A bit about non-obviousness and theories

It has been said that the reception of any successful new scientific hypothesis goes through three predictable phases before being accepted. First, it is criticized for being untrue. Secondly, after supporting evidence accumulates, it is stated that it may be true, but it is not particularly relevant. Thirdly, after it has clearly influenced the field, it is admitted to be true and relevant, but the same critics assert that the idea was not original

Zihlman, A.L., Pygmy chimps, people, and the pundits. New Scientist 104, 39–40 (1984).

A model of inventiveness for theories

The dismissal-resistance-appropriation pattern called the “stages of truth” has been noted for well over a century (Shallit, 2005). Zihlman’s reference to “the same critics” suggests that the attempt to appropriate a new idea for tradition overlaps with, or closely follows, the stage of active resistance. This blog about appropriation uses recent examples to illustrate how pundits normalize or domesticate new results, claiming them for tradition. These examples indicate that the gatekeepers who challenge the validity and importance of a new idea are also the same people who attack its originality, both by selective quote-mining, and by mashing up new ideas with older ideas, so as to make the new ideas seem more incremental.

This presents a dual challenge to scientists attempting to advance knowledge via new theories, who face both (1) the ordinary scientific challenge of communicating the new idea and arguing for its importance and plausibility, and (2) the struggle to distinguish the new idea and defend its novelty against the work of gatekeepers. A new idea will not get the attention it deserves if gatekeepers are successful in convincing everyone that the idea is not new.

Although I knew from the beginning that we would face this dual challenge over the theory of arrival biases, the naked brutality of the appropriation process continues to stun me. The first shock was Lynch’s (2007) ridiculously bad take “The notion that mutation pressure can be a driving force in evolution is not new” (explained here) citing Charles Darwin, ourselves, and about a half-dozen others, none of whom proposed the same theory. The first major commentary on mutation-biased adaptation by someone not directly involved came out in TREE in 2019: it was a shameful hit-piece that misrepresented the theory and the empirical case, and offered multiple attempts at appropriation— the theory is merely part of the neutral theory, it comes from Haldane and Fisher, it is nothing more than contingency, it is the traditional view, etc (when I say “shameful hit piece”, I mean that TREE cooked up a highly negative piece without getting feedback from the people whose work was targeted, and when we objected to the garbage they published, we were not given space for a rebuttal).

Apparently I did not learn from these experiences, because I was once again dumbstruck when Cano, et al. (2022) came out, showing an effect of mutation-biased adaptation predicted from theory, and one press release presented this work literally as “helping to return Darwin’s second scenario to its rightful place in evolutionary theory” as if the main idea came from Darwin.

However, my focus here is not on this process of appropriation or theft, but on what makes a theory new, and how to evaluate newness. The starting point is simply that something is profoundly wrong with suggesting that a population-genetic theory of arrival biases— proposing a specific linkage between tendencies of variation and predictable tendencies of evolution— is not new, when the theory appeared only in 2001 and is still unknown to most evolutionary biologists. You won’t find it in your textbook or in the Oxford Encyclopedia of Evolution, or in the canonical texts of the Modern Synthesis, or in the archives of classical population genetics.

Clearly we need some different way to think about scientific novelty beyond “whatever I can link to tradition via vague statements of dead authorities is not new.”

Here I’m going to use the patent process as an example. Patenting an invention and proposing a theory are two different things, but the comparison is useful in my opinion. The law is often where philosophy meets practice: where abstract principles become the basis for adjudicating concrete issues between disputing parties— with life, liberty and treasure at stake.

Patent law instantiates a theory of novelty, and it hinges on non-obviousness. Under US patent law, a successful patent application shows that an invention meets the 4 criteria of eligibility (patentability), newness, usefulness, and non-obviousness. Eligibility is mostly about whether the proposed invention is a manufacturing process, rather than something non-patentable. I will set aside that criterion as irrelevant for our purposes. I will address usefulness in a moment. An invention is new if it is not found in prior art. In patent law, prior art is defined in a very permissive way, to include any prior representation, whether or not it was ever manufactured or made public, whereas in science, we might want to restrict the scope of prior art to widely available published knowledge.

