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 utilized 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 both circular and logically invalid because 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 correction scales with effective population size and, at realistic human values, ranges from 16 percent to 100 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 answer no material questions in population genetics or evolutionary biology.