The N ≠ Nₑ Problem: A Foundational Error in Neutral Theory

Kimura's neutral theory rests on the theorem that the neutral substitution rate equals the mutation rate (k = μ), independent of population size. This result derives from a cancellation: 2Nμ mutations arise per generation, each with fixation probability 1/(2N), yielding k = μ. We demonstrate that this derivation contains a critical equivocation: the N in the mutation supply term represents census population size (individuals replicating DNA), while the N in the fixation probability derives from Wright-Fisher assumptions where it represents effective population size. For the cancellation to hold, census N must equal N_e—a condition violated by every natural population. In mammals, census populations exceed diversity-derived N_e by 19- to 46-fold. This error, present in both Kimura's 1968 Nature paper and his 1983 monograph, propagates into molecular clock calibrations, coalescent inference, and divergence time estimates across the tree of life.