Thus, newness is easy to understand: make one small improvement on prior art, and that is considered new under patent law. But improvement or newness is not enough. In order to be patentable, a new and useful invention must be a non-obvious improvement— non-obvious to a practitioner or knowledgeable expert. In the patent law for some other countries (e.g., Netherlands), the latter two criteria are sometimes combined by saying that the invention must be inventive, meaning both new and non-obvious. An example of an obvious improvement would be to take a welding process widely used with airframes and apply it to bicycle frames.

The most distinctive (i.e., potentially non-obvious) aspects of the theory from Yampolsky and Stoltzfus (2001) are that (1) it focuses on the introduction process (the transient of an allele frequency as it departs from zero) as a causal process that leads to distinct rules that clash with the classic conception of population-genetic causes as mass-action forces shifting frequencies of pre-existing alleles; (2) it links tendencies of evolution to tendencies of variation without requiring neutrality or high mutation rates, in conflict with the mutation-pressure theory of Haldane and Fisher; and (3) it purports to unite disparate phenomena including effects of mutation bias, developmental bias, and the findability of intrinsically likely forms.

The non-obviousness of a pop-gen theory of arrival biases

Thus, as outlined above, we may consider this theory as a useful and possibly non-obvious improvement on the prior art of Haldane and Fisher.[1] Is it non-obvious relative to all prior art? Because we are asking about the prior non-obviousness, this is a somewhat hypothetical question that must be guided by our understanding of history. Would the theory have been non-obvious before 2001? What was the state of the art (in theoretical population genetics) bearing on the question of internal variational biases as possible causes of directionality or trends in evolution?

Just because something is obvious does not mean it will be proposed. An idea could be obvious but no one writes it down because no one cares enough to do so. Indeed, a big problem here is that, typically, the people with the population-genetics expertise are not the same people as the developmentalists and paleontologists searching for internal causes. Population geneticists are obsessed with selection, Fisher, selection, standing variation and selection. We could search through stacks of population genetics papers without finding out what anyone thinks about generative biases. I never tire of pointing out that Edwards (1977) is a book about theoretical population genetics, with hundreds of equations, and it does not have a mutation rate anywhere.

We could solve this problem with a time machine: go back into the 20th century, and get some theoreticians together with internalists to see if they could combine the classic idea of internal variational biases with population genetics. For instance, we could go back to the 1980s and get together some population geneticists with those early evo-devo pioneers like Pere Alberch literally calling for attention to developmental biases in the introduction of variation. Maybe we could add some philosophers of science.

In fact, we do not need a time machine, because this meeting of the minds actually happened, with results recorded in the scientific literature. In the late 1970s and early 1980s, Gould, Alberch and others began to suggest some kind of important evolutionary role for developmental “constraints” that might was not included in traditional thinking. I will quote from the wikipedia page on this:

Similar thinking [about generative biases acting prior to selection] featured in the emergence of evo-devo, e.g., Alberch (1980) suggests that “in evolution, selection may decide the winner of a given game but development non-randomly defines the players” (p. 665)[23] (see also [24]). Thomson (1985), [25] reviewing multiple volumes addressing the new developmentalist thinking— a book by Raff and Kaufman (1983) [26] and conference volumes edited by Bonner (1982) [27]  and Goodwin, et al (1983) [28] — wrote that “The whole thrust of the developmentalist approach to evolution is to explore the possibility that asymmetries in the introduction of variation at the focal level of individual phenotypes, arising from the inherent properties of developing systems, constitutes a powerful source of causation in evolutionary change” (p. 222). Likewise, the paleontologists Elisabeth Vrba and Niles Eldredge summarized this new developmentalist thinking by saying that “bias in the introduction of phenotypic variation may be more important to directional phenotypic evolution than sorting by selection.” [29]

They are literally talking about biases in the introduction of variation. In 1984, a group of scientists and philosophers, all highly regarded, convened to consider how development might shape evolution. In 1985, these 9 eminent scientists and philosopers collaborated to publish “Developmental constraints and evolution”:

