narrative: make the intellectual contribution explicit

Two insertions answering the editor's implicit questions. Introduction
gains "stated as a problem": the four recurring decisions a model-
population operator cannot currently answer from principle (replay
budget; compose-or-damage; pre-merge detection; separate-vs-consolidate)
and the framework's counterintuitive answers — averaging cancels the
multi-parent benefit exactly in the tail regime; specialisation/
divergence produced no incompatibility anywhere tested while conflicting
conventions always did; weight distance carried no predictive signal
while cheap behavioural disagreement did; and the theory's numbers land
on the replay constants practice converged to independently
(unexpectedness + problem-solved + external check, at reviewer-hardened
calibration). Discussion gains a closing "Outlook: the evolution of
language models": the ecosystem's trajectory is consolidating on exactly
these operators, and the framework's fork is concrete and measurable —
either models stay freely recombinable (one interbreeding population;
levers = per-capability grounding budgets + deliberate diversity) or
long-horizon specialisation at scale begins emergent speciation (a
routed archipelago of diverging lineages), decidable now with the
pre-merge conflict instruments tested here. Design rules tie back to the
posed decisions. 5.2k words, citation invariant intact, 20 pp.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v

paper/pnas/body.tex

@@ -20,6 +20,8 @@ In machine learning's own terms, the problem this frame addresses is the field's
 
 We are explicit about what kind of contribution each claim is, distinguishing \emph{interpretation} (an existing result understood in population-genetic terms), \emph{explanation} (the transferred mechanism accounts for observations existing accounts leave open), and \emph{prediction} (the framework forecasts an unmeasured outcome). The paper is strongest on the first; makes concrete progress on the second (separating merge failures that are coordinate artefacts from those that are functional); and reports a first, bounded step on the third: a controlled predictive test in which pre-merge functional-disagreement measures, chosen by the framework, predicted merge damage on a constructed task grid while the tested weight-geometry baselines showed no detectable association.
 
+Stated as a problem: an operator of a model population today has no principled answer to four recurring decisions. How much verified real data does retraining need before a lineage decays? Will combining two particular models compose their abilities or damage them? Can incompatibility be detected before paying for a failed merge? And when should specialists be kept separate rather than consolidated? Current practice answers these with folklore constants and trial-and-error searches. The framework prices each decision, and several of its answers are not the intuitive ones. Averaging, the default combining operator, cancels the benefit of multiple parents to first order precisely in the regime where that benefit matters most, the rare-capability tail. Specialisation and divergence, widely treated as the threat to mergeability, produced no incompatibility in any regime we tested; conflicting conventions always did. Weight distance, the field's default compatibility signal, carried no detectable predictive signal in our controlled test, while a cheap behavioural measure did. And where the framework's numbers can be checked against settled practice, they land on it: the replay fractions that continual learning converged on empirically sit at the minimal model's threshold.
+
 The correspondences we develop, summarised in Table 1: single-teacher retraining is \emph{asexual reproduction}, and the irreversible arm of its decay shares the defining consequence of \emph{Muller's ratchet} (46): once every copy of a rare capability is gone from all parents and sources, no recombination can rebuild it, which is why remedies must act before fixation-by-loss (a consequence- level correspondence: the minimal model lacks the ratchet's recurrent deleterious-mutation mechanism, so irreversible loss alone does not identify that specific mechanism). Injecting verified real data is \emph{immigration} from a non-drifting source (32, 47, 48). Model merging is \emph{recombination}, and its central payoff, a merged model exceeding every parent, is the \emph{Fisher--Muller effect} (49, 50). Merging entangled skills courts \emph{outbreeding depression}; screening many candidate merges is engineered recombination with unusually flexible parent choice and pre-deployment screening (we use the shorthand \emph{directed sex}); restricting who merges with whom is \emph{population structure}. Merging's hard limit, models too diverged in function to combine, is \emph{reproductive isolation}, for which the Bateson--Dobzhansky--Muller theory of incompatibilities (51, 52) supplies the structure. The nearest precursor to this programme reads sex as an algorithm for mixability in the theory of computation (53), pre-dating model merging; the model-merging literature itself has strong empirical operators (4, 54, 55) and emerging merge-success predictors (56, 57), to which our delta is mechanism: \emph{when and why} failure is coordinate versus functional, and what moves the boundary.
 
