style: remove herald sentences (announcer claudisms)

Nine sentences of the 'The diagnosis comes first.' genus removed or
folded — announcements that add nothing over the sentence that follows:
'This population also reproduces.', 'One consequence of drift deserves
its genetic name.', 'It is also only the entry point.' (folded), 'The
question this paper addresses is...', 'I begin with a result...', 'The
engineering point survives the definition:' (rewritten plain), 'The
supported conclusion, stated conditionally:', 'The strongest constraint
comes from...' (inverted to content-first), 'The framework's reading of
that trajectory is concrete.'. Functional enumerator colons and content-
bearing topic sentences kept. 19 pp rebuild clean.

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

paper/pnas/body.tex

@@ -10,19 +10,19 @@ AI development increasingly resembles a population process. Models are specialis
 
 \section*{Introduction}
 
-Machine learning has become a population-scale phenomenon. Public repositories host millions of models (Hugging Face alone grew past three million by 2026), and these are not independent creations: the overwhelming majority are fine-tunes, distillations, or merges of a small number of foundation models, forming large family trees whose lineage structure, inherited traits, and mutation dynamics are already being mapped with explicitly phylogenetic methods (1--3). This population also reproduces. Weight-space \emph{model merging}, the direct combination of trained parents into a new model, is mainstream community practice with standard tooling and thousands of hybrid checkpoints, including leaderboard-topping ones (4--7), and the engineering literature describes it in evolutionary vocabulary: ``crossover,'' ``mutation,'' ``mate choice,'' populations of merging models that climb benchmarks (5, 8--10).
+Machine learning has become a population-scale phenomenon. Public repositories host millions of models (Hugging Face alone grew past three million by 2026), and these are not independent creations: the overwhelming majority are fine-tunes, distillations, or merges of a small number of foundation models, forming large family trees whose lineage structure, inherited traits, and mutation dynamics are already being mapped with explicitly phylogenetic methods (1--3). Weight-space \emph{model merging}, the direct combination of trained parents into a new model, is mainstream community practice with standard tooling and thousands of hybrid checkpoints, including leaderboard-topping ones (4--7), and the engineering literature describes it in evolutionary vocabulary: ``crossover,'' ``mutation,'' ``mate choice,'' populations of merging models that climb benchmarks (5, 8--10).
 
 The generations are coupled through data as well as through weights. Successive models increasingly learn from model output rather than from fresh human experience: frontier alignment pipelines are now predominantly synthetic (over 98\% in documented cases; 11, 12), self-generated instruction data seeds whole lineages of descendants (13), a large and growing share of the public web is machine-generated or machine-translated text (14, 15), and the stock of human text is projected to be exhausted by frontier training within this decade (16). Meanwhile persistent multi-agent systems and emerging agent economies put many interacting models into sustained contact (17--20). A population whose members inherit from one another, recombine, and retransmit under these conditions is an evolving population in the technical sense, and that observation motivates this work. Here I transfer the quantitative framework of the branch of biology built for exactly this situation, the population genetics of the evolution of sex, and use it to treat multigenerational model populations as systems whose inheritance, diversity, and compatibility can be measured, predicted, and managed.
 
