voice: first-person singular for single authorship

All 37 first-person-plural instances converted: 'I' where the author
acts or judges (I transfer, I measured, I aligned, to my knowledge, the
only anchor I trust — 18 instances, ~one per 260 words), impersonal
constructions elsewhere (the simulator, the tested settings, this paper
poses). 'What is borrowed and what is ours' -> 'what is new'; 'Ours is
the framework-level synthesis' -> 'New here is'. Reference titles
containing 'we' untouched. 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

@@ -1,10 +1,10 @@
 \section*{Significance statement}
 
-Artificial intelligence increasingly consists of populations of models rather than single systems. Models are fine-tuned from common ancestors, trained on data that earlier models generated, and combined by weight merging. These practices couple model generations the way reproduction couples biological generations, and they raise the same question: how does a population retain and accumulate abilities over time? We transfer the population genetics of sexual reproduction to this setting and test it in simulations, small neural networks, and language models. The framework recasts continual learning at the population scale and yields design rules: how much real data retraining requires, when to combine models, when to keep them separate, and how to anticipate a failed combination before making it.
+Artificial intelligence increasingly consists of populations of models rather than single systems. Models are fine-tuned from common ancestors, trained on data that earlier models generated, and combined by weight merging. These practices couple model generations the way reproduction couples biological generations, and they raise the same question: how does a population retain and accumulate abilities over time? I transfer the population genetics of sexual reproduction to this setting and test it in simulations, small neural networks, and language models. The framework recasts continual learning at the population scale and yields design rules: how much real data retraining requires, when to combine models, when to keep them separate, and how to anticipate a failed combination before making it.
 
 \section*{Abstract}
 
-AI development increasingly resembles a population process. Models are specialised, retrained on model output, and recombined by weight merging, and the practice is described in evolutionary vocabulary with little use of evolutionary theory. We treat multigenerational model populations as systems whose inheritance, diversity, and compatibility must be managed, and we transfer the quantitative framework of the evolution of sex. Its starting point, that training on model output is genetic drift and model collapse its signature, is by now established from several independent directions; we develop the structure that follows from it. In a minimal inheritance model that is exactly Wright--Fisher, and measurably Wright--Fisher plus estimator bias in trained networks, we derive and test remedies. Grounding acts as immigration: a real-data fraction far below one retained most equilibrium diversity, with a per-capability observation floor that makes the rarest knowledge expensive under unstratified sampling. Refitting a child to the mean of its parents' output distributions cancels the multi-parent gain to first order in the rare-item regime; union-preserving operators realise it. Merged language-model specialists exceeded every parent in replicated experiments. Blind recombination fails on rugged task landscapes; screening candidate offspring restores the gain. The optimal mating breadth narrows as skills entangle. Finally, we introduce model speciation: a merge barrier remaining after permutation-and-rescaling alignment tracks functional conflict, isolation did not emerge from compatible specialisation, and in a controlled test pre-merge functional disagreement predicted merge damage while weight-geometry baselines showed no detectable association.
+AI development increasingly resembles a population process. Models are specialised, retrained on model output, and recombined by weight merging, and the practice is described in evolutionary vocabulary with little use of evolutionary theory. I treat multigenerational model populations as systems whose inheritance, diversity, and compatibility must be managed, and transfer the quantitative framework of the evolution of sex. Its starting point, that training on model output is genetic drift and model collapse its signature, is by now established from several independent directions; I develop the structure that follows from it. In a minimal inheritance model that is exactly Wright--Fisher, and measurably Wright--Fisher plus estimator bias in trained networks, I derive and test remedies. Grounding acts as immigration: a real-data fraction far below one retained most equilibrium diversity, with a per-capability observation floor that makes the rarest knowledge expensive under unstratified sampling. Refitting a child to the mean of its parents' output distributions cancels the multi-parent gain to first order in the rare-item regime; union-preserving operators realise it. Merged language-model specialists exceeded every parent in replicated experiments. Blind recombination fails on rugged task landscapes; screening candidate offspring restores the gain. The optimal mating breadth narrows as skills entangle. Finally, I introduce model speciation: a merge barrier remaining after permutation-and-rescaling alignment tracks functional conflict, isolation did not emerge from compatible specialisation, and in a controlled test pre-merge functional disagreement predicted merge damage while weight-geometry baselines showed no detectable association.
 
 \medskip\hrule\medskip
 
@@ -12,17 +12,17 @@ AI development increasingly resembles a population process. Models are specialis
 
 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).
 
-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 we 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 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.
 
-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, we 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.
+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.
 
 \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 we exploit as an engineering gate: our 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.
+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 we 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 we 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). 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).
 
