Getting beyond abstruse theorems to science

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 theoreticalworks, 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 theory, 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.

To summarize,

  • 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.

98 thoughts on “Getting beyond abstruse theorems to science

  1. OMagain: You just can’t quite bring yourself to complete the thought can you?

    So, yes, all of that. And then what?

    The designer steps in and makes the right mutation happen at the right time? Or is it all on a downward trend from the original perfection from the garden of eden? It’s like you’ve never even thought about your own position, you’ve concentrated so hard on attacking something you’ve never understoof.

    Also, can you think of a way that a random change in the genetic material that is highly detrimental to the organism, perhaps even fatal, that might limit the spread of that mutation in the gene pool?

    What are you talking about?
    You disagree with this comment without justification, again?
    OMGain! Please tell us all that you have more up your sleeve than an unsubstantiated belief of yours.
    People are watching… Don’t disappoint them!
    Joe? Can you help your brother? He is confused, OmniMegaagain…

  2. Could we say, as an approximation, that most molecular change is drift, and most adaptive change is maintained by selection?

  3. petrushka:
    Could we say, as an approximation, that most molecular change is drift, and most adaptive change is maintained by selection?

    Anything can be said… proving it is a problem unless you are Joe F….
    He has all the experimental evidence… and more along with arlin the new kid on the block that has gone beyond the speculative ‘science of population genetics….

  4. petrushka:
    Could we say, as an approximation, that most molecular change is drift, and most adaptive change is maintained by selection?

    The slight confusion, though, is that drift is limited by negative (purifying) selection. (Adaptive change would be under positive selection.)

  5. J-Mac: OK. Why is it unreasonable to expect the perfections from this process?
    What would you change to make it perfect? No errors..

    Let’s say, just hypothetically, that some past lineages approximated perfect, error-free replication. If so, that lineage would stop evolving, and lose the arms race to organisms all around them who continue to improve their arms.

    The dynamic, then, would be that what would evolve most successfully would be an ideal non-zero error rate. Too much error, the organisms don’t survive; too little, they don’t evolve. And this ideal error rate would be determined by trial and error, like everything else in biology.

  6. J-Mac: Joe? Can you help your brother? He is confused,

    Why? It’s clear to all but J-Mac that J-Mac doesn’t understand this topic. J-Mac is saying, in effect, that we need to explain why a typographical error leads to a word being misspelled.

  7. Joe Felsenstein: Why?It’s clear to all but J-Mac that J-Mac doesn’t understand this topic.J-Mac is saying, in effect, that we need to explain why a typographical error leads to a word being misspelled.

    What are you talking about Joe?

    I was hoping you’d help OMagain with the clarification of my comment that contained this statement about the power of mutations:

    In a sense, it is a destructive force, making random changes in the genetic material. In any highly adapted organism such changes are overwhelmingly likely to be detrimental. The usual analogies we make in such cases involve making random adjustments in a finely constructed watch, or making random alterations of a carefully-written poem. While one will occasionally improve the timing of the watch or the effectiveness of the poem by random changes, with much greater probability one will make things worse..

  8. Hi Joe

    Glad to see you are still around.

    I read through Arlin’s critique and I attempted my own historical summary of FSNL and OMS as best I could and in terms I best understood… admitedly limited and most incomplete.

    I am no Stephen Jay Gould in writing skill nor academic insight…

    … but for the life of me I cannot penetrate Arlin’s logic.

    TheoryC vs TheoryH ?!?!

    Gimme a break. OK… there was phenomena and genetics Darwin did not know, ditto the modern synthesizers, particularly at a molecular level.

    Does that vindicate a TheoryC vs TheoryH distinction?

    I am still scratching my head over that one.

    What am I missing?

  9. J-Mac: I was hoping you’d help OMagain with the clarification of my comment that contained this statement about the power of mutations:

    And I was hoping you’d step in and explain how your “position” avoids the issue.