-The diagnosis comes first. Training each generation of a model on the previous generation's output degrades it (\emph{model collapse}): rare capabilities vanish first, and the lineage drifts toward its own most common behaviour (21). That degradation is, mathematically, \emph{genetic drift}, the loss of rare variants that any finite population suffers when each generation is a finite sample of the last. The identification has been made repeatedly and independently: for sequential inference chains before deep learning (22), for language-model text ecosystems (23), as a closed-form first-extinction law placing collapse onset at the Wright--Fisher first-extinction time (24), and in quantitative-genetic form for self-consuming diffusion models (25). A diagnosis reached so often, from such different starting points, marks population genetics as the natural mathematics of the setting. It is also only the entry point. Population genetics is not, at heart, a theory of decay; it is a theory of the mechanisms that maintain and build populations despite decay (immigration, recombination, selection, population structure) and of where those mechanisms reach their limits. This paper develops that fuller structure for model populations: the arc from drift through its remedies to its limit, reproductive isolation, carried as one framework from closed forms to trained networks to language models.
+Training each generation of a model on the previous generation's output degrades it (\emph{model collapse}): rare capabilities vanish first, and the lineage drifts toward its own most common behaviour (21). That degradation is, mathematically, \emph{genetic drift}, the loss of rare variants that any finite population suffers when each generation is a finite sample of the last. The identification has been made repeatedly and independently: for sequential inference chains before deep learning (22), for language-model text ecosystems (23), as a closed-form first-extinction law placing collapse onset at the Wright--Fisher first-extinction time (24), and in quantitative-genetic form for self-consuming diffusion models (25). A diagnosis reached so often, from such different starting points, marks population genetics as the natural mathematics of the setting, though only as its entry point: population genetics is not, at heart, a theory of decay; it is a theory of the mechanisms that maintain and build populations despite decay (immigration, recombination, selection, population structure) and of where those mechanisms reach their limits. This paper develops that fuller structure for model populations: the arc from drift through its remedies to its limit, reproductive isolation, carried as one framework from closed forms to trained networks to language models.
 
-The question this paper addresses is what to do with that diagnosis. An operator of a model population faces recurring decisions for which there is no principled guidance: 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? In practice these are settled by convention and by trial-and-error search. They are also, recognisably, machine learning's oldest problem at a new scale: \emph{continual learning}, the struggle to acquire new abilities without losing old ones (26, 27), transposed from a single network to a population whose members inherit from one another. Population genetics, I will argue, prices these decisions. Table 1 summarises the correspondences on which the argument runs; the sections that follow develop them from closed-form theory to experiments in trained networks and language models.
+An operator of a model population faces recurring decisions for which there is no principled guidance: 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? In practice these are settled by convention and by trial-and-error search. They are also, recognisably, machine learning's oldest problem at a new scale: \emph{continual learning}, the struggle to acquire new abilities without losing old ones (26, 27), transposed from a single network to a population whose members inherit from one another. Population genetics, I will argue, prices these decisions. Table 1 summarises the correspondences on which the argument runs; the sections that follow develop them from closed-form theory to experiments in trained networks and language models.
 
 \section*{The minimal model, and where its exactness ends}
 
 Knowledge is modelled as a distribution \texttt{p\_t} over \texttt{K} discrete items (capabilities, facts, modes of behaviour), with a fixed true distribution \texttt{p*} whose rare tail carries the knowledge most at risk. One generation is: *draw \texttt{n} samples from the parent's distribution, optionally mix in \texttt{m} verified real samples (``grounding'', \texttt{g = m/(n+m)}), and refit the child\emph{. In this minimal inheritance model the resampling step }is* the Wright--Fisher process: the same equations, which I exploit as an engineering gate: the simulator reproduces the classical closed forms (heterozygosity decay \texttt{E[H\_t] = H\_0(1 − 1/n)\textasciicircum{}t}; the exact immigration--drift equilibrium; the closed-form multi-teacher union) to within 0.5\%, and these are standing tests in the codebase, not one-off checks.
 
