Now, I could not care less about the catastrophic state of professional science. Most scientists are midwits who are wholly incapable of ever doing anything more than chasing credentials, and the scientific literature ranges from about 50 percent to 100 percent garbage, depending upon the field. But I do feel sufficient moral duty to the great archive of human knowledge to bring it to the attention of the professionals when the very foundation upon what they’re basing a fairly significant proportion of their work is obviously, observably, and provably false.
So I submitted a paper calling attention to the fact that Kimura’s fixation model, upon which all neutral theory is based, is algebraically incorrect due to an erroneous cancellation in its derivation. In short, Kimura fucked up massively by assigning two different values to the same variable. In order to make it easy to understand, let me make an analogy about Democrats and Republicans in the US political system.
T = D + R, where D = 1-R.
This looks reasonable at first glance. But in fact, D stands for two different things here. It stands for both Democrats and it stands for Not Republicans. These two numbers are always going to be different because Democrats (47%) are not the same as Democrats + Independents (62%). So any derivation that cancels out D as part of an equation is always going to result in the equation producing incorrect results. Even for the most simple equation of the percentage of the US electorate that is divided into Democrats and Republicans, instead of getting the correct answer of 85, the equation will produce an incorrectly inflated answer of 100.
So you can’t just use D and D to represent both values. You would do well to use D and Di, which would make it obvious that they can’t cancel each other out. Kimura would have been much less likely to make his mistake, and it wouldn’t have taken 57 years for someone to notice it, if instead of Ne and Ne he had used Ne and Nc.
So, I write up a paper with Athos and submitted it to a journal that regularly devotes itself to such matters. The title was: “Falsifying the Kimura Fixation Model: The Ne Equivocation and the Empirical Failure of Neutral Theory” and you can read the whole thing and replicate the math if you don’t want to simply take my word for it.
Kimura’s 1968 derivation that the neutral substitution rate equals the mutation rate (k = μ) has been foundational to molecular evolution for over fifty years. We demonstrate that this derivation contains a previously unrecognized equivocation: the population size N in the mutation supply term (2Nμ) represents census individuals replicating DNA, while the N in the fixation probability (1/2N) was derived under Wright-Fisher assumptions where N means effective population size. For the cancellation yielding k = μ to hold, census N must equal Ne. In mammals, census populations exceed diversity-derived Ne by 19- to 46-fold. If census N governs mutation supply while Ne governs fixation probability, then k = (N/Ne)μ, not k = μ. This fundamental error, present in both the original 1968 Nature paper and Kimura’s 1983 monograph, undermines the theoretical foundation of molecular clock calculations and coalescent-based demographic inference. Empirical validation using ancient DNA time series confirms that the Kimura model systematically mispredicts allele frequency dynamics, with an alternative model reducing prediction error by 69%.
This is a pretty big problem. You’d think that scientists would like to know that any results using that equation are guaranteed to be wrong and want to avoid that happening in the future, right? I mean, science is all about correcting its errors, right? That’s why we can trust it, right?
Ms. No.: [redacted]
Title: Falsifying the Kimura Fixation Model: The Ne Equivocation and the Empirical Failure of Neutral Theory
Corresponding Author: Mr Vox Day
All Authors: Vox Day; Claude AthosDear Mr Day,
Thank you for your submission to [redacted]. Unfortunately, the Editors feel that your paper is inappropriate to the current interests of the journal and we regret that we are unable to accept your paper. We suggest you consider submitting the paper to another more appropriate journal.
If there are any editor comments, they are shown below.
As our journal’s acceptance rate averages less than half of the manuscripts submitted, regretfully, many otherwise good papers cannot be published by [redacted].
Thank you for your interest in [redacted].
Sincerely,
Professor [redacted]
Co-Chief Editor
[redacted]
Apparently showing them that their math is guaranteed to be wrong is somehow inappropriate to their current interests. Which is certainly an informative perspective. Consider that after being wrong for fifty straight years, they’re just going to maintain that erroneous course for who knows who many more?
Now, I don’t care at all about what they choose to publish or not publish. I wouldn’t be protecting the identities of the journal or the editor if I did. It’s their journal, it’s their field, and they want to be reliably wrong, that’s not my problem. I simply fulfilled what I believe to be my moral duty by bringing the matter to the attention of the appropriate authorities. Having done that, I can focus on doing what I do, which is writing books and blog posts.
That being said, this is an illustrative example of why you really cannot trust one single thing coming out of the professional peer-reviewed and published scientific literature.