Theory vs. Theory

What does it mean to invoke “evolutionary theory”? Is “neo-Darwinism” (or “Darwinism”) a theory, a school of thought, or something else? What gives a theory structure and meaning (e.g., axioms, themes, formulae)? What is the relationship between mathematical formalisms and other statements of “theory” (e.g., what does it mean for a lecturer to show a key equation of quantitative evolutionary genetics and assert “this is neo-Darwinism” 1)? Who decides how a theory is defined, or redefined (e.g., is Ohta’s “nearly neutral” theory an alternative to, or a variant of, Kimura’s Neutral Theory of Molecular Evolution)?

For various purposes, I would like to begin developing a framework for productively discussing “theory” and “theories”.  Here I begin by addressing an ambiguity in the use of the word “theory”, partly because this particular ambiguity is important, and partly as an exercise in addressing semantics. 2

Definitions

Dictionaries provide definitions that can be helpful to clarify the meanings of words and the complications of their usage.  A difficulty with dictionaries arises given that, within an isolated community, e.g., a scientific discipline, words can take on special meanings.   The discipline-specific use of a term can be nailed down by looking at examples of usage. For evolutionary biology, the discipline-specific use of a term is to be found in the research literature, and also in the secondary literature of monographs, textbooks, and other disciplinary writings.

Definitions can be descriptive, telling us how a word is used, or prescriptive, telling us how it ought to be used. Obviously we would have not have much use for a pure un-reduced description, covering all uses including erroneous ones, or for a pure prescription that does not even try to make sense of how the word is actually used.  If the meaning of a word is unclear or ambiguous, what we really want is some guidance on how to use the word clearly while respecting past usage, and this may involve developing some kind of clarifying proposal.

Two meanings of “theory”

What I will suggest here is a clarifying proposal.   I think that most uses of “theory”, at least in the sort of sources that I read regularly, fit closely with one of these 2 definitions:

  1. theoryC: a major conjecture or systematic hypothesis to account for observed phenomena, as in “prion theory of disease” or “Lamarck’s theory of evolution”;
  2. theoryA: the body of abstract principles relevant to some discipline, methodology or problem area, as in “music theory” or “population genetics theory”

That is, a theoryC (concrete, conjectural) is a grand hypothesis, a conjecture about the actual world, while a theoryA (abstract, analytical) is a collection of principles or models or other formalisms that might apply only in an imagined world.  I believe this is a clarifying proposal because I have used it myself for years to keep these two things straight.

Fisher (1930) famously said that “No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes; yet what else should he do if he wishes to understand why the sexes are, in fact, always two?” Theoreticians aren’t necessarily good with facts, so we’ll ignore the fact that the sexes (in the sense of mating types) are not always two. Fisher clearly encourages us to work out formalisms for imagined or hypothetical cases. The collection of all these models or formalisms about sexes would constitute the theoryA of sexes. A theoryC of sexes might propose a causal explanation for the actual historic phenomenon of the origin and maintenance of sexual reproduction in animals, addressing such issues as the heterogametic basis of sex determination. 3

These two meanings are well established in scientific usage. Gilbert’s “Exon Theory of Genes” (Gilbert 1987) is the conjecture that genes evolved from exons (i.e., large protein-coding genes emerged by joining primordial exon-minigenes). The prion theoryC of disease clearly revolves around a conjecture that there are actual diseases caused by actual prions. By contrast, population genetics theoryA is not the conjecture that populations have genetics; likewise, the theoryA of stochastic processes is not a conjecture that stochastic processes occur, but consists of a body of abstract principles that might be applicable to such stochastic processes as might occur in some actual or imagined universe.

The use of the abstract noun, as in “let’s talk about theory” as opposed to “let’s talk about { a | the | this } theory”, often signals the use of theoryA. For instance, the title of a report by the National Academy of Sciences on “The Role of Theory in Advancing 21st Century Biology” signals a likely emphasis on theoryA, and indeed, the report emphasizes the development of formalisms more than conjectures, and says that “a useful way to define theory in biology is as a collection of models”, clearly a reference to theoryA. The report also mixes in some references to theoriesC.

