# 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.