-The boundary of the exactness matters, and I measured it rather than assumed it. Real training adds approximation, optimisation noise, and inductive bias, and when trained networks are fit against the exact drift null they deviate in \emph{opposite, architecture-specific} directions: a smoothing recurrent network resists collapse (keeping spurious variants alive), while a sharpening image generator accelerates it. A one-parameter \emph{learning kernel} (a smoothing knob and a sharpening knob on the refit) reproduces both. Throughout, a real learner is therefore treated as Wright--Fisher \emph{plus a signed, measurable estimator bias}, and the drift signs (rare-first loss; the grounding response) survived that bias in every architecture I tested, including a convolutional VAE retrained on its own generated digits, where the dry lineage collapses to a single blurred digit class while 10\% grounding holds all thirty modes (Fig. 1). One consequence of drift deserves its genetic name. Retraining on a single parent is \emph{asexual reproduction}, and sustained loss under it carries the defining consequence of \emph{Muller's ratchet} (28): once every copy of a rare capability is gone from all parents and sources, no recombination can rebuild it, so remedies must act before fixation-by-loss (a consequence-level correspondence; the minimal model lacks the ratchet's recurrent-mutation driver).
+The boundary of the exactness matters, and I measured it rather than assumed it. Real training adds approximation, optimisation noise, and inductive bias, and when trained networks are fit against the exact drift null they deviate in \emph{opposite, architecture-specific} directions: a smoothing recurrent network resists collapse (keeping spurious variants alive), while a sharpening image generator accelerates it. A one-parameter \emph{learning kernel} (a smoothing knob and a sharpening knob on the refit) reproduces both. Throughout, a real learner is therefore treated as Wright--Fisher \emph{plus a signed, measurable estimator bias}, and the drift signs (rare-first loss; the grounding response) survived that bias in every architecture I tested, including a convolutional VAE retrained on its own generated digits, where the dry lineage collapses to a single blurred digit class while 10\% grounding holds all thirty modes (Fig. 1). Retraining on a single parent is \emph{asexual reproduction}, and sustained loss under it carries the defining consequence of \emph{Muller's ratchet} (28): once every copy of a rare capability is gone from all parents and sources, no recombination can rebuild it, so remedies must act before fixation-by-loss (a consequence-level correspondence; the minimal model lacks the ratchet's recurrent-mutation driver).
 
 \textbf{Table 1.} The dictionary. Each correspondence is stated with the level of support it currently has (exact = closed form in the minimal model; empirical = measured in trained systems; hypothesis = stated with a falsifier, untested or unconfirmed). The full claim-by-claim ledger with assumptions and known limits is SI Appendix, Table S1.
 
@@ -45,7 +45,7 @@ Selection on a fitness function & Verifier-anchored selection (``reality that ca
 
 \subsection*{Grounding is immigration: cheap, with a floor}
 
-In the minimal model, grounding from a fixed real source is \emph{immigration} into a drifting population (29--31), and the equilibrium diversity has a closed form the simulator matches exactly. That equilibrium is \emph{smooth} in the grounding fraction (there is no phase transition in aggregate diversity), so the practical number is an operational threshold, and I define it as such: under the tested population size and Zipf source distribution, \texttt{g \(\approx\) 0.05} retained most (\(\geq\)95\%) of equilibrium diversity indefinitely, with the required fraction depending on sample size, source distribution, and the chosen retention target (dependencies in SI). The engineering point survives the definition: verified real data is cheap insurance at fractions far below one. But the same analysis yields a floor the field's average-loss framing misses: under unstratified sampling from the source, a capability of rarity \texttt{p} appears in a real-data batch of size \texttt{m} with probability \texttt{1 − e\textasciicircum{}{−m\(\cdot\)p}}, so \texttt{m\(\cdot\)p \(\approx\) 1} marks roughly a 63\% chance of one example per batch: a soft observation floor, with higher confidence priced accordingly, and with distinct consequences for continuous retention, stationary occupancy, and reintroduction after loss (immigration can restore an absent item; SI separates these). Protecting the rarest knowledge under unstratified grounding is therefore priced per item at cost \texttt{\(\propto\) 1/p}; targeted or stratified sampling changes that cost, and recombination can recover rare capabilities \emph{that are still retained across complementary parents} (next section). In trained networks the \emph{sign} of the grounding response transfers everywhere I looked, with two deviations, both traced to the estimator bias above: sharp thresholds soften, and support-counting metrics decouple from truth (forward-KL is the operative collapse metric for a smoothing learner). On real images (Fig. 1B), dry self-training collapses a convolutional VAE to one mode while \textasciitilde{}10\% grounding holds all thirty (the trained model needs roughly twice the exact-operator fraction, the measured price of the estimator bias).
+In the minimal model, grounding from a fixed real source is \emph{immigration} into a drifting population (29--31), and the equilibrium diversity has a closed form the simulator matches exactly. That equilibrium is \emph{smooth} in the grounding fraction (there is no phase transition in aggregate diversity), so the practical number is an operational threshold, and I define it as such: under the tested population size and Zipf source distribution, \texttt{g \(\approx\) 0.05} retained most (\(\geq\)95\%) of equilibrium diversity indefinitely, with the required fraction depending on sample size, source distribution, and the chosen retention target (dependencies in SI). Verified real data remains, on any of these definitions, cheap insurance at fractions far below one. But the same analysis yields a floor the field's average-loss framing misses: under unstratified sampling from the source, a capability of rarity \texttt{p} appears in a real-data batch of size \texttt{m} with probability \texttt{1 − e\textasciicircum{}{−m\(\cdot\)p}}, so \texttt{m\(\cdot\)p \(\approx\) 1} marks roughly a 63\% chance of one example per batch: a soft observation floor, with higher confidence priced accordingly, and with distinct consequences for continuous retention, stationary occupancy, and reintroduction after loss (immigration can restore an absent item; SI separates these). Protecting the rarest knowledge under unstratified grounding is therefore priced per item at cost \texttt{\(\propto\) 1/p}; targeted or stratified sampling changes that cost, and recombination can recover rare capabilities \emph{that are still retained across complementary parents} (next section). In trained networks the \emph{sign} of the grounding response transfers everywhere I looked, with two deviations, both traced to the estimator bias above: sharp thresholds soften, and support-counting metrics decouple from truth (forward-KL is the operative collapse metric for a smoothing learner). On real images (Fig. 1B), dry self-training collapses a convolutional VAE to one mode while \textasciitilde{}10\% grounding holds all thirty (the trained model needs roughly twice the exact-operator fraction, the measured price of the estimator bias).
 