Obviously, there is a connection between the two.  The abstract principles of theoryA, when suitably limited by measurable or observable quantities from the actual world, can provide the basis of a theoryC, and conversely, theoriesC draw on theoryA for logical structure. Kimura’s Neutral Theory (Kimura 1983) provides a clear example because the theoryC and theoryA were developed separately: Kimura combined pre-existing theoryA (of stochastic population genetics) with the concrete assertion that the values of certain quantities (relating to population sizes and mutant effects) were such that, for DNA and protein sequences, neutral evolution by mutation and random fixation would be far more common than anyone had imagined previously.  The definition of effectively neutral alleles (perpetually misunderstood by critics) and the probability of fixation under pure drift were known to the canonical founders of population genetics (Wright 1931; ch. IV of Fisher 1930; appendix of Haldane 1932).

Development and application of theoryC and theoryA

We treat the two kinds of “theory” differently, and rightly so.

A theoryC contains a major supposition or unproved conjecture about the world. Kimura’s Neutral Theory is the conjecture that most changes at the “molecular level” represent the random fixation of effectively neutral alleles. Darwin proposed, but could not prove, that all large-scale evolutionary changes were built from infinitesimal increments of change that emerged by a process of hereditary “fluctuation”. A theoryC takes risks: in Popperian terms, it’s subject to empirical refutation; in the words of Huxley, a beautiful theoryC can be “killed by an ugly fact.”

The relevant standard of validity for theoryA is not verisimilitude (trueness to life), but correctness: the principles derived in the theory are consistent with its assumptions. Importantly, new principles added to a body of theoryA are consistent with previous principles (except in the sense that a body of theoryA may be subdivided into branches that make different assumptions). If they are not, a logical error has occurred.

While new theoryA is consistent with existing theoryA, theoriesC often stimulate interest precisely because they conflict with previous theoriesC. Of course theoriesC strive to be internally consistent, but in biology at least, theoriesC are not axiomatic, and often encompass ambiguities that make rigorous analysis difficult. A theoryC can be brought down by a contradiction that arises internally, e.g., one part can be found to contradict another part.

While a theoryC is about the actual world, and thus is judged by verisimilitude, principles of theoryA need not apply to the real world.  A statement in theoryA can refer to something imaginary, like an infinite population: it is either logically valid, or not, independent of any facts about the world.

Another indication of the distinctness of theoryC and theoryA is that opponents of the Neutral TheoryC, who deny the truth of the theoryC, are nonetheless quite happy to make use of its theoreticalA infrastructure, as in Kreitman’s (1996) review.In fact, the paradox implicit in Kreitman’s title “The neutral theory is dead. Long live the neutral theory” is perfectly resolved by the fact that it refers first to a theoryC and then to the associated parts of theoryA.  A neutral model for some particular set of conditions X will yield a particular result Y.  That is, theoryA provides a logical syllogism if X then Y (expected outcome).    If we do not see Y, then we may use reasoning (modus tollens) to reject X (either neutrality, or the background conditions), because we trust that the model is correctly derived.

So, saying that a statement of theoryA is valid means that it is correctly derived, and this is not at all the same thing as claiming that it is true in the sense of verisimilitude.  Furthermore, claiming that it has verisimilitude is not the same as saying that it is complete, in the sense of sufficiently accounting for the phenomena of evolution. For instance, the theoryA of quantitative evolutionary genetics is based on the assumption of infinitesimal variation, but the theoryA itself does not claim that all traits, nor even any single trait, evolved in this manner– that would be a theoryC issue. Kimura’s diffusion equations are a part of population genetics theoryA that provides a way to work out the probability of fixation of alleles under ideal conditions, but it doesn’t assert that the results are applicable to any particular case.

