Giorgio Gilestro
db9452c9d4
New analytic result for the evolution-of-sex paper: how far can two lineages diverge before recombination (model merging) stops working? Frames merge failure as biological reproductive isolation via Bateson-Dobzhansky-Muller incompatibilities. src/knowledge/speciation.py, kind: speciation, on the E7-E11 genotype machinery (pure seeded NumPy, bitwise-reproducible; no external simulator whose separate RNG would break that). - BDM construction (E12.yaml): ancestor + two lineages substituting disjoint loci (each parent adaptive, incompatibility-free), a fraction rho of cross-lineage pairs are BDMIs. Sweeping divergence d reproduces the predicted compatible -> outbreeding depression -> hybrid inviability curve; the isolation cliff moves to lower d as epistasis density rises (iso at d=20: 0.00/0.03/0.50 for rho 0.1/0.25/0.5); incompatibilities snowball ~ (d/2)^2 (Orr-Turelli). - NK variant (E12_nk.yaml): parents = hill-climbed local optima; the epistasis wedge — recombination gain flips 0 -> -0.13 and OD rate 0 -> 0.90 as ruggedness K rises. At matched divergence, mergeability is governed by epistasis, the axis no divergence-only ML merge predictor captures. plot_E12.py (3-panel), +7 tests (138 green), README with honest positioning (concedes the empirical phenomenon to Pari 2024 / Zhou 2026 + permutation artefacts to Git Re-Basin; claims the predictive theory + the epistasis wedge). Wired into make layer1. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
47 lines
3.8 KiB
Markdown
47 lines
3.8 KiB
Markdown
# 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/layer1/E12.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/layer1/E12_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.
|