  • John Maynard Smith, population geneticist trained with Haldane
  • Richard Burian, philosopher of science
  • Stuart Kauffman, later wrote the Origins of Order
  • Pere Alberch, developmental biologist and evo-devo pioneer
  • John H Campbell, evolutionary theorist and philosopher of science
  • Brian Goodwin, developmental biologist, author of How the Leopard got its Spots
  • Russ Lande, developer of the multivariate generalization of QG (trained with Lewontin)
  • David Raup, paleontologist
  • Lewis Wolpert, developmental biologist

The authors raised the question of what might give developmental biases on the production of variation a legitimate causal status, i.e., the ability to “cause evolutionary trends or patterns.” The only accepted theory of evolutionary causation was that evolution is caused by the forces of population genetics, i.e., mass-action pressures acting on allele frequencies. They confronted the issue thus:

Although they clearly call for a “reexamination”, they did not provide one, other than some vague suggestions of neutral evolution, which are unsatisfactory because proposing neutrality, though consistent with Haldane-Fisher reasoning, was not a satisfactory basis for claiming some special promise of evo-devo not included in standard thinking.

Another way of articulating the prior art would be to point to the verbal theories noted above, e.g., the highly developed example of Vrba and Eldredge (1984).[2] Is the population-genetic theory of Yampolsky and Stoltzfus (2001) an obvious improvement on this verbal theory? Does it merely supply the math that would be obvious from reading Vrba and Eldredge? Again, we can answer this question by reading Maynard Smith, et al (1985), because they are clearly representing the verbal theory from evo-devo, of which Pere Alberch (one of the authors) had helped to promote. So, if a population-genetic theory of arrival biases was an obvious clarification of this verbal theory, then Pere Alberch could have asked John Maynard Smith and Russ Lande to translate his verbal theory so as to yield a proper population-genetic grounding for his claims. Clearly that did not happen.

I could cite some other examples, but the case could be made entirely on Maynard Smith, et al. (1985). Why does a single paper make such a strong case? First, the author list includes a set of people who are clearly experts on the relevant topics. Second, the authors were clearly focused on the right issue, and were clearly motivated to find a theory to account for the efficacy of biases in variation to influence the course of evolution, arguably the central claim of the paper. Third, this was a seminal paper that got lots of attention and became highly cited (today: 1800 citations). This means that hundreds of other experts must have read and discussed the paper: if this particular set of 9 authors had missed something, others would have pointed it out in response. Instead, years later, critics such as Reeve and Sherman (1993) complained that Maynard Smith, et al. had never provided an evolutionary mechanism.

Thus, experts in the field of evolutionary biology confronted the issue of how biases in variation could act as a population-genetic cause, and these experts cited the prior art of Haldane and Fisher and the verbal claims of the developmentalists, but they did not find a causal grounding for these internalist claims in a population-genetic theoory of arrival biases.

Thus, a population-genetic theory of arrival biases was non-obvious in 1985.

Indeed we could just take this back to 1930, referring to Haldane and Fisher and the opposing-pressures argument. They confronted the issue of whether internal biases in mutation could be the cause of tendencies or trends, and concluded against this idea, on the grounds that this would require high mutation rates unopposed by selection. Loyalists are going to object to this and say that they were just addressing evolution by mutation pressure, not introduction biases, but this objection is based on hindsight. Haldane and Fisher did not say “This is a narrow argument based on mutation pressure, don’t apply it to introduction biases.” The opposing pressures argument is important precisely because it was presented as a general and rigorous theoretical argument about the possible sources of direction in evolution. Fisher’s (1930) argument, as given, is fully general, e.g., it justifies his advice to researchers to ignore the causes of mutation on the grounds of being irrelevent to how evolution turns out:

“For any evolutionary tendency which is supposed to act by favouring mutations in one direction rather than another, and a number of such mechanisms have from time to time been imagined, will lose its force many thousand-fold, when the particulate theory of inheritance, in any form, is accepted…

The whole group of theories which ascribe to hypothetical physiological mechanisms, controlling the occurrence of mutations, a power of directing the course of evolution, must be set aside, once the blending theory of inheritance is abandoned. The sole surviving theory is that of Natural Selection, and it would appear impossible to avoid the conclusion that if any evolutionary phenomenon appears to be inexplicable on this theory, it must be accepted at present merely as one of the facts which in the present state of knowledge seems inexplicable. The investigator who faces this fact, as an unavoidable inference from what is now known of the nature of inheritance, will direct his inquiries confidently towards 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.’’

