Joe Felsenstein recently posted a rebuttal of a critique of Fisher’s fundamental theorem of natural selection (FTNS). The authors, Basener and Sanford, argue that if new mutation (missing from the original FTNS) is taken into account, the theorem shows that Darwinism is impossible rather than inevitable. I agree with each point of Joe’s rebuttal.
Yet, I think that no discussion of this topic is complete without explaining that Fisher’s view, and more generally the original Modern Synthesis, is inadequate precisely because of the rejection of mutation-limited dynamics.
To begin, I want to introduce a distinction in how scientists invoke “theory” (explained here):
- theoryC (concrete, conjectural): a major conjecture or systematic hypothesis to account for observed phenomena, as in “prion theory of disease” or “Lamarck’s theory of evolution”;
- theoryA (abstract, analytical): the body of abstract principles relevant to some discipline, methodology or problem area, as in “music theory” or “population genetics theory”
A theoryC can be refuted by facts, but the abstract truths or principles in a body of theoryA cannot; a theoryC refers to the actual world, but statements in theoryA may invoke imaginary things like chickens with 3 sexes, or infinite populations.
Fisher was a highly productive theoreticianA who applied his formidable rhetorical skills to promoting a falsifiable theoryC of evolution. This theoryC holds that the population-genetics of natural populations fall into just the right regime to ensure that evolution can be understood as the short-term selective optimization of traits based on shifting the frequencies of available alleles with infinitesimal effects. The details of mutation are canceled out of the evolutionary equation. The researcher who understands this, Fisher (1930) says,
will direct his inquiries confidently toward a study of the selective agencies at work throughout the life history of the group in their native habitats, rather than to speculations on the possible causes which influence their mutations.
Evolutionary research today is not based on this theoryC. Evo-devo rejects Fisher’s position that it is fruitless to study the origin of phenotypic variants. Molecular evolutionists study mechanisms and patterns of mutation precisely because we know this helps us to understand evolution, e.g., Dettman, et al. 2016, Stoltzfus and McCandlish, 2017.
Basener and Sanford say that “we cannot overstate the essential role of new mutations”, but they lack a firm grasp of how our thinking has changed on this issue. This is not addressed by Joe either. To be fair, they are not trying to focus on this issue. They are focused on whether pure mathematical reasoning allows us to conclude in favor of Darwinism or against it, and I’m just trying to point out that we already know that Darwinism in the sense of Fisher’s theoryC is not correct, and we should be adjusting our thinking rather than having an abstruse debate about how far theoryA alone can take us.
But let’s quickly review what Joe is saying. His rebuttal focuses on the claim that theoretical evolutionary genetics is founded on FTNS. We could rebut this logically by showing that the allelic selection model, or the Hardy-Weinberg equilibrium, do not depend on assuming FTNS. Joe makes his argument historically: he lists various key innovations that appeared before the FTNS in 1930.
He states his conclusion in two ways. One statement is that “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”. I agree that “did not wait” and “did not rely on” are literally correct and not misleading. The FTNS just is not the basis of evolutionary theory, and it is not even the basis of theoretical population genetics considered narrowly.
However, his other conclusory statement is “the mathematics of mutation and natural selection had been well worked-out before R. A. Fisher published his 1930 book”. This implies that our current understanding of the role of mutation was well worked out before 1930, and this is not correct. All of these early theoreticalA works, and the main works of the Modern Synthesis in the next 4 decades, fail to achieve generality in covering the role of mutation in evolution, because they do not adequately cover the introduction process or provide a theory of mutation-limited dynamics. This lack of generality is not an accident, but a choice: it arises from a deliberate rejection of the non-Darwinian idea that the course of evolution might depend on the timing and character of events of mutation, i.e., the “lucky mutant” view or mutationism.
To understand the formal structure of this limitation, consider some statements from eminent evolutionary geneticists, e.g., 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 post-1969 (post-Synthesis) 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 the short-term evolution depicted in classical population genetics (“the dynamics of the relative frequency of a finite, fixed set of geneotypes”) and 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
All of these authors identify a traditional approach in which evolution is equated with sorting out initial variation, without new mutations; the alleles relevant to the outcome of evolution are present initially, and evolution is just a matter of shifting their frequencies.
Does the phrase “evolution is shifting gene frequencies” sound familiar? This is what it means. The original Modern Synthesis (OMS) theoryC held that all of evolution is understandable from the short-term process of shifting gene frequencies, i.e., macroevolution follows from microevolution.
The OMS does not say that new mutations don’t occur, just that that we don’t have to understand their dynamics to understand evolution: we can treat evolution as if the challenge to adapt is always addressed with available variation, on the grounds that natural species have a “gene pool” that “maintains” abundant infinitesimal variation in all traits. When the environment changes, selection crafts an adaptive response from this abundance. Dobzhansky, Stebbins, Mayr and others were so confident about this theoryC that they presented it as an established fact (see the supplement to this piece).