 \begin{figure*}[p]\centering  % fig1
 \includegraphics[width=\textwidth]{figs/fig1.pdf}
@@ -54,7 +54,7 @@ In the minimal model, grounding from a fixed real source is \emph{immigration} i
 
 \subsection*{Recombination: a conservation law, its operators, and offspring that exceed every parent}
 
-The largest returns from the transfer concern merging. I begin with a result about the most common operator, stated with its assumptions. \textbf{Proposition (blending inheritance, rare-item regime).} Let K parents independently retain a rare item (mass \texttt{p} when retained), and let the child draw \texttt{n} samples either from one parent chosen at random or from the \emph{mean of the parents' output distributions}. Expected item mass is identical under the two schemes; and in the rare-item regime \texttt{n\(\cdot\)p/K \(\ll\) 1}, where per-item survival is first-order in sampled mass, expected \emph{survival} is also identical: the 1/K dilution of averaging cancels the K-parent union gain to first order, so in this regime adding parents through the output-mean does not increase expected tail retention. Two boundaries: outside that regime, survival is a convex function of mixed mass, so the variance reduction from averaging can \emph{reduce} extinction relative to a randomly chosen single parent; the cancellation is a first-order result about rare items, not a universal impossibility; and the contrasting union operator (keep each item's strongest source, then renormalise, which itself redistributes mass and presupposes a verifier or oracle to identify the strongest source) increases expected retention with K in all regimes in the minimal model. The practically important operators, \emph{weight averaging} (a nonlinear network's weight-mean does not compute its parents' output-mean) and \emph{routing among intact specialists} (32) (different storage and inference budgets from a single child), are its empirical cousins, and the measured bridge is a \emph{headroom rule}, stated qualitatively: in language models, union-preserving operators beat the weight-average where that average falls short of attainable performance, and add nothing where it does not (easy-versus-hard contrasts at two scales; a quantitative form of the relationship is untested). On easy tasks a capable base's average is already at ceiling and refinements add nothing; on hard tasks the average dilutes a fragile specialist below even the best single parent and routing wins by a wide margin (Fig. 6A--B).
+The largest returns from the transfer concern merging. \textbf{Proposition (blending inheritance, rare-item regime).} Let K parents independently retain a rare item (mass \texttt{p} when retained), and let the child draw \texttt{n} samples either from one parent chosen at random or from the \emph{mean of the parents' output distributions}. Expected item mass is identical under the two schemes; and in the rare-item regime \texttt{n\(\cdot\)p/K \(\ll\) 1}, where per-item survival is first-order in sampled mass, expected \emph{survival} is also identical: the 1/K dilution of averaging cancels the K-parent union gain to first order, so in this regime adding parents through the output-mean does not increase expected tail retention. Two boundaries: outside that regime, survival is a convex function of mixed mass, so the variance reduction from averaging can \emph{reduce} extinction relative to a randomly chosen single parent; the cancellation is a first-order result about rare items, not a universal impossibility; and the contrasting union operator (keep each item's strongest source, then renormalise, which itself redistributes mass and presupposes a verifier or oracle to identify the strongest source) increases expected retention with K in all regimes in the minimal model. The practically important operators, \emph{weight averaging} (a nonlinear network's weight-mean does not compute its parents' output-mean) and \emph{routing among intact specialists} (32) (different storage and inference budgets from a single child), are its empirical cousins, and the measured bridge is a \emph{headroom rule}, stated qualitatively: in language models, union-preserving operators beat the weight-average where that average falls short of attainable performance, and add nothing where it does not (easy-versus-hard contrasts at two scales; a quantitative form of the relationship is untested). On easy tasks a capable base's average is already at ceiling and refinements add nothing; on hard tasks the average dilutes a fragile specialist below even the best single parent and routing wins by a wide margin (Fig. 6A--B).
 