    J-Mac: In a sense, it is a destructive force, making random changes in the genetic material. In any highly adapted organism such changes are overwhelmingly likely to be detrimental. The usual analogies we make in such cases involve making random adjustments in a finely constructed watch, or making random alterations of a carefully-written poem. While one will occasionally improve the timing of the watch or the effectiveness of the poem by random changes, with much greater probability one will make things worse.

    So, given all that, the onus is on you to explain why mutational meltdown has not been observed. For example, why are bacteria continually able to evolve resistance to antibiotics if all mutations make things worse?

    J-Mac: People are watching… Don’t disappoint them!

    Those people can clearly see that your argument, such as it is, is a purely negative one.

  10. J-Mac: While one will occasionally improve the timing of the watch or the effectiveness of the poem by random changes, with much greater probability one will make things worse..

    Out of interest, would a watch that performed it’s job with more accuracy, even if it was made more accurate by a mistake, then other watches be favoured when people are deciding what type of watch to make next? Would such a watch take over the population of watches due to its increased desirability? Over time would we observe that watches are becoming more accurate?

    Is anybody still using sand clocks for reasons other then aesthetics?

  11. J-Mac: Just because you are an narcissistic ass who responds before reading the comments?

    Psychological projection is a defense mechanism people subconsciously employ in order to cope with difficult feelings or emotions. Psychological projection involves projecting undesirable feelings or emotions onto someone else, rather than admitting to or dealing with the unwanted feelings.

  12. J-Mac: What are you talking about Joe?

    My bad. I was actually reacting to J-Mac’s utterly ludicrous statement that:

    J-Mac: I agree…So, the real question should be ‘why we have replication errors’ leading to mutations? Right Joe?

    … which is rather like asking why, if there is a typographical error, there is a misspelling.

  13. Joe Felsenstein: My bad.I was actually reacting to J-Mac’s utterly ludicrous statement that:

    … which is rather like asking why, if there is a typographical error, there is a misspelling.

    Hi Joe: how narcicistic of you to correct J-Mac so decisvively

    Perhaps you are mistaken because you are restricting your thought processes to classical mathematics and thereby ignoring the quantum tunnelling effect J-Mac was obviously alluding to.

  14. TomMueller: Hi Joe: how narcicistic of you to correct J-Mac so decisvively

    Perhaps you are mistaken because you are restricting your thought processes to classical mathematics and thereby ignoring the quantum tunnelling effect J-Mac was obviously alluding to.

    You obviously have no idea what quantum tunnelling is…
    Isn’t everything, including life, on subatomic level, dependent on or based on quantum mechanics?

  15. OMagain: And I was hoping you’d step in and explain how your “position” avoids the issue.

    So, given all that, the onus is on you to explain why mutational meltdown has not been observed. For example, why are bacteria continually able to evolve resistance to antibiotics if all mutations make things worse?

    Those people can clearly see that your argument, such as it is, is a purely negative one.

    I’m sorry OMGain, but I don’t think Joe Felsenstein understands the issue regarding mutations being a destructive force..
    If he did, he obviously would have saved you by now…

  16. J-Mac: Isn’t everything, including life, on subatomic level, dependent on or based on quantum mechanics?

    Are you asking a question or making a statement?

  17. OMagain: Are you asking a question or making a statement?

    You don’t know what question mark is for?
    I’m talking to Tom… He should know what I’m talking about…

  18. I’m surprised how quiet Joe Felsenstein had been on this OP… Arelin, another speculative scientist, attacked another speculative scientist (Joe F) and I guess when that happens, in the real science world, it is just as good as experimental evidence, or more…

  19. @J-Mac

    Yes, I recall our earlier discussion in regard to the quantum dynamics of a potato sitting on the kitchen counter

    You should get a life

  20. arlin,

    I haven’t commented yet on the substance of your post.

    On the issue of whether we need to call the current version of the modern synthesis a “new” synthesis, I tend to think that we should stick with calling it the modern synthesis rather than declare new replacements, especially since there is a long line of people, each waiting to declare a new synthesis to replace that of the person ahead of them in line. So I would say to each of them, be careful what you wish for.