 We support the framework at three tiers of evidence, in ascending realism and descending exactness: a \emph{minimal analytic model} validated against closed forms to a fraction of a percent; \emph{small trained networks} (MLPs, recurrent networks, an MNIST image generator) where the operators are measured in real weights; and \emph{language models} (LoRA-specialised Qwen models, 0.5B locally and 7B on a compute cluster) where the claims are tested as signs under seed replication. Negative results are reported with the same prominence as confirmations; they include the failure of an internal pre-registered prediction, a null on emergent speciation that bounds the analogy, and the sensitivity analyses on the predictive test.
@@ -127,7 +129,7 @@ Predictive test & 13 conditions \(\times\) 3 seeds (0.5B) & Merge penalty vs ora
 
 \section*{Discussion}
 
-\textbf{Design rules.} As engineering guidance, the results reduce to rules that an operator of a model population can apply. \emph{Ground every generation} in verified reality --- a few percent retained most diversity in our tested settings --- but price the rarest capabilities individually (observation probability \texttt{1 − e\textasciicircum{}{−m\(\cdot\)p}} per batch under unstratified sampling), consider targeted sampling for the deep tail, and use recombination to recover rare capabilities still retained across complementary parents. \emph{Merge, don't blend, when there is headroom}: keep specialists intact and route, or breed-and-screen candidate merges, whenever the naive average is far from ceiling; plain averaging is adequate only where a strong base has already composed the skills. \emph{Match the operator to entanglement}: merge freely when skills are additive; sparingly, with offspring selection, when they entangle; and expect the champion-optimal mating breadth to narrow as landscapes roughen. \emph{Preserve diversity as a first-class objective}, because selection can only preserve variety that exists, and in the tested society its removal produced a distinct failure mode. \emph{Before merging, measure functional conflict} --- cheap, pre-merge, and in our controlled setting predictive where the tested weight-distance baselines were not; and \emph{do not treat divergence or specialisation alone as evidence of incompatibility} --- in every regime we tested, what broke merging was conflicting conventions on shared circuitry, which is the thing to detect.
+\textbf{Design rules.} As engineering guidance, the results reduce to rules that an operator of a model population can apply, answering the four decisions posed in the Introduction. \emph{Ground every generation} in verified reality --- a few percent retained most diversity in our tested settings --- but price the rarest capabilities individually (observation probability \texttt{1 − e\textasciicircum{}{−m\(\cdot\)p}} per batch under unstratified sampling), consider targeted sampling for the deep tail, and use recombination to recover rare capabilities still retained across complementary parents. \emph{Merge, don't blend, when there is headroom}: keep specialists intact and route, or breed-and-screen candidate merges, whenever the naive average is far from ceiling; plain averaging is adequate only where a strong base has already composed the skills. \emph{Match the operator to entanglement}: merge freely when skills are additive; sparingly, with offspring selection, when they entangle; and expect the champion-optimal mating breadth to narrow as landscapes roughen. \emph{Preserve diversity as a first-class objective}, because selection can only preserve variety that exists, and in the tested society its removal produced a distinct failure mode. \emph{Before merging, measure functional conflict} --- cheap, pre-merge, and in our controlled setting predictive where the tested weight-distance baselines were not; and \emph{do not treat divergence or specialisation alone as evidence of incompatibility} --- in every regime we tested, what broke merging was conflicting conventions on shared circuitry, which is the thing to detect.
 