Digressions

The distinction between theoryC and theoryA is hidden in the ambiguous word “theory”, but I think it comes out more clearly in specific derivatives and grammatical usages, e.g., as when the abstract noun signals theoryA. I’m also convinced that when we refer to a “theoretician”, we do not mean someone like Cavalier-Smith whose scientific output consists of bold conjectures or systematic hypotheses (we might call such people “theorizers”), but instead someone like Felsenstein whose work focuses on mathematical or algorithmic foundations, i.e., theoryA.

A new definition of “theory” has emerged for the purpose of rebutting the creationist argument that evolution is “just a theory”.  According to NCSE screeds, scientists reserve the word “theory” only for constructions that have been extensively verified and are accepted as true, thus the use of “theory of evolution” among scientists means that evolution is well supported.  Likewise, the NAS web site helpfully explains, in regard to evolutionary biology, that a theory is “a comprehensive explanation of some aspect of nature that is supported by a vast body of evidence”.

A facsimile of a page from Dalton’s notebooks from p. 45 of Roscoe and Harden (online version)

However, this definition is contradicted by the long established pattern of scientists of using “theory” to refer to conjectures that are not well established, as with the Neutral Theory, and even with the examples invoked by NAS, such as atomic theory and plate tectonics.   Roscoe and Harden (1896, A New View of the Origin of Dalton’s Atomic Theory. London: MacMillan and Co.) published an account of the origins of Dalton’s atomic theory, based on notebooks, correspondence and so on.  On p. 11, Dalton is quoted referring to his “theory of mixed gases” (a precursor to the atomic theory); on p. 45, we see a facsimile of a notebook page dated 1803 (figure, right), referring to a “New theory of the constitution of the ult. [ultimate] atoms of Bodies”; and on p. 253, one finds Dalton’s colleague Thomson writing  about his “theory” and about other incompatible “theories”.  Clearly, they did not wait for widespread acceptance before using the word “theory”. 

The theory of continental drift proposed in 1912 by Wegener remained controversial for a half-century due to lack of evidence, and lack of a credible idea for what forces could move continents, and yet was known during this period as the “drift theory” or “continental drift theory”, e.g., as in a 1928 symposium reviewed in Nature. Wegener himself referred to it as the “displacement theory”, e.g., his 1929 book begins immediately with a section on the origin of the displacement theory (“Entstehung der Verschiebungstheorie”).

I could go on at length with examples: Darwin’s references to “my theory”; De Vries’s “Die MutationsTheorie”; Mereschkowski’s endosymbiotic theory; Wright’s “shifting balance theory”; and so on.  What these examples tell us is that, for 200 years, actual scientists have invoked conjectures using the word “theory”, without waiting for the conjecture to be firmly established.

In short, the NAS-NCSE definition is wrong, wrong, wrong, and anyone with internet access can prove that in 5 minutes of searching for how actual scientists use the word.

Evolutionists have recourse to a body of theoryA (formalisms or models or principles), ranging from purely phenomenological models of branching and character-state change used in phylogenetics, to the breeder’s equation used in quantitative genetics, to detailed formulas for population-genetics processes, and so on. We accept the validity of these abstractions in the theoryA sense of validity, i.e., we accept that they are derived without error, so as to be logically consistent with their assumptions. This body of abstractions, principles, or formalisms (in NAS parlance, this collection of models) is evolutionary theoryA.

We could make the same kind of reference to the theoryA for other fields such as chemistry, physics, geology, etc.

However, evolutionary biology is different from these other fields in a particular way.   Just as people once doubted that prions could cause disease, and that mitochondria are endosymbiotic in origin, they once doubted that species emerge by a natural process of evolution.  There was a time when evolution itself was a bold conjecture.   Therefore, we can speak of a theoryC of evolution in a way that we would not do for chemistry.