    As to whether the happenstance of directions of mutations has an effect, yes, it must. As to whether we can say that this revives the 1800s mechanism of orthogenesis, I doubt that it can. Orthogenesis attributed long-term trends to an inherent directive force that was intrinsic to the organism, and it rejected the idea that natural selection could change that. In their view, dinosaurs got bigger because of this directive force, and then went extinct when it made them too big to survive. I don’t think that your view is close to that.

    More on waiting-for-mutation in the next comment …

  21. arlin,

    Some thoughts on waiting for mutation.

    1. Imagine a large population in which an allele can occur by mutation with probability \mu, and would be deleterious with selection coefficient s_0 against it. There would in the long term be a frequency \mu / s_0 of that allele in the population.

    2. Now imagine that environment changes and the allele is now advantageous with selection coefficient s. There are is a frequancy of \mu brand copies of the mutation each generation. So if one of the copies succeeds in rising to fixation, the probability that is one of the brand-new ones is \mu / (\mu + \mu/s_0), which is s_0/(1+s_0). Thus if s_0 = 0.01, only 0.01/1.01 of the time will the mutant that succeeds be a brand new one.

    3. So in that sense, we are mostly not “waiting for mutations”, unless the populations are small. However that leaves your point about the potential influence of the pattern of mutations intact, because if there are two possible mutant alleles that are equally good at responding to that environmental change, and they have mutation rates \mu_1 and \mu_2, and are equally fit after the environmental change, then the probabilties of each being fixed are in proportions \mu_1 : \mu_2.

    I have a feeling that this may be somewhere in this paper (I do not remember):

    McCandlish, D. M., and A. Stoltzfus. 2014. Modeling Evolution using the Probability of Fixation: History and Implications. Quarterly Review of Biology 89(3):225-52.

  22. J-Mac: OK. Why is it unreasonable to expect the perfections from this process?
    What would you change to make it perfect? No errors..

    I don’t know why expecting perfection could be reasonable. I can’t think of anything in nature that IS perfect. I see no way to make this error-free.

    sean s.

  23. Joe Felsenstein:
    arlin,

    As to whether the happenstance of directions of mutations has an effect, yes, it must.As to whether we can say that this revives the 1800s mechanism of orthogenesis, I doubt that it can.Orthogenesis attributed long-term trends to an inherent directive force that was intrinsic to the organism, and it rejected the idea that natural selection could change that.In their view, dinosaurs got bigger because of this directive force, and then went extinct when it made them too big to survive.I don’t think that your view is close to that.

    More on waiting-for-mutation in the next comment …

    Joe

    What am I missing?

    Why is anybody having this conversation after the Luria–Delbrück experiment (1943) ?

  24. Moved a comment to guano. Please address the content, not the author of the content.

    All other things taken equally, J-Mac’s comments on quantum-tunneling were, if I recall correctly, proposed as an explanation for mutations. Nothing that esoteric is required. Ordinary chemical behavior at the atomic or molecular levels suffice. Quantum effects may be invoked also (to explain behavior at the atomic level), but the “mystery” of mutation is exaggerated.

    sean s.

  25. Joe Felsenstein:
    On the issue of whether we need to call the current version of the modern synthesis a “new” synthesis, I tend to think that we should stick with calling it the modern synthesis rather than declare new replacements, especially since there is a long line of people, …

    Ha. Obviously you haven’t read the article I was referencing. I’m calling bull**** on the synthesis narrative.

    As to whether the happenstance of directions of mutations has an effect, yes, it must. As to whether we can say that this revives the 1800s mechanism of orthogenesis, I doubt that it can.Orthogenesis attributed long-term trends to an inherent directive force that was intrinsic to the organism, and it rejected the idea that natural selection could change that.In their view, dinosaurs got bigger because of this directive force, and then went extinct when it made them too big to survive.I don’t think that your view is close to that.