However, it is impossible to win arguments with loyalists about the holy trinity, so I’m not going to make my case with Haldane and Fisher. I’m going to make my case with Maynard Smith, et al.

More non-obviousness with Maynard Smith and Kauffman

To further explore this issue of non-obviousness, let us considerJohn Maynard Smith’s knowledge of King’s (1971) codon argument. As I have explained (e.g., this blog, or in my book), King’s codon argument can be read as an early intuitive appeal to an implication of arrival biases. King argued that the amino acids with more codons would be more common in proteins (as indeed they are) because the offer more options, explaining this with an example implying an effect of variation and not selection. Originally, King and Jukes (1969) proposed this as an implication of the neutral theory, but King (1971) quickly realized that this did not depend on neutrality, but would happen even if all changes were adaptive [3].

The way we would explain this today is that the genetic code is a genotype-phenotype map that assigns more codon genotypes to certain amino-acid phenotypes. Because these amino acids occupy a greater volume of the sequence-space of genotypic possibilities, they have more mutational arrows pointed at them from other parts of sequence space: this makes them more findable by an evolutionary process that explores sequence space (or genotype space) via mutations. Because of this effect of findability or “the arrival of the frequent”, the amino acids with the most codons will tend to be the most common in proteins. This argument does not require neutrality, but merely a process subject to the kinetics of introduction. The form of the argument maps to a more general argument about the findability of intrinsically likely phenotypes, which is one of the meanings of Kauffman’s (1993) concept of self-organization.

Maynard Smith literally invented the concept of sequence space (Maynard Smith, 1970). He also knew about King’s codon argument, which he quoted it in his 1975 book, in a passage contrasting the neutralist and selectionist views:

“Hence the correlation does not enable us to decide between the two.  However, it is worth remembering that if we accept the selectionist view that most substitutions are selective, we cannot at the same time assume that there is a unique deterministic course for evolution.  Instead, we must assume that there are alternative ways in which a protein can evolve, the actual path taken depending on chance events.  This seems to be the minimum concession the selectionists will have to make to the neutralists; they may have to concede much more.” 

p. 106 of Maynard Smith J. 1975 (same text in 1993 version). The Theory of Evolution. Cambridge: Cambridge University Press.

This just drives home the point about non-obviousness even further. To someone who knows the theory already, King’s argument might look familiar, but Maynard Smith does not recognize a theory connecting generative biases with evolutionary biases that would be useful for understanding evo-devo and solving the challenge of “constraints”. Instead, he refers only to a theory that allows “chance events” to affect the outcome of evolution.[4]

A few years later, Kauffman (1993) published his magnum opus, The Origins of Order, offering findability arguments under the heading of “self-organization.” In Kauffman’s thinking, selection and “self-organization” worked together to produce order. But Kauffman never offered a causal theory explaining self-organization as a population-genetic process. His simulations typically didn’t include the introduction process because they did not include any population genetics at all (in his models, evolutionary change happens when a discrete particle takes an evolutionary step in a discrete space). So, his claims were a bit of a mystery to population geneticists. But there is no need for mystery: we now know that the findability effect is a matter of biases in the introduction process. This “arrival of the frequent” effect, in regard to the findability of RNA folds, has been demonstrated clearly in work from Ard Louis’s group (see Dingle, et al., 2022). So, we can count Kauffman (1993) as another famous example illustrating non-obviousness, because clearly the theory was non-obvious to Kauffman, and his book was widely read and discussed.

This is an important lesson for traditionalists who tend to assume that theories are timeless universals per Platonic realism and that they are all obvious from assembling the parts. Maynard Smith had the parts list, in a sense, and approached the issue from multiple angles. He got useful clues from the thinking of Jack King. In the circumstances leading up to the famous 1985 paper, Maynard Smith and another brilliant population geneticist (Russ Lande) were placed (figuratively) on an island with some developmental biologists, a philosopher, a paleontologist, and 2 unclassifiable deep thinkers (Campbell and Kauffman), and they were tasked with making sense of the causal role of developmental biases. In the end, they did not articulate a theory of arrival biases as a potential solution to this problem.

