The Pan Paradox: MITTENS Applied to Chimpanzee Subspecies Divergence

The MITTENS framework (Mathematical Impossibility of The Theory of Evolution by Natural Selection) demonstrated a 220,000-fold shortfall in the fixation capacity required to explain human-chimpanzee divergence. A natural objection holds that this represents a special case—perhaps the human-chimp comparison uniquely violates the model's assumptions. We test this objection by applying MITTENS to divergence within the genus Pan: the split between bonobos and chimpanzees, and the subsequent radiation of chimpanzee subspecies. Using genomic data from the Kuhlwilm et al. (2025) Great Ape Genome Diversity Panel comprising 67 wild Pan individuals, we identify 1,811,881 fixed differences between subspecies and calculate achievable fixations given published divergence times and effective population sizes. Using 20-year generations (shorter generations favor the standard model) and the empirically-derived Selective Turnover Coefficient d = 0.86 for wild chimpanzees, the bonobo-chimpanzee split (930,000 years, 40,000 effective generations) permits a maximum of 25 fixations—a shortfall of at least 13,000-fold against the observed fixed differences. Subspecies divergences show comparable failures: Western versus Central chimpanzees (460,000 years) fail by ~7,500-fold; Central versus Eastern (200,000 years) fail by ~3,600-fold. Paradoxically, observed F_ST values are consistently lower than drift expectations despite millions of fixed differences—a pattern incoherent under standard theory. The mechanism fails at every scale tested. MITTENS is not a special case; it is a systematic failure of the substitution-fixation model across all primate divergence levels.