 The generative payoff is the \emph{Fisher--Muller effect} (33, 34): recombination assembles, in one offspring, complementary variants that arose in different lineages, producing a genotype fitter than any parent. In the multi-locus model, sexual merging of decorrelated specialists climbs to the global optimum, a genotype no parent held, while the best single parent and the blended average both plateau below (Fig. 2). In real language models the signature replicates under seed replication: merges of three LoRA (35) specialists beat every parent overall (decisively at 7B: 0.87 vs 0.77), and on the sharper worst-family metric the merged models are the only ones competent everywhere, in every seed (Fig. 6A).
 
@@ -85,7 +85,7 @@ Recombination presupposes compatible parents. In biology, lineages pushed far en
 
 In trained networks, the claim must survive a known alternative: merge barriers between independently trained networks are famously \emph{coordinate artefacts}, removable by re-aligning hidden units (40); richer symmetry groups remove more (41), with known failures beyond the shared-data regime (42). I therefore aligned under the composition of permutation matching and exact per-unit rescaling (the unit symmetry group of plain ReLU MLPs, as the search space) and decomposed the barrier (Fig. 5 C and D): two networks trained from different initialisations on the \emph{same} task have a barrier that this alignment removes essentially entirely (residual \(\approx\) 0.001, the aligned merge performing at parent level): coordinate, not functional; two networks trained on \emph{conflicting} label maps have a barrier the same alignment leaves largely unchanged (0.502 \(\rightarrow\) 0.497), with the merged model functionally dead. The tested alignment removes the same-task barrier but leaves the conflict-associated barrier intact, supporting a functional-conflict interpretation without proving optimal alignment: exact recovery of a permuted-and-rescaled copy validates a special case, so the removable share is a lower bound and the residual an upper bound. Sweeping conflict traces the cliff as hybrid fitness, 0.97 \(\rightarrow\) 0.03. The conflict floor itself is information-theoretic (no single model can satisfy contradictory conventions; SI Appendix, Proposition S2), with the framework's role being the \emph{structure around it}: which divergences generate conflict, and what moves the cliff.
 