    Fisher, Haldane, and Wright argued that mutation could not be influential in causing a tendency in evolution, because this would require extraordinarily high mutation rates. Provine (1978. The role of mathematical population geneticists in the evolutionary synthesis of the 1930s and 1940s. Stud Hist Biol. 2:167-192) identifies this specific argument as one of the influential theoretical arguments for establishing the OMS, because it seemed to eliminate the possibility that directions of evolution could have internal causes.

    In 2001, I showed theoretically why this argument is mistaken. If the introduction process is taken into account, then biases in introduction can impose biases on evolution. When Joe says “yes, it must”, this is his way of giving me credit for my novel contribution to population genetics theory. It’s common for theoreticians to say that something is obvious once you have provided a demonstration. Last year another eminent theoretician told me this is obvious after I spent about 90 minutes explaining it– after all, he didn’t think of it first. So, receiving credit in this grudging way is considered a great compliment. Thanks, Joe!

    Now, let’s talk about the strawman of orthogenesis. Within the Synthesis, it’s a thing for people to repeat campfire stories about how all the alternatives are bat**** crazy ideas. This enforces the Synthesis doctrine that There Is No Alternative. In the article cited above, Futuyma repeats the no-one-believed-in-selection-during-the-eclipse campfire story and gets taken down hard for that. The campfire story that Synthies tell each other about orthogenesis is that it is an appeal to magic, to occult forces, because they have never read primary sources such as Eimer, who wrote that

    In my view development can take place in only a few directions because the constitution, the material composition of the body, necessarily determines such directions and prevents indiscriminate modification. (p. 22 of Eimer, 1898. On Orthogenesis. Chicago: Open Court Publishing Co)

    Obviously, Fisher, Haldane and Wright were not trying to argue against mystical inner directions when they put forth the argument against the efficacy of mutation pressure as a source of direction. Provine identifies this as an important argument because it addresses a serious idea that many people thought must be true: if the variational inputs to evolution are biased, then surely the outputs will be biased. But Fisher, Haldane and Wright said no, that is not how it works because mutation is a weak pressure easily overcome by selection. The argument was repeated for generations.

    Again, we have the opportunity to mark a scientific milestone here. Something is known that was not known before.

  26. Joe Felsenstein:
    [idea for effect of mutation bias mediated by standing variation]
    I have a feeling that this may be somewhere in this paper (I do not remember):

    McCandlish, D. M., and A. Stoltzfus. 2014. Modeling Evolution using the Probability of Fixation: History and Implications. Quarterly Review of Biology 89(3):225-52.

    The idea here is that we can make a model of adaptation from standing variation where there is an effect of mutation bias, because the frequency in standing variation reflects the input mutation rate. In a narrow regime, it will be a proportional effect, like the effect of biases in the introduction process in the origin-fixation regime. This is a way of separating the issue of whether mutational biases are influential, from the issue of whether they are influential due to the introduction process.

    That is funny you should suggest this. It was not in our paper, but we definitely discussed this kind of model privately, building on Orr & Betancourt, 2002. My co-author did not want to speculate on this so we left it out.

    In general, we think it is an important direction for theoretical work to consider how biases in variation might be influential outside of the strict origin-fixation regime, which is narrow.

  27. arlin: In 2001, I showed theoretically why this argument is mistaken. If the introduction process is taken into account, then biases in introduction can impose biases on evolution. When Joe says “yes, it must”, this is his way of giving me credit for my novel contribution to population genetics theory.

    I will freely acknowledge that you have done a great service by pointing to the effects of mutational biases. Yes, I was generally not thinking of them before you and McCandlish pointed to them and worked on them.

    arlin: In my view development can take place in only a few directions because the constitution, the material composition of the body, necessarily determines such directions and prevents indiscriminate modification. (p. 22 of Eimer, 1898. On Orthogenesis. Chicago: Open Court Publishing Co)

    Have I misunderstood orthogenesis? I thought that it went far beyond simply arguing that there were constraints in evolution — that it argued that these constraints overpowered natural selection. Whereas since the Modern Synthesis evolutionary biologists have thought of natural selection as optimizing (at least, approximately optimizing) within those parts of the phenotype space allowed by the constraints. I don’t think that orthogenesists thought that way.

