MachineSex/results/fig5_speciation_bdm/README.md

E12 — Model speciation: when two diverged models are too incompatible to merge

Claim tested. The sexual society (E7–E11) recombines complementary parents. E12 asks the limit: how far can two lineages diverge before recombination (model merging) stops working? In biology the answer is reproductive isolation via Bateson–Dobzhansky–Muller incompatibilities (BDMIs) — alleles benign on their own lineage's background but deleterious in combination, which a recombinant inherits untested. A merged model is a single recombinant (an F2-like hybrid-breakdown / recombination-load object, not an F1), so the predicted signature as parental divergence grows is compatible → outbreeding depression → hybrid inviability, arriving earlier the more epistatic the capability landscape.

Setup. Pure seeded NumPy on the E7–E11 genotype machinery (bitwise-reproducible; no external simulator, whose separate RNG would break that guarantee). Two landscapes:

• BDM (configs/inheritance/fig5_speciation_bdm.yaml, headline): an ancestor; two lineages each substitute a disjoint set of loci (each parent adaptive, neither carrying an incompatibility); a fraction ρ of cross-lineage locus pairs are BDMIs (penalty s), biting only when a hybrid inherits both derived alleles. Sweep divergence d (substitutions) for several ρ; L=20, 15 reps.
• NK (configs/inheritance/speciation_bdm_nk.yaml): parents are local optima (hill-climbed) on a Kauffman NK landscape; sweep ruggedness K. The emergent version.

Results

• The three-regime collapse (BDM). Parent fitness rises linearly with divergence; hybrid fitness tracks it while compatible, then peels off, peaks, and crashes. At dense epistasis (ρ=0.5) hybrids peak near d≈8 and fall to −1.0 by d=20 (below the ancestor = inviable); at sparse epistasis (ρ=0.1) there is mild outbreeding depression and no isolation.
• The isolation cliff moves with epistasis density. Reproductive-isolation rate (P hybrid inviable) at d=20: ρ=0.1→0.00, ρ=0.25→0.03, ρ=0.5→0.50 — the cliff arrives at lower divergence the denser the epistasis.
• The Orr–Turelli snowball. The number of incompatibilities grows ~(d/2)² (≈48 at d=20, ρ=0.5 ≈ 0.5·10²), so hybrid fitness falls super-linearly — divergence is punished faster than it accrues.
• The epistasis wedge (NK). At K=0 (additive) recombination is neutral (no isolation — and the two parents can't even diverge, since there is one peak); as ruggedness rises, recombining two adapted local-optimum parents flips from a gain to outbreeding depression (recombination gain 0 → −0.13; OD rate 0 → 0.90 across K=0→10). At matched divergence, mergeability is governed by epistasis — the axis no divergence-only merge predictor captures.

Why it matters / positioning

The ML phenomenon that "specialization/divergence eventually breaks merging" is known empirically (Pari et al. 2024; Zhou et al. 2026), and part of the apparent incompatibility is a permutation artefact (Git Re-Basin). E12's contribution is the predictive theory those lack: the functional form (compatible→OD→inviability), the snowball onset, and the epistasis wedge — merge failure as a Dobzhansky–Muller phenomenon whose onset is set by divergence and epistasis, not divergence alone. The design rule: before merging, check divergence against the landscape's ruggedness; beyond the cliff, route (allopatry), don't merge. Falsifier (not triggered): no OD/isolation progression as d and ρ grow — instead the full progression appears, and the additive control shows none. Real-weight confirmation (merging at increasing divergence with permutation alignment, isolating the residual epistatic incompatibility) is the flagged next step; here the analytic model is the anchor.