-The strongest constraint comes from the pre-registered \emph{emergent test}: true BDM incompatibilities are emergent (each lineage's changes harmless alone), so I let children diverge with \emph{no conflicting signal anywhere}, using complementary class specialists and divergent input conventions, to 6.4\(\times\) the base training. No isolation emerged (residual 0.000 throughout); instead the merge \emph{rescued} the two catastrophically-forgetting specialists (parents \(\approx\) 0.50, merge \(\approx\) 0.955, a sustained Fisher--Muller rescue). The same double result appears at the language-model tier (Fig. 5 E and F): conflicting conventions produce \emph{function-specific} hybrid breakdown (the merge scores below both parents on the conflicted function, while a budget-controlled design shows the disjoint skills merge unharmed), and over-training disjoint specialists 1\(\rightarrow\)12 epochs (cf. the merging literature's expert-duration effect; 43) produces no isolation at all --- the merge improves. Across every tier tested, isolation had to be provoked by functional conflict; specialisation alone did not speciate --- a bound on the analogy that sharpens the design rule: what breaks merging is conflicting conventions on shared circuitry, not divergence per se.
+The pre-registered \emph{emergent test} constrains the claim most: true BDM incompatibilities are emergent (each lineage's changes harmless alone), so I let children diverge with \emph{no conflicting signal anywhere}, using complementary class specialists and divergent input conventions, to 6.4\(\times\) the base training. No isolation emerged (residual 0.000 throughout); instead the merge \emph{rescued} the two catastrophically-forgetting specialists (parents \(\approx\) 0.50, merge \(\approx\) 0.955, a sustained Fisher--Muller rescue). The same double result appears at the language-model tier (Fig. 5 E and F): conflicting conventions produce \emph{function-specific} hybrid breakdown (the merge scores below both parents on the conflicted function, while a budget-controlled design shows the disjoint skills merge unharmed), and over-training disjoint specialists 1\(\rightarrow\)12 epochs (cf. the merging literature's expert-duration effect; 43) produces no isolation at all --- the merge improves. Across every tier tested, isolation had to be provoked by functional conflict; specialisation alone did not speciate --- a bound on the analogy that sharpens the design rule: what breaks merging is conflicting conventions on shared circuitry, not divergence per se.
 
 \begin{figure*}[p]\centering  % fig5
 \includegraphics[width=\textwidth]{figs/fig5.pdf}
@@ -96,7 +96,7 @@ The strongest constraint comes from the pre-registered \emph{emergent test}: tru
 
 The framework's prediction-level claim was put to a designed test (Fig. 6C). Thirty-nine parent pairs (13 conditions \(\times\) 3 seeds; rows are not independent --- parents share task-data seeds across conditions, so inference is condition-clustered, and because shared seeds also couple rows \emph{across} conditions I report per-seed and leave-one-seed-out sensitivity alongside) span three axes decorrelated by construction: \emph{conflict} (contradictory conventions on shared prompts, private budgets fixed), \emph{compatible overlap} (the same shared prompts under the same convention --- overlap and volume without conflict), and \emph{duration} (weight divergence with zero conflict). Before merging, six predictors are computed: \emph{confidence-weighted functional conflict} (bilateral confident disagreement on probes drawn blind to where conflict lives --- a proposed proxy for merge-relevant interactions, motivated by the observation that raw disagreement counts harmless complementation, one parent merely ignorant, as conflict), raw disagreement, gradient alignment at the shared base (44), LoRA-delta cosine and distance, and a cross-task performance baseline. The pre-registered outcome is the merge penalty against oracle parent potential (the hybrid-load analogue), also reported against best- and mean-parent references because the predictor ordering is sensitive to that choice.
 
-The supported conclusion, stated conditionally: across this controlled grid, pre-merge functional disagreement predicted merge penalties (clustered bootstrap CIs excluding zero; held-out leave-one-condition-out \(\rho\) \(\approx\) 0.35--0.40), whereas LoRA-delta cosine and L2 showed no statistically detectable association; gradient alignment carried intermediate signal. Head-to-head predictor differences are not individually significant at this sample size; only these baselines were tested; and with three seeds, uncertainty about seed generalisation remains substantial --- though the seed sensitivity favours the functional measures (per-seed \(\rho\) stable at +0.37 to +0.53 in each seed alone, geometry \(\approx\) 0 in every seed, gradient alignment seed-unstable at −0.11 to −0.55). Two further results bound the claim: the initial two-axis grid's best predictor was delta-cosine (\(\rho\) = +0.60) --- an overlap artefact that the compatible-overlap control was added to expose, and did (collapse to +0.03); and the pre-registered internal prediction that confidence weighting would beat raw disagreement \emph{failed} (they are statistically indistinguishable as rank predictors), so the present evidence favours functional disagreement generally, not the DMI-specific refinement. The framework motivated the measurement and the controls; their success does not validate the specifically population-genetic mechanism. Whether the prediction improves a budget-matched operator choice, and whether it generalises to unfamiliar conflict structures and real task pairs, are the experiment's open front.
+Across this controlled grid, pre-merge functional disagreement predicted merge penalties (clustered bootstrap CIs excluding zero; held-out leave-one-condition-out \(\rho\) \(\approx\) 0.35--0.40), whereas LoRA-delta cosine and L2 showed no statistically detectable association; gradient alignment carried intermediate signal. Head-to-head predictor differences are not individually significant at this sample size; only these baselines were tested; and with three seeds, uncertainty about seed generalisation remains substantial --- though the seed sensitivity favours the functional measures (per-seed \(\rho\) stable at +0.37 to +0.53 in each seed alone, geometry \(\approx\) 0 in every seed, gradient alignment seed-unstable at −0.11 to −0.55). Two further results bound the claim: the initial two-axis grid's best predictor was delta-cosine (\(\rho\) = +0.60) --- an overlap artefact that the compatible-overlap control was added to expose, and did (collapse to +0.03); and the pre-registered internal prediction that confidence weighting would beat raw disagreement \emph{failed} (they are statistically indistinguishable as rank predictors), so the present evidence favours functional disagreement generally, not the DMI-specific refinement. The framework motivated the measurement and the controls; their success does not validate the specifically population-genetic mechanism. Whether the prediction improves a budget-matched operator choice, and whether it generalises to unfamiliar conflict structures and real task pairs, are the experiment's open front.
 