This is no criticism of Maynard Smith. Maynard Smith himself understood the point that I am trying to make. I had the opportunity to meet him several times in the 1990s when I was with the Canadian Institute for Advanced Research program in evolutionary biology, and he was some kind of outside advisor who came to our meetings. Anyone who met Maynard Smith in those days knows he was a great one for sharing stories and talking science with students and post-docs over a beer. He once told a series of humorous anecdotes about scientific theories he failed to discover but almost discovered. He had run some numbers on the logistic growth equation and found some odd behavior, and then set the problem aside— only to realize much later that he had stumbled on deterministic chaos. The neutral theory was another theory that he claimed to have almost-but-not-quite discovered. I can’t remember the other ones.

Confronting attempts at appropriation and minimnization

Now, with this background in mind, we can reconsider attempts to appropriate or minimize the theory of Yampolsky and Stoltzfus. Lynch (2007) and Svensson and Berger (2019) appear to be suggesting that the theory is now new, but is merely part of a tradition going back a century or more.

In science, the way to establish X in prior art is to find a published source and then cite it. Let us consider what this might look like:

“Stoltzfus and Yampolsky (2001) were not the first to propose and demonstrate a population-genetic theory for the efficacy of mutational and developmental biases in the introduction of variation: such a theory was already proposed and demonstrated by Classic Source and subsequently was cited in reviews such as Well Known Review and textbooks such as Popular Textbook”.

Of course they say nothing like that, because they can’t: no such sources exist. In appropriation arguments, this gap between the pundit’s purpose and reality is filled with misleading citations and hand-waving arguments. To go back to the analogy with patents: if this were a patent law case, every one of the arguments of Svensson and Berger (2019) would be rejected as irrelevant because they simply do not articulate a theory of biases in the introduction of variation as a cause of orientation or direction in evolution.

For instance, Svensson and Berger say that the theory is part of the neutral theory, citing no source for this absurd and fabricated claim. Kimura wrote an entire book about the neutral theory, along with hundreds of papers. Surely if Svensson and Berger were serious, they could cite a publication from Kimura where the theory is expressed. But they have not done this. None of the sources that they cite articulates a theory of arrival biases. Their insinuation that our work-product is not original relative to work cited from Kimura, Haldane, Fisher, or Dobzhansky must be rejected as, not merely false, but frivolous. Likewise, Lynch’s bad take is so bad it falls in the “not even wrong” category.

Now, having dismissed attacks on the newness of the theory, let us consider the critique of Svensson and Berger (2019) as an attack on non-obviousness, i.e., they may be insinuating that the theory, though new, fails the criterion of being non-obvious, and therefore is not a genuine invention worthy of recognition. This is one way to read their argument in Box 1, in which they derive an equation that can be used to model the theory, building on other equations from Haldane, Fisher and Kimura.

The implication is that the theory is obvious because one can put it together from readily available bits. But this just begs the question: does that really mean that it is obvious? If anyone can put the theory together from readily available bits, why didn’t Fisher and Haldane do this? Why didn’t Maynard Smith and Lande in 1985?

The attitude of Svensson and Berger (2019) seems to be a case of inception: we planted this theory in their heads, and now they see it everywhere. Yet before we proposed this theory, vastly greater minds than Svensson and Berger had access to the same Modern Synthesis canon and failed to see the theory.

Clearly mathematical complexity or cleverness is not the right standard for judging the non-obviousness of scientific theories. The equation is, at best, a model of the theory, useful if you already understand what the theory says. Writing down an equation with the form of a ratio of origin-fixation rates does not give you the theory, e.g., Lewontin has a structurally similar equation on p. 223 of his 1974 book (it is a ratio of steady-state origin-fixation rates for beneficial vs. neutral changes, which reduces to 4Ns ub / un). If Lewontin had understood the theory of arrival biases, he could have put it in the Spandrels paper and this would have made the arguments about the role of non-selective factors much more credible.

Why was a population-genetic theory of arrival biases so non-obvious? I’ve been arguing for years that this reflects a “blind spot” in evolutionary thinking, the combined effect of ingrained habits of thought, convenient approaches to modeling, specific notions of causation, and the overwhelming influence of neo-Darwinism.