 \textbf{What this offers continual learning.} Read into the field where these results most directly land: (i) a first-principles account of the \emph{replay ratio}: the field's constants (\(\approx\)1\%, 5\%, 25\%; 28, 29) acquire an equilibrium theory and a sharper prediction, that the required fraction is set by the rarest capability one refuses to lose (the \texttt{1 − e\textasciicircum{}{−m\(\cdot\)p}} law) rather than by average loss, which is testable against published replay sweeps; (ii) a \emph{failure theory for generative replay}: self-generated rehearsal is safe for short horizons and compounds into collapse across generations unless verifier-filtered back into grounding (30--33); (iii) \emph{pre-merge interference prediction with a mechanism}: where the current state of the art fits regressions over candidate metrics (56), the functional-conflict measure arrives at a convergent signal from principle and comes with an operator prescription --- when conflict is high, do not average; route or breed-and-screen; (iv) a candidate \emph{decision rule for the consolidate-versus-stay-modular question} that currently splits the field's practice (keep adapters separate vs merge them; 54--58): union-preserving operators where headroom exists, fusion where the base composes, consolidation as the slow-store step; and (v) \emph{tail monitoring as the leading indicator}: continual-learning evaluation that averages over capabilities hides exactly the losses that drift theory says come first and, past a threshold, become irreversible. On that last point we note the standing objection that apparent forgetting can be skewed task-inference over latent capability rather than erasure (66); our irreversibility results concern oracle-measured behavioural distributions, and distinguishing latent from extinct capability at language-model scale is an open experiment whose outcome would be decisive for both readings.
 
@@ -135,6 +137,8 @@ Predictive test & 13 conditions \(\times\) 3 seeds (0.5B) & Merge penalty vs ora
 
 \textbf{Limits and open problems.} The demonstrations are deliberately small: exact where small is a virtue, sign-level and seed-replicated at the language-model tier, on constructed task families with a trivially separable router and one model lineage (Qwen, 0.5B--7B). The composed society has not been built at language-model scale. The predictive test's next bars, in order of value: generalisation to \emph{unfamiliar} conflict structures and real task pairs; a demonstrably better \emph{budget-matched} merging decision; then scale replication. Beyond engineering, the framework's hardest open problem is the fitness function itself: selection optimises what is measured, and for knowledge systems the persuasive and the true compete --- grounding against a reality that can refuse is the only anchor we trust, and institutionalising that anchor (verification, replication, and challenge among models) is the society-level problem we pose but do not solve. What biology receives in return is a new model system: populations of learners where every genotype, environment, and mating decision is observable and manipulable --- where the evolution of sex can be studied with interventions (unbounded parents, offspring preview, directed mating) that no living system permits.
 
+\textbf{Outlook: the evolution of language models.} The Introduction's premise, that the model ecosystem is an evolving population, is also a forecast about where these results matter next. Language-model development is consolidating around exactly the operators studied here: synthetic-data flywheels (inheritance), merging and routing of specialist fine-tunes (recombination and population structure), verifier-gated data pipelines (grounded selection), and periodic consolidation of adapters into new bases. The framework's reading of that trajectory is concrete. If coming model generations remain what our tested regimes found, freely recombinable in the absence of conflicting conventions, then the ecosystem evolves as one interbreeding population, and the levers that matter are grounding budgets priced per rare capability and diversity preserved deliberately. If instead long-horizon specialisation at scale begins to produce emergent incompatibility, as the expert-training-duration observations hint (65) and our small-scale null does not rule out, then lineages will begin to speciate, and the ecosystem's future is a set of diverging species connected by routing rather than by merging. Which of the two it will be is measurable now, with the pre-merge conflict instruments this paper tested.
+
 \section*{Materials and Methods}
 