 \begin{figure*}[p]\centering  % fig6
 \includegraphics[width=\textwidth]{figs/fig6.pdf}
@@ -129,7 +129,7 @@ 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 I trust, and institutionalising that anchor (verification, replication, and challenge among models) is the society-level problem this paper poses but does 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 the 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 (43) and the small-scale null here 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.
+\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. If coming model generations remain what the 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 (43) and the small-scale null here 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}
 

paper/pnas/main.md

@@ -47,8 +47,8 @@ millions of models (Hugging Face alone grew past three million by 2026), and the
 independent creations: the overwhelming majority are fine-tunes, distillations, or merges of a small
 number of foundation models, forming large family trees whose lineage structure, inherited traits,
 and mutation dynamics are already being mapped with explicitly phylogenetic methods (1–3).
-This population also reproduces. Weight-space *model merging*, the direct combination of trained
+Weight-space *model merging*, the direct combination of trained parents into a new model, is
-parents into a new model, is mainstream community practice with standard tooling and thousands of
+mainstream community practice with standard tooling and thousands of
 hybrid checkpoints, including leaderboard-topping ones (4–7), and the engineering literature
 describes it in evolutionary vocabulary: "crossover," "mutation," "mate choice," populations of
 merging models that climb benchmarks (5, 8–10).
@@ -66,7 +66,7 @@ transfer the quantitative framework of the branch of biology built for exactly t
 population genetics of the evolution of sex, and use it to treat multigenerational model populations
 as systems whose inheritance, diversity, and compatibility can be measured, predicted, and managed.
 
-The diagnosis comes first. Training each generation of a model on the previous generation's output
+Training each generation of a model on the previous generation's output
 degrades it (*model collapse*): rare capabilities vanish first, and the lineage drifts toward its own
 most common behaviour (21). That degradation is, mathematically, *genetic drift*, the loss of rare
 variants that any finite population suffers when each generation is a finite sample of the last. The
@@ -74,15 +74,14 @@ identification has been made repeatedly and independently: for sequential infere
 learning (22), for language-model text ecosystems (23), as a closed-form first-extinction law placing
 collapse onset at the Wright–Fisher first-extinction time (24), and in quantitative-genetic form for
 self-consuming diffusion models (25). A diagnosis reached so often, from such different starting
-points, marks population genetics as the natural mathematics of the setting. It is also only the entry
+points, marks population genetics as the natural mathematics of the setting, though only as its entry
-point. Population genetics is not, at heart, a theory of decay; it is a theory of the mechanisms that
+point: population genetics is not, at heart, a theory of decay; it is a theory of the mechanisms that
 maintain and build populations despite decay (immigration, recombination, selection, population
 structure) and of where those mechanisms reach their limits. This paper develops that fuller structure
 for model populations: the arc from drift through its remedies to its limit, reproductive isolation,
 carried as one framework from closed forms to trained networks to language models.
 
