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)?

In this post, we’ll begin the process of developing a shared framework for productively discussing “theory” and “theories”. We will 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


Dictionaries provide definitions that can be helpful to clarify the meanings of words and the complications of their usage. Definitions can be descriptive, telling us how a word is used, or prescriptive, telling us how it ought to be used. But, as most of us don’t like to be told what we ought to do, I suspect that you share my belief in studying how words are used, in order to determine their denotations (what the word says) and connotations (what the word hints or implies). The English dictionaries used in America typically agree: the definitions that they provide reflect patterns of common usage, not the decrees of authorities.

A difficulty with dictionaries arises given that, within an isolated community, e.g., a scientific discipline, words can take on special meanings. So, dictionaries can be helpful, with the proviso that we need to be sensitive to the special use of terms within a discipline.

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.

Two meanings of “theory”

A good dictionary will distinguish several different senses of the word “theory”, including the following two that I believe are the most relevant for our discourse:

  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. 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 that the sexes (in the sense of mating types) are not, in fact, 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 not just recognized in dictionaries, but are 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 scientific theoriesC and scientific theoryA. One way of thinking about the connection is that 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)).

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 theoryC and then to theoryA.

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 consistency: 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 cover non-overlapping universes. 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. Indeed, no amount of conflicting data will cause us to discard a principle of theoryA that is properly derived: a beautiful piece of theoryA cannot be killed by an ugly fact. Fisher’s fundamental theorem either is logically valid or is not logically valid, independent of any facts.


The distinction between theoryC and theoryA is hidden in the ambiguous word “theory”, but I think it comes out more clearly in specific word-derivatives and grammatical usages that seem to favor one meaning more than the other. I mentioned above that the abstract noun typically signals theoryA. I’m also convinced that when we refer to a “theoretician”, we typically do not mean someone like Tom Cavalier-Smith whose scientific output consists of bold conjectures or systematic hypotheses (we might call such people “theorizers”), but instead someone like Joe Felsenstein whose work focuses on mathematical or algorithmic foundations, i.e., theoryA. It’s a rare scientist, it seems to me, who is productive both as a theoretician and as a theorizer (e.g., Kimura, Hamilton).

Neither meaning of theory would cause us to relinquish the label “theory” for a proposition that lacks verisimilitude. Clearly the propositions of theoryA do not have to apply to the real world. And a theoryC is a conjecture, not necessarily a true conjecture. Thus, even opponents of the Neutral TheoryC, who believe that the theory does not fit the actual world, still refer to it as The Neutral Theory (Kreitman 1996).

I mention this because there is an absurd tendency in the literature of evolution advocacy, e.g., NCSE’s screeds, to say that, because scientists reserve the word “theory” only for constructions that have been extensively verified and are accepted as true, the use of “theory of evolution” among scientists means that evolution is well supported.

This argument clearly is false, and the proof does not depend on the theoryC vs. theoryA distinction, but only on the fact that scientists habitually choose to refer to Kimura’s theory or Lamarck’s theory or Gilbert’s theory as a “theory”, even if it is known to be wrong or is considered deeply suspect. This pattern holds, not just in biology, but in other disciplines. In astronomy, the geocentric theory remains a theory though it has been abandoned; in physics, the phlogiston theory, or the aether theory of light propagation (roughly, the theory that space must be substantive in order for waves to propagate in it) remain theories even though they were abandoned. So, write to the NCSE and tell them to stop using this lame argument. Really, we can do better than that.

The NCSE fallacy seems to arise from mixing together the proposed explanation of phenomena aspect of theoryC and the accepted as valid aspect of theoryA. This is suggested from the way that NCSE’s screed justifies its “well substantiated explanation” view of “theory” by citing the NAS report (quoted above), which is actually focused on theoryA  (“collection of models”).

Lets try to sort this out in terms of the distinction between theoryC and theoryA. 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.

But saying that this theoryA is valid is not at all the same thing as claiming that it is true in the sense of verisimilitude; and 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. Got it?


The wikipedia entry on 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 (and what does one learn from those)?

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

Think of a few theories in science, ideally in life sciences. I’m going to assert that they are not axiomatic, i.e., they are not completely encompassed by precisely stated propositions. 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 wikipedia 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 ideas 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.


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 1.2) 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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