    Peter Bowler in The Eclipse of Darwinism:

    The real distinguishing feature of orthogenesis was the claim that the internal factor in evolution was an orderly one producing linear developments over vast periods of time. (p. 146)

    Bowler does mention that later supporters of orthogenesis equated it to the tendency of variation to occur mostly in particular directions (see the bottom of page 147 in Bowler, Eclipse). But the earlier supporters tended to see it as teleological.

  28. When we are talking about a mutational bias, what are we talking about specifically? I can think of many ways mutations can be biased. From being biased towars so-called “hotspots” in the genome, to being biased towards transitions over transversions, duplications over deletions etc. etc.

    Is it “all of the above”?

    In any case, in what way should we think such biases cause “direction” in evolution? Can you elaborate on these points Arlin?

  29. Joe Felsenstein: Have I misunderstood orthogenesis? I thought that it went far beyond simply arguing that there were constraints in evolution — that it argued that these constraints overpowered natural selection. Whereas since the Modern Synthesis evolutionary biologists have thought of natural selection as optimizing (at least, approximately optimizing) within those parts of the phenotype space allowed by the constraints. I don’t think that orthogenesists thought that way.

    If you take the silliest or most extreme versions, then yes, othogenesis goes way beyond simply arguing for developmental constraints. However, the basic concept of “orthogenesis” vs. “ambigenesis” is that developmental modification tends to go in one direction rather than in every direction. The review by Popov, 2009 is terribly written but at least it has abundant primary sources.

    The concept of “overpowering natural selection” is not a simple issue. For instance, Eimer says that

    No absolutely injurious character could in the nature of the case continue to exist, but neither could natural selection, which Weismann assumes to be the only determining factor in transformation, have any efficacy unless something previously existed which from being already useful could be taken hold of by natural selection and so made to serve its purposes.

    You don’t have to allow “overpowering natural selection” to allow for a trend that is not per se adaptive. Think of the classic explanation for the Irish elk’s antlers. We get a trend that would be maladaptive if considered by itself, but selection doesn’t consider this by itself.

    It is certainly an implication both of orthogenesis and of biases in the introduction of variation that there can be trends in evolution that would be maladaptive in a hypothetical sense, compared to some hypothetical alternative trend. But this is not the same thing as going against selection, because selection is entirely local. For instance, if there is a bias toward AT rather than GC, and all evolutionary changes happen via selective fixations, then we can imagine a genome constantly evolving by locally beneficial AT mutations, even if the organism would be better off (in some hypothetical scenario) having a more GC rich genome. The “better off” in this case is merely hypothetical. It is not actually a matter of mutation overcoming selection, but a mutational trend prevailing over a hypothetical if-other-things-were-equal-but-they-aren’t adaptive difference.

  30. arlin,

    An interesting paper arguing for a bias-induced trend in a quantitative trait-space is by Julian Xue and colleagues. Here they are considering a very abstract trait like complexity. There might be a general mutational bias toward increased complexity. Then they create a problem where each change that increases or decreases complexity also has a randomly drawn effect on some trait linked to fitness. But because complexity-increasing traits are more mutationally like, complexity-increasing traits that happen to be beneficial are also more likely.

    I wish someone would just re-do this paper in a more familiar framework that quantitative geneticists would find respectable. In the current state, this work is being ignored.

  31. arlin: An interesting paper arguing for a bias-induced trend in a quantitative trait-space is by Julian Xue and colleagues. Here they are considering a very abstract trait like complexity. There might be a general mutational bias toward increased complexity. Then they create a problem where each change that increases or decreases complexity also has a randomly drawn effect on some trait linked to fitness. But because complexity-increasing traits are more mutationally like, complexity-increasing traits that happen to be beneficial are also more likely.

    That’s interesting. Completely antithesis to the usual talking points of creationists of course.