-The question this paper addresses is what to do with that diagnosis. An operator of a model
+An operator of a model population faces recurring decisions for which there is no principled guidance: how much verified
-population faces recurring decisions for which there is no principled guidance: 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? In practice these are settled by
@@ -113,8 +112,7 @@ refit) reproduces both. Throughout, a real learner is therefore treated as Wrigh
 estimator bias*, and the drift signs (rare-first loss; the grounding response)
 survived that bias in every architecture I tested, including a convolutional VAE retrained on its own
 generated digits, where the dry lineage collapses to a single blurred digit class while 10% grounding
-holds all thirty modes (Fig. 1). One consequence of drift deserves its genetic name. Retraining on a
+holds all thirty modes (Fig. 1). Retraining on a single parent is *asexual reproduction*, and sustained loss under it carries the defining consequence
-single parent is *asexual reproduction*, and sustained loss under it carries the defining consequence
 of *Muller's ratchet* (28): once every copy of a rare capability is gone from all parents and sources,
 no recombination can rebuild it, so remedies must act before fixation-by-loss (a consequence-level
 correspondence; the minimal model lacks the ratchet's recurrent-mutation driver).
@@ -146,8 +144,8 @@ In the minimal model, grounding from a fixed real source is *immigration* into a
 practical number is an operational threshold, and I define it as such: under the tested population
 size and Zipf source distribution, `g ≈ 0.05` retained most (≥95%) of equilibrium diversity
 indefinitely, with the required fraction depending on sample size, source distribution, and the
-chosen retention target (dependencies in SI). The engineering point survives the definition: verified
+chosen retention target (dependencies in SI). Verified real data remains, on any of these
-real data is cheap insurance at fractions far below one. But the same analysis yields a floor the field's
+definitions, cheap insurance at fractions far below one. But the same analysis yields a floor the field's
 average-loss framing misses: under unstratified sampling from the source, a capability of rarity `p`
 appears in a real-data batch of size `m` with probability `1 − e^{−m·p}`, so `m·p ≈ 1` marks roughly a
 63% chance of one example per batch: a soft observation floor, with higher confidence priced
@@ -166,8 +164,7 @@ fraction, the measured price of the estimator bias).
 
 ### Recombination: a conservation law, its operators, and offspring that exceed every parent
 
-The largest returns from the transfer concern merging. I begin with a result about the most common
+The largest returns from the transfer concern merging. **Proposition (blending inheritance, rare-item
-operator, stated with its assumptions. **Proposition (blending inheritance, rare-item
 regime).** Let K parents independently retain a rare item (mass `p` when retained), and let the child
 draw `n` samples either from one parent chosen at random or from the *mean of the parents' output
 distributions*. Expected item mass is identical under the two schemes; and in the rare-item regime
@@ -265,7 +262,7 @@ information-theoretic (no single model can satisfy contradictory conventions; SI
 Proposition S2), with the framework's role being the *structure around it*: which divergences
 generate conflict, and what moves the cliff.
 
-The strongest constraint comes from the pre-registered *emergent test*: true BDM incompatibilities are
+The pre-registered *emergent test* constrains the claim most: true BDM incompatibilities are
 emergent (each lineage's changes harmless alone), so I let children diverge with *no conflicting
 signal anywhere*, using complementary class specialists and divergent input conventions, to 6.4× the base
 training. No isolation emerged (residual 0.000 throughout); instead the merge *rescued* the two
@@ -298,7 +295,7 @@ baseline. The pre-registered outcome is the merge penalty against oracle parent
 hybrid-load analogue), also reported against best- and mean-parent references because the predictor
 ordering is sensitive to that choice.
 
-The supported conclusion, stated conditionally: across this controlled grid, pre-merge functional
+Across this controlled grid, pre-merge functional
 disagreement predicted merge penalties (clustered bootstrap CIs excluding zero; held-out
 leave-one-condition-out ρ ≈ 0.35–0.40), whereas LoRA-delta cosine and L2 showed no statistically
 detectable association; gradient alignment carried intermediate signal. Head-to-head predictor
@@ -417,7 +414,7 @@ an evolving population, is also a forecast about where these results matter next
 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
+bases. If coming model generations remain what
 the 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