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.

126 Replies to “Does all of evolutionary theory rest on Fisher’s Fundamental Theorem?”

  1. J-Mac
    Ignored
    says:

    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. Rumraket Rumraket
    Ignored
    says:

    J-Mac: But, faith keeps people alive…even if it’s blind…

  3. Rumraket Rumraket
    Ignored
    says:

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

  4. Corneel Corneel
    Ignored
    says:

    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”.

  5. J-Mac
    Ignored
    says:

    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

  6. J-Mac
    Ignored
    says:

    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…

  7. Alan Fox Alan Fox
    Ignored
    says:

    Moved a comment to guano.

  8. stcordova
    Ignored
    says:

    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. 🙂

  9. stcordova
    Ignored
    says:

    From the OP:

    …in a few days at Panda’s Thumb….

    I looked over there, and I found this sad news, RBH, who has posted here at occasionally TSZ and my website (creationevolutionuniversity.com) has passed away.

    Condolences to all who knew him. Richard Hoppe and I argued quite a bit over the last 15 years, but he was a scholar and gentleman.

    https://pandasthumb.org/archives/2018/01/PT-contributor-Richard.html#disqus_thread

  10. Entropy Entropy
    Ignored
    says:

    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.

  11. Dave Carlson Dave Carlson
    Ignored
    says:

    stcordova: I looked over there, and I found this sad news, RBH, who has posted here at occasionally TSZand my website (creationevolutionuniversity.com) has passed away.

    Condolences to all who knew him. Richard Hoppe and I argued quite a bit over the last 15 years, but he was a scholar and gentleman.

    https://pandasthumb.org/archives/2018/01/PT-contributor-Richard.html#disqus_thread

    Thanks for the heads up. That is very sad.

  12. arlin
    Ignored
    says:

    Yes, assuming that evolutionary theory is based on Fisher’s fundamental theorem is wrong. However, given the focus of Basener and Stanford, it is grossly misleading for Joe to state “the mathematics of mutation and natural selection had been well worked-out before R. A. Fisher published his 1930 book”. This literally misses the main point that Fisher’s view of evolution is inadequate precisely because he was willing to assume that population genetics in nature just happens to fall into the right regime to ensure that the detailed dynamics of the provision of variation are irrelevant, making Mendelism work out right for Darwinism. No one accepts this anymore except apparently Barton and Charlesworth. Even Futuyma admits mutation-limited evolution, then he solves the “we were right all along” problem by claiming that mutation-limited evolution was part of the Modern Synthesis.

    As I wrote recently,

    the development and use of mathematical models reveals unambiguously that the OMS [original Modern Synthesis] does not suffice to depict evolutionary dynamics, because it fails to cover mutation-driven dynamics. This failure is not a mistake or oversight, but an intentional feature of the OMS reflected in the explicit claims of Mayr, Dobzhansky, Simpson, Stebbins and others that selection uses abundant variation in the “gene pool” and does not wait for new mutations.

    i like to emphasize the influence of this “gene pool” on theoretical population genetics by pointing out that origin-fixation models (now a widely used branch of theory) did not emerge until 1969, well after advocates of the OMS declared victory.

    Eminent theoreticians have pointed repeatedly to exactly the same limitation. Yedid and Bell (2002) write:

    In the short term, natural selection merely sorts the variation already present in a population, whereas in the longer term genotypes quite different from any that were initially present evolve through the cumulation of new mutations. The first process is described by the mathematical theory of population genetics. However, this theory begins by defining a fixed set of genotypes and cannot provide a satisfactory analysis of the second process because it does not permit any genuinely new type to arise.

    Hartl and Taubes (1998) describe inadequacies in previous treatments of mutation, referring to neutralist origin-fixation models in the last sentence:

    Almost every theoretical model in population genetics can be classified into one of two major types. In one type of model, mutations with stipulated selective effects are assumed to be present in the population as an initial condition . . . The second major type of models does allow mutations to occur at random intervals of time, but the mutations are assumed to be selectively neutral or nearly neutral.

    In their treatment of adaptive dynamics, Eshel and Feldman (2001 in Orzack and Sober, Adaptationism and Optimality) stress the distinction between “short-term evolution” defined as “the dynamics of the relative frequency of a finite, fixed set of geneotypes” and the “long-term evolution”,

    the process, popularly termed “trial and error”, whereby mutation continuously introduces into the population new genotypes that are then subject to the forces of natural selection, sexual selection, recombination, and the like. Each new type may either be eliminated or become established within the population

    To summarize, in the 1990s, mainstream theoreticians acknowledged that the extrapolationist position of the OMS– all of evolution (macroevolution) follows from shifting gene frequencies (microevolution)– is inadequate because we now understand that we have to model, as part of evolution, the dynamics of the mutational introduction of new alleles, not just assume it is sufficient to define evolution as a process that starts with abundant variation.

  13. keiths keiths
    Ignored
    says:

    Bumping this so that Joe and others will see arlin’s comment.

