Falsifying the Kimura Fixation Model: The Ne Equivocation and the Empirical Failure of Neutral Theory

Kimura's neutral theory of molecular evolution rests on two foundational results: the substitution rate k = μ and the equilibrium diversity π = 4N_eμ. Both formulas employ effective population size (N_e), but we demonstrate that N_e cannot represent the same biological quantity in both contexts. The substitution rate derivation requires N_e to govern both mutation supply and fixation probability; however, mutations arise from the census population while fixation probability depends on drift dynamics. Using empirical data from three mammalian species (chimpanzees, gorillas, and killer whales), we show that census populations exceed diversity-derived N_e by 19- to 46-fold. This systematic discrepancy reveals that N_e functions as a post-hoc fitting parameter rather than an independent measurement. We further demonstrate that explaining these N_e reductions requires invoking pervasive selection. Combined with empirical falsification from ancient DNA time series (Bio-Cycle model reduces Kimura prediction error by 69%), we conclude that the Kimura model is degenerately parameterized and does not describe the evolutionary dynamics of sexually reproducing organisms with overlapping generations.