  32. Found the other citation from Soren Lovtrup (about Fisher), as I was cleaning up my office. It’s S. Lovtrup, “Semantics, Logic and Vulgate Neo-Darwinism,” Evolutionary Theory 4 (July 1979):157-172; p. 167:

    “I shall make the following comments: (1) Once more, Fisher (1930) demonstrated nothing, he made some calculations…”

    (“Demonstrated” in this quote should be in italics, but I’m too stupid to figure out how to make italics on this site.) Earlier in the same paper, Lovtrup said, re Fisher (1930):

    “I cannot help commenting on Fisher’s claim that it can be ‘rigorously demonstrated’ that a process of evolution will take place, leading to ‘more perfect adaptation’. Here we witness the confusion arising when the theoretician fails to distinguish between abstract symbols and biological reality. I believe that even today we are still missing the ‘rigorous demonstration’ that the process imagined by Darwin and Fisher has ever taken place, at least if it is supposed to involve an evolutionarily significant transformation, accomplished through the accumulation of many micromutations” (p. 162).

  33. Thank you Paul. I see you are also a fan of the methods of Arch-charlatan Henry Morris and his turgid screed That their words may be used against them.

    Of course, it was Morris who seems to have fathered the doctrine in so-called “scientific creationism” that when reality and doctrine differ, reality is wrong and doctrine is right.

    But don’t take my word for it:
    “…the main reason for insisting on the universal Flood as a fact of history and as the primary vehicle for geological interpretation is that God’s Word plainly teaches it! No geologic difficulties, real or imagined, can be allowed to take precedence over the clear statements and necessary inferences of Scripture.”
    – Henry Morris, Biblical Cosmology & Modern Science, pp 32-33 (1970)

    So, essentially, the modern creationist movement is founded on the principle of belief over fact. The real world be damned, we MUST find some way to either square the facts with our creationist beliefs, if not outright ignore them.

  34. I have to ask a question: suppose (hypothetically) that Fisher had never published his paper (in 1930). How would the study of genetic mutation and evolution be different today? After all, DNA was not identified as the physical manifestation of genetics until 20 years later; and I’d hope most of what we know about mutation, genetic change, and their roles in evolution, is based principally on our study of DNA. Abstract theories can supplement actual observation, but they cannot replace it.

    Given that the paper was published before DNA’s role in genetics was established, why does it matter anymore?

    I am no creationist, and being a non-technician; this does seem like a tempest in a tea cup. Can someone clarify the significance to me? I’m sure I’m missing something. or not well-enough informed.

    sean s.

  35. arlin: For instance, if there is a bias toward AT rather than GC, and all evolutionary changes happen via selective fixations, then we can imagine a genome constantly evolving by locally beneficial AT mutations, even if the organism would be better off (in some hypothetical scenario) having a more GC rich genome. The “better off” in this case is merely hypothetical. It is not actually a matter of mutation overcoming selection, but a mutational trend prevailing over a hypothetical if-other-things-were-equal-but-they-aren’t adaptive difference.

    Necessity of Quantum Coherence to Account for the Spectrum of Time-Dependent Mutations Exhibited by Bacteriophage T4

    Transcriptase measurements of quantum expectations due to time-dependent coherent states populating informational DNA base-pair sites, designated by G–C → *G–*C, G–C → G′–C′, and A–T → *A–*T, provide a model for transcription and replication of time-dependent DNA lesions exhibited by bacteriophage T4. Coherent states are introduced as consequences of hydrogen bond arrangement, keto-amino → enol-imine, where product protons are shared between two sets of indistinguishable electron lone-pairs and thus participate in coupled quantum oscillations at frequencies of ~1013 s−1. The transcriptase deciphers and executes genetic specificity instructions by implementing measurements on superposition proton states at *G–*C, G′–C′, and *A–*T sites in an interval Δt ≪ 10−13 s. Decohered states participate in Topal–Fresco replication, which introduces substitutions *C → T, *G → A, G′ → T, and G′ → C, but superposition *A–*T states are deleted. These results imply an evolutionary shift favoring A–T richness.