  14. Alan Fox Alan Fox
    Ignored
    says:

    Hi arlin, welcome to TSZ. Your name has cropped up here, before!

    Here’s a thread discussing your paper you linked to above. You’d be very welcome to author an OP. I’m sure there’d be plenty of interest. Your comment in this thread isn’t very visible, unfortunately.

  15. Alan Fox Alan Fox
    Ignored
    says:

    @ arlin

    You might like to see that Larry Moran commented here.

  16. Corneel Corneel
    Ignored
    says:

    Necromancing this thread still hasn’t worked. Here comes another bump.

    I’ll use the opprtunity to ask a question as well:

    arlin: To summarize, in the 1990s, mainstream theoreticians acknowledged that the extrapolationist position of the OMS– all of evolution (macroevolution) follows from shifting gene frequencies (microevolution)– is inadequate because we now understand that we have to model, as part of evolution, the dynamics of the mutational introduction of new alleles, not just assume it is sufficient to define evolution as a process that starts with abundant variation.

    How general is this claim? It seems to me that if the genetic architecture of a trait is highly polygenic (say length or weigth) the limiting effect of novel mutations can be safely ignored, whereas for other traits (say, resistance to toxins) stepwise selection of occasional mutations may be expected.

  17. Joe Felsenstein Joe Felsenstein
    Ignored
    says:

    arlin: To summarize, in the 1990s, mainstream theoreticians acknowledged that the extrapolationist position of the OMS– all of evolution (macroevolution) follows from shifting gene frequencies (microevolution)– is inadequate because we now understand that we have to model, as part of evolution, the dynamics of the mutational introduction of new alleles, not just assume it is sufficient to define evolution as a process that starts with abundant variation.

    Thanks, folks, for calling my attention to this part of the thread. I was engaged in an all-too-rare activity known as “sleeping”.

    A few points about where Arlin’s points fit in, or do not, in this discussion.

    1. Arlin is basically talking about what ought to be called part of the Modern Synthesis, and what needs a new name. That’s an interesting discussion, but it’s not the discussion of this thread, or of the OP here, or of Basener and Sanford’s paper.

    2. Unless I very much mistake him, Arlin is not agreeing with Basener and Sanford that most fixation of new mutant alleles in populations will be of deleterious alleles.

    3. The mathematics of the fate of new mutant alleles, and of fixation of new advantageous alleles was started out by R.A. Fisher in 1922 for the case of neutral alleles. It got a big boost from J.B.S. Haldane in 1927 for the case of advantagous mutants. It certainly had nothing to do with Fisher’s Fundamental Theorem. Nor did it wait for that — it was underway by 1927. Granted, there was more to do, with important work by A.N. Kolmogorov and by William Feller on diffusion processes. Sewall Wright derived his equilibrium distributions of gene frequencies in the late 1920s and published his major paper on them in 1931. Kolmogorov did some applications of his equations to genetics in 1937. In 1945, Sewall Wright realized that his equilibrium distributions could be derived from Kolmogorov’s equations. Leaving aside William Feller’s 1949 and 1951 technical work on boundary conditions on the diffusion processes, we can say that a very important step was the diffusion process work on fixation probabilities by Motoo Kimura in 1957 and 1962, which finally gave us good expressions for when deleterious alleles are expected to be able to fix. Again, the FTNS was not important to all to any of that later work, either.

    4. Fisher probably thought of mutation as replenishing the genetic variance that was in his FTNS. He wasn’t clear about that (that I know of).

    I’m not going to get into a big debate with Arlin here about whether or not we should declare a new Synthesis. Separate question. Whether we do so or not, the theoretical work in population genetics, did not wait for the Fundamental Theorem of Natural Selection, and subsequent theory after 1930 did not depend on the FTNS.

    I hope to publish in the next few days, with a very knowledgeable co-author, a careful consideration of Basener and Sanford’s work that shows why it got the result that it did, and why that shows its results to be of extremely limited interest. It will be posted either here or at Panda’s Thumb. I’ll let you know. And it will not be about what name we should call the Synthesis, or about when population geneticists’ understanding of models of fixation of new mutations can finally be called “truly adequate”.

  18. TomMueller
    Ignored
    says:

    Arlin’s post poses an interesting challenge.

    Unless I am missing something – much of what gainsayers regard as inadequacies of the OMS revolve about the unremarkable observation that no population ever attains their adaptive peaks and that much variation (especially at the molecular level) is non-adaptive, i.e “is just there”,

    To my jaundiced eye, this is reiterating exactly what Darwin set out to explain, at the outset.

    Offspring demonstrate variation – PERIOD! Variation provides grist for Evolution’s Mill. Of course, variation is of necessity random and happenchance and only a subset of variation is actually subject to Natural Selection. Of course, that must be true, in Darwinian terms! Otherwise, teleological processes would be occurring, and any such teleology was anathema to Darwin.

    If I understand Joe correctly – sceptics such as Arlin and Larry are “splitters” where others like Joe are “lumpers” and relevant distinctions become semantic.