However, understanding why the theory was non-obvious is a separate issue. Even if the theory is obvious today (a dubious claim, IMHO), it clearly was not obvious in the past, and the proof of this non-obviousness is that Maynard Smith, Lande, Kauffman, Lewontin and hundreds of other well qualified evolutionary thinkers had the motive and the opportunity to propose this theory and they did not.


King JL, Jukes TH. 1969. Non-Darwinian Evolution. Science 164:788-797.

King JL editor. 1972. Sixth Berkeley Symposium on Mathematical Statistics and Probability. 1971 Berkeley, California.

King JL. 1971. The Influence of the Genetic Code on Protein Evolution. In:  Schoffeniels E, editor. Biochemical Evolution and the Origin of Life. Viers: North-Holland Publishing Company. p. 3-13.

Mani GS, Clarke BC. 1990. Mutational order: a major stochastic process in evolution. Proc R Soc Lond B Biol Sci 240:29-37.

Maynard Smith J. 1970. Natural selection and the concept of a protein space. Nature 225:563-564.

Maynard Smith J. 1975. The Theory of Evolution. Cambridge: Cambridge University Press.

Maynard Smith J, Burian R, Kauffman S, Alberch P, Campbell J, Goodwin B, Lande R, Raup D, Wolpert L. 1985. Developmental Constraints and Evolution. Quart. Rev. Biol. 60:265-287.


Reeve HK, Sherman PW. 1993. Adaptation and the Goals of Evolutionary Research. Quarterly Review of Biology 68:1-32.

Shallit J. 2005. Science, Pseudoscience, and The Three Stages of Truth. PDF

Vrba ES, Eldredge N. (benchmark; co-authors). 1984. Individuals, hierarchies and processes: towards a more complete evolutionary theory. Paleobiology 10:146-171.


[1] The key bits of prior art, to my knowledge are

  • opposing pressures argument of Haldane (1927, 1932, 1933), Fisher (1930)
  • verbal arguments of King (1971, 1972). See note 3.
  • verbal theory of Vrba and Eldredge (1984). See note 2.
  • Mani and Clarke (1990), which shows that mutational order is influential but treats it as a stochastic variable, rather than proposing a theory of biases and generalizing on that

[2] The piece by Vrba and Eldredge, 1984 is part of the paleo debate of the 1970s and 1980s. They use very general abstract language, following on early authors such as Oster and Alberch. They refer to biases in the introduction (or production) and sorting (reproductive sorting, to include selection or drift), making a neat dichotomy that they apply at each level of a hierarchy. So, clearly, they see this as a fundamental kind of causation that can be extrapolated to a hierarchy. The strange thing about the argument is the implicit assumption that biases in the introduction of variation are a kind of causation already recognized at the population level, which is not correct. So, the argument is not situated properly. And, because it includes no demonstration, one could not be sure (in 1984) whether the theory would actually work or not.

[3] King 1971 presents a verbal argument with a concrete example that is the closest thing I have seen to an earlier statement of the theory of Yampolsky and Stoltzfus (2001). First, he clearly means for this idea to be general. That is the significance of the diagram with the arrows coming out from a point in a blank space, with some pointing up (beneficial), some laterally (neutral), and many down (deleterious). I have used diagrams like that myself. So, he is clearly aiming for generality. But he has almost nothing to say on where the biases come from. His motivating example is the genetic code but he does not cite any other example. He does not reference prior art and does not explain how his theory is different. He does not offer proof of principle other than the verbal model. So, a reader would have to question whether this idea would be consistent with pop gen.

[4] I have seen this kind of reaction many times. Saying that chance affects evolution is a familiar thing. Evolutionary biologists are accustomed to a dichotomy of selection (or necessity) and chance, and it is familiar to invoke “chance” as if it were a cause. But it is not familiar in evolutionary biology to refer to generative processes as evolutionary causes that impose biases on the course of evolution. As of today, there is no language for this that is acceptable to traditionalists. So, when traditional thinkers are confronted with the theory of Yampolsky and Stoltzfus (2001), they often translate this into a familiar selection-vs-chance dichotomy and say that this is a theory about how “chance” affects evolution, or refer to “contingency.”

Leave a Reply

Your email address will not be published / Required fields are marked *