The Intrinsic Irrelevance of Kimura’s Substitution Rate
Kimura’s neutral substitution rate (k = μ) is the most widely cited result in molecular evolution. We show that it is intrinsically irrelevant to every single real-world question it has ever been deployed to answer. The identity contains no time term and therefore cannot address whether any number of fixations can complete in any given window. Its sole practical application, the calibration of the molecular clock, is circular and logically invalid: divergence dates are derived from the identity, then cited as independent confirmation of the identity. When the time-dependent fixation dynamics that Kimura’s own framework supplies are properly integrated into the substitution calculation, using the exact transient formula E[F(T)] = μL ∫₀ᵀ F_X(u) du rather than the naive product μLT, the leading-order correction subtracts the mean fixation time from the available window. The fraction consumed scales with effective population size and, at realistic human values, ranges from 16 percent to 48 percent of the total available time frame. While Kimura’s derivation is mathematically correct, it is a limited steady-state identity that is almost always improperly applied and the results it produces answers no real-world questions in evolutionary biology or population genetics.
The full paper is available on Zenodo. It is a tactical nuclear strike on both Neutral Theory as well as on the Postmodern Polythesis that many evolutionary biologists erroneously describe as “the Modern Synthesis”. It’s much more destructive than my previous critiques of Kimura’s algebra, as it is constructed upon a Portuguese mathematician’s correction of Kimura’s math and the demonstration of how it is a steady-state identity that can never be used for the purposes for which it has been improperly used for decades by population geneticists and evolutionary biologists alike.
It has not been submitted to peer review for the obvious and observable reason that I have no peers.