    Where I may be getting lost, is the apparent (at least to my jaundiced eye) assumptions some are evidently making here; which Mayr referred to as bean-bag genetics.

    A while ago when P Z Myers and Steve Pinker were still on good speaking terms, Myers addressed this fallacy with an outstanding blog post:

    https://freethoughtblogs.com/pharyngula/2011/12/19/steve-pinkers-hair-and-the-muscles-of-worms/

    So – obviously, the notion of gene becomes as difficult as nailing Jello to a wall. If I understand correctly, Biochemists such as Larry would prefer that any non-junk transcript = one gene. Others such as Doolittle are suggesting the definition of a “gene” is no longer so straight-forward.

    I am also having difficulty with another issue when following the mathematics of such discussions; namely the assumptions inherent in estimating population size – i.e. count of individuals. Exactly how are individuals to be identified?

    For example: if single celled organisms proliferate, all the while maintaining communication with each other – should each cell is deemed an individual? What happens when a similar expansion results in colonies while individual cells still maintain communication with each other? And we can push the envelope further and further… In Biological terms when does the term “N” drop from many to few? … and what happens to the mathematical assumptions when doing so?

    But I digress.

  19. stcordova
    Ignored
    says:

    A technical question, once a deleterious allele gets fixed by drift, what happens to the S-coefficient. That S-coefficient was only stated in terms of a competitive environment with other alleles, it doesn’t necessarily say anything about the reproductive success of the entire population after it is fixed. Doesn’t everything get re-normalized anyway after fixation, so, hypothetically we can have lots of deleterious mutations fixed, but we will not see the population go extinct.

    I’m thinking of that experiment with Drosophilla bomaraded with high radiation doses and causing lots of defects, but the population size didn’t change!

  20. arlin
    Ignored
    says:

    Corneel:
    How general is this claim? It seems to me that if the genetic architecture of a trait ..

    I am only saying that some evolution is mutation-limited, and this makes the theory that evolution is not mutation-limited “inadequate”. If you want examples, think of the Lenski experiment, or any of the innumerable studies of molecular evolution that show influences of mutation rates or mutation biases.

    This makes your question hard to interpret. By analogy, some swans are black, I assert “some swans are black”, and you are asking how general is my claim. Either you want to know what proportion of swans are black, or perhaps you want to know the proportion, over some list of N different conditions (e.g., different countries), how often it is true that swans in that condition are sometimes black.

    I can’t answer either question quantitatively. I could only follow the pattern in your response above and begin listing cases that I think are mutation-limited and others that are not. But I think that this is probably the wrong question to be asking, and the right question will refer to something like the extent to which there are predictable influences of tendencies of variation in evolution, analogous to the predictable influences of fitness on evolution.

    That is, this question is a good target for re-framing. McCandlish and Stoltzfus (2014) suggestion some ways to clarify questions about the importance of mutation-limited evolution.

  21. arlin
    Ignored
    says:

    Alan Fox:
    … You’d be very welcome to author an OP. I’m sure there’d be plenty of interest.

    OK, I’ll take you up on that. How do I proceed?

  22. Alan Fox Alan Fox
    Ignored
    says:

    arlin,

    You already have author privileges. Logged in you should see a link to your dashboard. Under posts, choose “New post” from the drop-down and you should see the editor. You can, of course, write it elsewhere and paste in the text but it’s worth reviewing before posting. A page-break after a paragraph or two is appreciated. PM me through the messages tab on the front page if you have any problems.

    Look forward to your contribution.

  23. arlin
    Ignored
    says:

    Joe Felsenstein: Arlin is basically talking about what ought to be called part of the Modern Synthesis, and what needs a new name. That’s an interesting discussion, but it’s not the discussion of this thread, or of the OP here, or of Basener and Sanford’s paper.

    I agree completely that I am raising a different issue from the focus of your post. However, it is not an entirely different issue from what Basener and Sanford address.

    Fisher attempted to execute a theoretical masterstroke by showing that, once Mendelism is accepted, Darwinism is inevitable and all other views must be set aside. This argument was incredibly influential. Basener and Sanford are aware of this and it is a focus of much of their text.

    They point out that Fisher’s position turned out to be wrong, which is true. Their take on Fisher may be completely messed up, but for the people here who are interested in science, not merely in the structure of arguments, it is important to explain how Fisher’s (and the Modern Synthesis) view of evolution is wrong, and also to explain why Fisher reached the wrong conclusions by not considering new mutations, both in his argument against the possibility of orthogenesis, and in his argument for infinitesimalism.

    I will try to write a separate post about this, to explain the whole issue.

  24. TomMueller
    Ignored
    says:

    arlin: I will try to write a separate post about this, to explain the whole issue.

    Yes please.

  25. arlin
    Ignored
    says:

    Alan Fox,

    I left a draft in the system without publishing it. At 2200 words, it is a bit too long. If you or anyone with privileges wants to look at it and make comments about how to tighten the focus, I’ll take that into account.

  26. Alan Fox Alan Fox
    Ignored
    says:

    arlin,

    Seems fine to me. You even inserted a page break! Published.

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