  36. sean samis:
    I have to ask a question: suppose (hypothetically) that Fisher had never published his paper (in 1930). How would the study of genetic mutation and evolution be different today? After all, DNA was not identified as the physical manifestation of genetics until 20 years later; and I’d hope most of what we know about mutation, genetic change, and their roles in evolution, is based principally on our study of DNA. Abstract theories can supplement actual observation, but they cannot replace it.

    Mutation was known starting soon after 1900, even if its molecular basis was not. For example, in the late 1920s H.J. Muller and others showed that radiation could induce mutations. The papers I cited in a post preceding this one worked out the population genetics of natural selection and mutation. They did this before 1930.

    Given that the paper was published before DNA’s role in genetics was established, why does it matter anymore?

    I am no creationist, and being a non-technician; this does seem like a tempest in a tea cup. Can someone clarify the significance to me? I’m sure I’m missing something. or not well-enough informed.

    It matters if it were true that Fisher’s Fundamental Theorem is the only foundation of modern theoretical population genetics, and one can somehow invalidate it.

    Actually, the FTNS is not the basis for most modern work on the mathematics of natural selection and mutation. So it’s important to point that out.

    The work since 1953 has mostly led to consideration of a broader range of models of mutation and natural selection.

  37. Joe Felsenstein:

    It matters if it were true that Fisher’s Fundamental Theorem is the only foundation of modern theoretical population genetics, and one can somehow invalidate it.

    Actually, the FTNS is not the basis for most modern work on the mathematics of natural selection and mutation.So it’s important to point that out.

    Joe,

    I read your comment as boiling down to “it doesn’t actually matter” since Fisher’s theorem, “is not the basis for most modern work on the mathematics of natural selection and mutation.”

    Correct? My instinct, after reading the OP was to wonder why anyone cares. Historically interesting, but otherwise not so much. It’s like getting excited about contemporary airline safety based on the construction of a Jenny.

    sean s.

  38. sean samis: I have to ask a question: suppose (hypothetically) that Fisher had never published his paper (in 1930). How would the study of genetic mutation and evolution be different today? After all, DNA was not identified as the physical manifestation of genetics until 20 years later; and I’d hope most of what we know about mutation, genetic change, and their roles in evolution, is based principally on our study of DNA. Abstract theories can supplement actual observation, but they cannot replace it.

    Fisher wasn’t that important for the development of genetical concepts. A theory of genetics was developed early in the century, before DNA, based on the tools available to observe the results of hereditary phenomena. Before we knew about the molecular details of DNA, genes and mutations, there was a set of basic concepts based on what you can see and infer from classical genetics, from breeding experiments with pedigrees and measured phenotypes. We can map differences to a point on a chromosome. That’s what “locus” means. There can be different hereditary states at this locus. Those are “alleles”.   One allelic state can mutate into another state. This is how Fisher, Haldane and Wright understood genetics.

    Eventually, these concepts were re-imagined in molecular terms. A locus is a map interval on a chromosome. An allele is a specific sequence for that locus. A mutation changes one allele into another allele by changing one sequence into another sequence.

    Fisher had nothing to do with this.

  39. arlin,

    Between your comments and Joe’s, I’m satisfied that this is much ado about nothing. Creationists finding flaws in old theories and imputing them into current scientific understanding.

    sean s.

  40. OMagain: destructive

    OMgain.

    OMagain: J-Mac: In a sense, it is a destructive force, making random changes in the genetic material. In any highly adapted organism such changes are overwhelmingly likely to be detrimental. The usual analogies we make in such cases involve making random adjustments in a finely constructed watch, or making random alterations of a carefully-written poem. While one will occasionally improve the timing of the watch or the effectiveness of the poem by random changes, with much greater probability one will make things worse.
    You just can’t quite bring yourself to complete the thought can you?
    So, yes, all of that. And then what?
    The designer steps in and makes the right mutation happen at the right time? Or is it all on a downward trend from the original perfection from the garden of eden? It’s like you’ve never even thought about your own position, you’ve concentrated so hard on attacking something you’ve never understoof.
    Also, can you think of a way that a random change in the genetic material that is highly detrimental to the organism, perhaps even fatal, that might limit the spread of that mutation in the gene pool?