Yet, the OMS quickly proved inadequate. In the 1960s, patterns of molecular evolution demanded theories relating the rate of evolution directly to the rate of mutation. To address this need, origin-fixation models emerged in 1969; subsequently, they have grown into a major branch of theoryA with many applications (McCandlish and Stoltzfus, 2014). This is why I wrote recently that
the development and use of mathematical models reveals unambiguously that the OMS 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.
That is, we have rejected a major claim of generality from the OMS, a major theoryC. This is precisely what scientific progress is supposed to look like. However, establishing this point (which I’ve been writing about since 2001) has been an uphill battle against the efforts of false conservatives to turn the words “Modern Synthesis” into a moving target. The OMS clearly failed to predict and to explain patterns of molecular evolution uncovered in the 1960s. For 20 years, leading thinkers refused to admit that the theoryC had failed. The most they would admit is that the OMS holds for visible evolution but there may be an invisible “molecular level” where things may look different.
In the 1980s and 1990s, defenses of the “Modern Synthesis” began to shift. Rather than invoking the theoryC of Mayr, et al., or any falsifiable theoryC , defenders now defined the “Modern Synthesis” as an expandable framework of population genetics, or as an evolving research tradition. If Fisher influences Haldane, who influences Kimura, whose work is invoked in contemporary models, we can depict that as the culmination of a continuous research tradition going back to Fisher— without ever pointing out that (for instance) origin-fixation models used in molecular evolution today contradict Fisher’s theoryC.
Because of this kind of goal-post-shifting, historians gave up trying to define the Modern Synthesis as a theoryC, e.g., Smocovitis (p 43) writes that
by the late 1980s the notoriety of the evolutionary synthesis was recognized… So notorious did ’the synthesis’ become, that few serious historically minded analysts would touch the subject, let alone know where to begin to sort through the interpretive mess left behind by the numerous critics and commentators.
- The OMS is a theoryC based on extrapolation from (1) microevolution, the kind of short-term process of shifting gene frequencies seen in experimental populations of animals and plants, to (2) macroevolution, i.e., all of evolution.
- By the 1990s, mainstream evolutionary geneticists acknowledged that evolution cannot be understood solely in terms of microevolution as conceived in the OMS, because we have to model the dynamics of new mutations.
- The context to demarcate this major scientific advance is missing, because the OMS has been flushed down the memory hole and replaced with a slippery “Modern Synthesis”
Now, back to the FTNS. Fisher was trying to hit a home-run: to establish a theoryC with pencil and paper, by showing that the gradual increase in fitness is inevitable. The FTNS is only a part of this argument, as is clear from the treatment by Basener and Sanford, who are also trying to hit a home run, playing for the opposing team.
For a theoretician, to succeed at this game— to short-cut empirical science and reach grand conclusions from analytical arguments alone— is to execute a masterstroke. The early 20th century featured a loud and inconclusive debate about the role of different factors in evolution— Lamarckism, continuous shifts vs. discrete mutations, external selection vs. biased variation, and so on. Fisher stepped in and boldly declared that, once Mendelism is accepted, Darwinism is inevitable and all other views must be set aside. The smallest possible changes are the most likely. Internal factors influencing which mutations occur cannot influence the course of evolution because mutation rates are too small, therefore internal tendencies cannot be evolutionary factors.
Fisher’s masterstroke was a great success, giving Darwinism an air of logical inevitability.
Alas, it was wrong. The most likely changes in evolution are not the smallest possible changes, but changes of intermediate size. Biases in variation are a source of evolutionary tendencies.
Fisher was wrong on these points precisely due to his theoryC commitment to rejecting a role for new mutations. The result that intermediate changes are the most likely emerged when Kimura re-considered Fisher’s argument for infinitesimalism (Fisher’s geometric model) within a mutationist framework of evolution as an origin-fixation process (for explanation, see the end of this PDF). Fisher, Haldane and Wright reach the wrong conclusion about the possibility of variation-induced trends (orthogenesis) for the same reason. My colleagues and I have shown that mutational or developmental biases in the introduction of variation can cause evolutionary biases (see a recent blog). However, in a theoretical model where the alleles relevant to the outcome of evolution are assumed to be present initially, there is no introduction process, thus no chance for this kind of causation to operate.
This shows the importance of theoriesC in science. Without them, we can only interpret Fisher’s position as a technical error, which is, in fact, how Fisher’s position is treated today. One author writes that “Fisher erred here and his conclusion (although not his calculation) was flawed. Unfortunately, his error was only detected half a century later, by Motoo Kimura” (source). Yet, it is absurd to suggest that Fisher forgot to compute expectations for the mutationist view of evolution that he ridiculed and despised. Fisher’s original argument is correct and complete, given his theoryC that evolution can be understood adequately as a deterministic process of shifting frequencies of available alleles. The problem is that the theoryC is inadequate.