious allele that was recurring by mutation. Sewall Wright and he then debated this back and forth in that journal in 1929, with Wright arguing that the strength of selection on modifiers of dominance would be too weak to be effective, and that the recessiveness of many mutants was inherent in the biochemical kinetics of the genes. (Wright was backed up in this later by Haldane and by H. J. Muller).

7. Wright was already at work on the distributions of gene frequencies under natural selection, mutation, migration, and genetic drift. This work, which was the foundation of modern work using diffusion equations, was not published in full until 1931. An abstract Wright published in 1929 shows that Wright had many of the results by then.

Conclusion: the mathematics of mutation and natural selection had been well worked-out before R. A. Fisher published his 1930 book. That book puts forward many important and original arguments in addition to summarizing in verbal form the mathematics of natural selection and mutation. The Fundamental Theorem of Natural Selection is one of the least consequential things in the book — Fisher did not give a precise derivation, and what the terms mean has been the subject of a recent literature, with papers by the late George Price, by Anthony Edwards, and by Warren Ewens. The conclusions leave considerable doubt as to the fundamentalness of the theorem.

Thus the literature on the theory of natural selection, of mutation, and of their joint action, did not wait until 1930, and in its 1920s development did not rely at all on the Fundamental Theorem of Natural Selection. In addition, “Fisher’s Theorem”, so-called by Basener and Sanford, will not be found in Fisher’s work — he was in fact quite critical of Sewall Wright’s 1932 arguments that highlighted maximization of mean fitness as a major principle in evolutionary genetics.

I hope to follow this post up with one at Panda’s Thumb in the next few days, showing that the ineffectiveness of natural selection in Basener and Sanford’s simulations comes from an unfortunate choice of the parameters in their simulation.

111 thoughts on “Does all of evolutionary theory rest on Fisher’s Fundamental Theorem?

  1. Corneel: It is a definitional thing. Mutational meltdown is usually reserved for situations where mutation pressure and genetic drift overwhelm purifying selection. This is expected to result in a decrease in population size and eventual extinction.
    It is confusing to use this term for instances of regressive evolution, because flightless birds and blind cave critters are doing just fine.

    This is a typical example of evolutionary-population genetics speculative schmaltz when facts contradict the narrative..

    But, faith keeps people alive…even if it’s blind…

  2. J-Mac: This is a typical example of evolutionary-population genetics speculative schmaltz when facts contradict the narrative..

    Not fair, if Sal writes something you don’t understand, you call it “keen insight”.

  3. Rumraket:
    I have to agree with J-mac on the faith point.

    “If you have faith big enough facts don’t count”

    I have to agree with Rumraket on the faith point.
    The only difference between the loonie-churches and Darwinian one is that Darwin’s faithful call their faith science
    Can’t argue with that… lol

  4. Rum and Corneel,

    Don’t forget that “…your commitment to materialism must be absolute, since you can’t allow a divine foot in the door …”
    This type of commitment reaches beyond faith… It’s an ideology…right or wrong…

  5. Corneel: Thanks for that. .. That may not generalize well to all instances of adaptive evolution. Agree?

    Agree! See, I’m agreeable, and occasionally we can agree. 🙂

  6. J-Mac: The only difference between the loonie-churches and Darwinian one is that Darwin’s faithful call their faith science

    I’ve never met a Darwinian faithful, but I kind of remember some religious nut calling some biblical crap science. Some shit about stretched tents. Go figure.

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