    OMgain, my entire comment is a quote from Joe Felsenstein book….so you obviously see the problem here..
    Now, can you explain why you disagree with world’s renown population geneticist on his statement on the destructive power of mutations?
    The way I see it, you disagree with anything people like me write without thinking about it…You obviously see and understand my concern why you would such a thing…
    I tried to warn you several times and I have asked Joe to help you out but no response from him…
    If your faith is built on authority like Joe F, you certainly have proved that your faith is blind…How else can you explain your disagreement with my comment that was a quote of Joe F unless that is true?
    If you hate God and people who try to defend his works you have just proven that…

  41. J-Mac: Now, can you explain why you disagree with world’s renown population geneticist on his statement on the destructive power of mutations?

    It’s “a world renowned” by the way.

    But let’s deal with this. This comment is where you quote Joe. Note the lack of a blockquote.

    You post that quote in response to a question from me:

    OMagain: Even if that’s the case in what way does it support your contention that mutations happen under conscious direction?

    For context here is your response:

    J-Mac: Mutations should not happen..

    In a sense, it is a destructive force, making random changes in the genetic material. In any highly adapted organism such changes are overwhelmingly likely to be detrimental. The usual analogies we make in such cases involve making random adjustments in a finely constructed watch, or making random alterations of a carefully-written poem. While one will occasionally improve the timing of the watch or the effectiveness of the poem by random changes, with much greater probability one will make things worse.

    So it appears to me that the answer to my question is: mutations should kill us but they don’t therefore ID?

    Is that about right?

    J-Mac: How else can you explain your disagreement with my comment that was a quote of Joe F unless that is true?

    It is the case that most random changes will be negative. Perhaps you can quote me where I disagree with that? But to concentrate on only that aspect is to miss an important piece of the puzzle – selection.

    So it seems what I’m really asking you is in your mind is the role of “selection” replaced by an Intelligent Designer?

    If mutations are are harmful, why are there still bacteria? Does your designer step in to prevent mutational meltdown?

    J-Mac: If you hate God and people who try to defend his works you have just proven that…

    Actually if there is a god then I’m sure it’ll be displeased at your defense of ignorance over knowledge.

    J-Mac: The way I see it, you disagree with anything people like me write without thinking about it

    It’s rare that people like you actually say anything that can be disagreed with. Perhaps if you were to answer the questions in this post then that might be something that can be disagreed with, if you actually take a position on how your designer stops mutational meltdown.

  42. J-Mac: If you hate God and people who try to defend his works you have just proven that…

    Out of interest, what “work” is it you think you are defending here? Be specific, if such is possible for you.

  43. arlin: The idea here is that we can make a model of adaptation from standing variation where there is an effect of mutation bias, because the frequency in standing variation reflects the input mutation rate. In a narrow regime, it will be a proportional effect, like the effect of biases in the introduction process in the origin-fixation regime. This is a way of separating the issue of whether mutational biases are influential, from the issue of whether they are influential due to the introduction process.

    I want to mention why I say “narrow regime” here. If you are ever seriously considering invoking a frequency in mutation-selection balance, e.g., f = u/s for semi-dominant, then you are by definition outside of the regime where stochastic effects are important, and instead you are in a regime where the more fit allele wins every time. You have to imagine the kind of case where the allele favored 3-fold by a higher rate of mutational origin has an expected number of 9, and the less favored allele an expected number of 3. If the numbers are 5-fold higher than this, then both alleles have escaped stochastic loss and the problem is quasi-deterministic (best allele wins regardless of starting frequency). If the numbers are just 5-fold lower, then we are no longer talking about standing variation– we are back to something like an origin-fixation problem.

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