Furthermore, evolution is partly a historical science, like cosmology.   We can use evolutionary concepts and models prospectively to make predictions about natural or experimental evolution, e.g., the evolution of resistance to anti-microbial drugs.  But there is also a clearly demarcated explanandum, which is the 4 BY of change leading to the present diversity of species with their features and distributions.  When we talk about evolutionary biology, and the challenges of the field, we are mostly talking about scientists’ effort to account for this history.  We can have competing theoriesC for how this happened, e.g., a simple example would be Woese’s progenote theory, which invokes early stage when cells and genomes weren’t so clearly defined, from which 3 types of cells emerged.  Sometimes there are bitter struggles between evolutionist to establish particular aspects of history.

We can also have competing theoriesC  that assign different degrees of importance to general causes.

These correspond to the two primary concerns of evolutionary biology.  Most of us devote our career mostly to one or the other: reconstructing history or understanding general causes.  Most of the heat in evolutionary debates over the past century has been about theories regarding general causes.  The architects of the Modern Synthesis promulgated a theoryC  for how evolution works, based on shifting gene frequencies in the gene pool.

Homework

The wikipedia entry on theory (http://en.wikipedia.org/wiki/Theory) has a “List of Notable Theories” that clearly mixes up theoriesC or grand conjectures (the cell theory, the phlogiston theory) with theoriesA or bodies of abstract principles (music theory, extreme value theory). What are some other clear examples of theoryC and theoryA in this list?

Which examples are difficult to classify?  How exactly does one interpret “Social evolution theory predicts that if the mutants and wild-type are cheats and cooperators, respectively, then the relative fitness of the mutants will be greatest when they are rarer, because then they will be better able to exploit the cooperators” (source)?

Who, besides Kimura, was productive as both a theoretician and as a theorizer?

In evolution, we have had grand theories or big ideas such as the “Modern Synthesis”, “orthogenesis”, “neo-Darwinism” and so on that are sufficiently complex that there is not agreement on how to define them.  Given this, how do we really know what defines the theory? If we know a theory from the verbal statements in a body of literature (i.e., “things people say”), what is the relationship of an individual expression (e.g., a paper, a monograph, a quotation) to the theory? Is it the instantiation of a platonic form or essence? How do we get to the essence? Is the distribution of expressions of a theory its “reaction norm”, representing environmental noise in the expression of an underly structure (the theory’s “genotype”)?

The Modern Synthesis as theoryC: into the memory hole

The folks at NCSE and NAS are not the only ones blurring the issues. The Modern Synthesis or modern neo-Darwinism 4 was put forth originally as a falsifiable theoryC of evolution, but evolutionists themselves began backing away from that almost immediately. For instance, in Maynard Smith’s defense of “neo-Darwinism” (Maynard Smith 1969), the only kinds of falsifying observations he can imagine are cases that seem to introduce supernatural forces, e.g., if the spots on a fish always appeared in prime numbers, he says this would contradict neo-Darwinism. He does not imagine variation-induced trends, discontinuous jumps based on individual mutations, or extensive neutral evolution as contradictions of “neo-Darwinism”, though these are all physically possible things that were rejected by the architects of modern neo-Darwinism.

Maynard Smith makes the claim in regard to the Neutral Theory that “I have never seen any reason why, as a naive Darwinist, I should reject this theory” (Maynard Smith 1995). It seems that, for Maynard Smith, “neo-Darwinism” is not a theoryC at all, but merely indicates a commitment to scientific materialism, i.e., seeking natural causes through observation and experiment.