 \textbf{Analytic tier.} Pure NumPy/SciPy Wright--Fisher simulator over \texttt{K}-item distributions (knowledge as \texttt{p\_t}; Zipf-tailed truth \texttt{p*}; drift--grounding--refit generations), extended with a learning kernel (smoothing/sharpening refit), multi-locus genotypes on additive and Kauffman NK landscapes, n-parent crossover, and finite-population society loops. All parameters live in per-experiment YAML configs; every run derives all randomness from one master seed (\texttt{SeedSequence.spawn}) and is bitwise reproducible; scientific-validation tests assert the closed forms (heterozygosity decay, immigration equilibrium, closed-form union) to <0.5\% and run in CI with 151 further correctness tests.

paper/pnas/main.md

@@ -114,6 +114,20 @@ predictive test in which pre-merge functional-disagreement measures, chosen by t
 predicted merge damage on a constructed task grid while the tested weight-geometry baselines showed
 no detectable association.
 
+Stated as a problem: an operator of a model population today has no principled answer to four
+recurring decisions. How much verified real data does retraining need before a lineage decays?
+Will combining two particular models compose their abilities or damage them? Can incompatibility be
+detected before paying for a failed merge? And when should specialists be kept separate rather than
+consolidated? Current practice answers these with folklore constants and trial-and-error searches.
+The framework prices each decision, and several of its answers are not the intuitive ones. Averaging,
+the default combining operator, cancels the benefit of multiple parents to first order precisely in
+the regime where that benefit matters most, the rare-capability tail. Specialisation and divergence,
+widely treated as the threat to mergeability, produced no incompatibility in any regime we tested;
+conflicting conventions always did. Weight distance, the field's default compatibility signal, carried
+no detectable predictive signal in our controlled test, while a cheap behavioural measure did. And
+where the framework's numbers can be checked against settled practice, they land on it: the replay
+fractions that continual learning converged on empirically sit at the minimal model's threshold.
+
 The correspondences we develop, summarised in Table 1: single-teacher retraining is *asexual
 reproduction*, and the irreversible arm of its decay shares the defining consequence of *Muller's
 ratchet* (46): once every copy of a rare capability is gone from all parents and sources, no
@@ -377,7 +391,7 @@ are the experiment's open front.
 ## Discussion
 
 **Design rules.** As engineering guidance, the results reduce to rules that an operator of a model
-population can apply. *Ground every generation* in verified reality — a few percent retained most diversity in our tested
+population can apply, answering the four decisions posed in the Introduction. *Ground every generation* in verified reality — a few percent retained most diversity in our tested
 settings — but price the rarest capabilities individually (observation probability `1 − e^{−m·p}` per
 batch under unstratified sampling), consider targeted sampling for the deep tail, and use
 recombination to recover rare capabilities still retained across complementary parents. *Merge, don't blend, when there is headroom*: keep specialists
@@ -439,6 +453,21 @@ system: populations of learners where every genotype, environment, and mating de
 and manipulable — where the evolution of sex can be studied with interventions (unbounded parents,
 offspring preview, directed mating) that no living system permits.
 
+**Outlook: the evolution of language models.** The Introduction's premise, that the model ecosystem is
+an evolving population, is also a forecast about where these results matter next. Language-model
+development is consolidating around exactly the operators studied here: synthetic-data flywheels
+(inheritance), merging and routing of specialist fine-tunes (recombination and population structure),
+verifier-gated data pipelines (grounded selection), and periodic consolidation of adapters into new
+bases. The framework's reading of that trajectory is concrete. If coming model generations remain what
+our tested regimes found, freely recombinable in the absence of conflicting conventions, then the
+ecosystem evolves as one interbreeding population, and the levers that matter are grounding budgets
+priced per rare capability and diversity preserved deliberately. If instead long-horizon
+specialisation at scale begins to produce emergent incompatibility, as the expert-training-duration
+observations hint (65) and our small-scale null does not rule out, then lineages will begin to
+speciate, and the ecosystem's future is a set of diverging species connected by routing rather than by
+merging. Which of the two it will be is measurable now, with the pre-merge conflict instruments this
+paper tested.
+
 ## Materials and Methods
 
 **Analytic tier.** Pure NumPy/SciPy Wright–Fisher simulator over `K`-item distributions (knowledge as