Other authoritative sources suggest that the Modern Synthesis is no longer viewed as a falsifiable conjecture. In Hull’s Encyclopedia of Evolution article on the history of evolutionary thought (Hull 2002), the Modern Synthesis is presented as an open-ended “theory” that merely assumes the principle of selection and the rules of genetics, and which has swallowed up the neutral theory along with all other useful ideas:

“Any criticism of the synthetic theory that turned out to have some substance was subsumed in a modified version of this theory. Instead of being a weakness, this ability to change is one of the chief strengths of the synthetic theory of evolution. As in the case of species, scientific theories evolve” (p. E16)

Hull’s conception of the Modern Synthesis sounds more like an extensible set of principles, theoryA, than the theoryC of Mayr, Simpson, Ayala, etc (which is extensible in some ways but closed and falsifiable in others). I’m not necessarily going to say it’s wrong for scientists to decide that the Modern Synthesis is no longer a theoryC, but can someone please tell me when, and on what basis, did we make this decision? Is there a citation for that? And who decided that we wouldn’t tell Richard Dawkins, leaving the poor fellow stuck in 1959 defending the original Modern Synthesis? 5

Literature cited

Dawkins, R. 2007. Review: The Edge of Evolution. Pp. 2. International Herald Tribune, Paris.

Fisher, R. A. 1930. The Genetical Theory of Natural Selection. Oxford University Press, London.

Gilbert, W. 1987. The exon theory of genes. Cold Spring Harbor Symp. Quant. Biol. 52:901-905.

Haldane, J. B. S. 1932. The Causes of Evolution. Longmans, Green and Co., New York.

Hull, D. L. 2002. History of Evolutionary Thought. Pp. E7-E16 in M. Pagel, ed. Encyclopedia of Evolution. Oxford University Press, New York.

Kimura, M. 1983. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge.

Kreitman, M. 1996. The neutral theory is dead. Long live the neutral theory. Bioessays 18:678-683.

Maynard Smith, J. 1969. The Status of Neo-Darwinism. Pp. 82-89 in C. H. Waddington, ed. Towards a Theoretical Biology 2. Sketches. Edinburgh Universeity Press, Edinburgh.

Maynard Smith, J. 1995. Life at the Edge of Chaos? Pp. 28-30. New York Review of Books, New York.

Wright, S. 1931. Evolution in Mendelian populations. Genetics 16:97.

Notes

1 At the ESEB meeting in 2005, James Cheverud showed a slide with the breeder’s equation and said “This is neo-Darwinism”. It would be unreasonable to suggest that the MS is defined by any particular equation: the MS negotiates words (including words from the sacred texts) and equations and facts into something that seems, at least superficially, self-consistent, but it is defined more by a set of themes or doctrines than by any token equation.  However, I think Cheverud’s statement is reasonable in the sense that this particular equation (representing the idealized version of quantitative genetics) is the closest that mathematical evolutionary genetics ever gets to justifying the verbal theory of Darwinism.

2 I thank Dr. Mike Coulthart for originally drawing my attention to the importance of this distinction.

3 If we were to propose just that the sexes are always 2 in number, simply because that is what we have seen in the past, I would call this an empirical generalization or “law”. Sometimes “theory” is used for such a generalization, but that usage does not correspond to either meaning of “theory” addressed here.

4 I’m using “modern neo-Darwinism” as a synonym for “Modern Synthesis”. Neo-Darwinism (for our purposes, Darwinism 1.1) is the pre-Mendelian theory of Weissman and Wallace emphasizing the supreme power of selection and infinitesimal variation to build adaptation (and rejecting Darwin’s reliance on Lamarckism). The Modern Synthesis (Darwinism 2.0) comes from this tradition and is often called “neo-Darwinism”, though “modern neo-Darwinism” is clearer.

5 Kidding aside, its quite useful to have a scholar still defending the actual Modern Synthesis. For instance, in his attempt to rebut Behe (Dawkins 2007), Dawkins claims that mathematical geneticists “have repeatedly shown that evolutionary rates are not limited by mutation” and that Behe’s critique based on the idea that evolution depends on specific mutations would mean that “the entire corpus of mathematical genetics, from 1930 to today, is flat wrong”. In making this claim, Dawkins is correctly representing the Modern Synthesis view that (due to the buffering effect of the “gene pool”) evolution does not depend on the rate of new mutations, a principle that he believes to be an infallible theoretical result.


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