 \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 our 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 we 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 we 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). 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).
 
 \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. We 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. 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 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).
 
@@ -72,7 +72,7 @@ Sex has risks and, for AI, an unfair advantage, both quantified on rugged (epist
 
 \subsection*{The society: grounding, recombination, and diversity make complementary contributions}
 
-Composing the operators (Fig. 4) requires one definitional distinction first. In the inheritance model, grounding is \emph{grounded inheritance}: external samples added to the reproduction process (the data channel). In the society model, grounding is \emph{grounded evaluation}: selection weights true fitness against conformity to the population's own consensus, \texttt{g}\(\cdot\)true-fitness + (1−g)\(\cdot\)conformity, the analogue of scoring models by the crowd's approval (the fitness channel). These are related design ideas, since both couple the lineage to a non-drifting external signal, but they are different operators, and we name them separately. In the tested society (a finite agent population on a rugged NK landscape), a four-arm ablation separates the failure modes: the full system (grounded evaluation + directed recombination + diversity-preserving selection (37)) climbs to near the global optimum while keeping its specialists; removing grounded evaluation converges the population confidently on an unfit consensus (self-consumption); removing recombination strands it on local optima; removing diversity converges it prematurely to a worse answer. Each removal fails differently; the three implementations make complementary contributions \emph{under the tested conditions}; general joint necessity is not established (alternative mutation, restart, archive, or selection schemes could alter the picture). At language-model scale this composed loop remains unbuilt; it is the paper's largest stated gap.
+Composing the operators (Fig. 4) requires one definitional distinction first. In the inheritance model, grounding is \emph{grounded inheritance}: external samples added to the reproduction process (the data channel). In the society model, grounding is \emph{grounded evaluation}: selection weights true fitness against conformity to the population's own consensus, \texttt{g}\(\cdot\)true-fitness + (1−g)\(\cdot\)conformity, the analogue of scoring models by the crowd's approval (the fitness channel). These are related design ideas, since both couple the lineage to a non-drifting external signal, but they are different operators, and I name them separately. In the tested society (a finite agent population on a rugged NK landscape), a four-arm ablation separates the failure modes: the full system (grounded evaluation + directed recombination + diversity-preserving selection (37)) climbs to near the global optimum while keeping its specialists; removing grounded evaluation converges the population confidently on an unfit consensus (self-consumption); removing recombination strands it on local optima; removing diversity converges it prematurely to a worse answer. Each removal fails differently; the three implementations make complementary contributions \emph{under the tested conditions}; general joint necessity is not established (alternative mutation, restart, archive, or selection schemes could alter the picture). At language-model scale this composed loop remains unbuilt; it is the paper's largest stated gap.
 
 \begin{figure*}[p]\centering  % fig4
 \includegraphics[width=\textwidth]{figs/fig4.pdf}
@@ -81,11 +81,11 @@ Composing the operators (Fig. 4) requires one definitional distinction first. In
 
 \subsection*{The limit of sex: model speciation}
 
-Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become separate species (\emph{reproductive isolation}) through Bateson--Dobzhansky--Muller incompatibilities (38, 39): changes harmless on their own background but deleterious in combination. A merged model is exactly the exposed hybrid. We built the analytic model (Fig. 5A): hybrid fitness tracks the parents while compatible, then peels off and crashes below the ancestor; the isolation cliff arrives earlier the denser the incompatibilities; and the incompatibility \emph{count} snowballs quadratically with divergence (39). We note that a super-linear count does not by itself entail a sharp performance cliff without the count-to-effect-size link, which the analytic model supplies under its assumptions and any neural test must establish separately.
+Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become separate species (\emph{reproductive isolation}) through Bateson--Dobzhansky--Muller incompatibilities (38, 39): changes harmless on their own background but deleterious in combination. A merged model is exactly the exposed hybrid. I built the analytic model (Fig. 5A): hybrid fitness tracks the parents while compatible, then peels off and crashes below the ancestor; the isolation cliff arrives earlier the denser the incompatibilities; and the incompatibility \emph{count} snowballs quadratically with divergence (39). Note that a super-linear count does not by itself entail a sharp performance cliff without the count-to-effect-size link, which the analytic model supplies under its assumptions and any neural test must establish separately.
 
-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). We 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.
+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 we 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 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.
 
 \begin{figure*}[p]\centering  % fig5
 \includegraphics[width=\textwidth]{figs/fig5.pdf}
@@ -94,7 +94,7 @@ The strongest constraint comes from the pre-registered \emph{emergent test}: tru
 
 \subsection*{A controlled predictive test: functional conflict, measured pre-merge, predicts merge damage}
 
-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 we 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 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.
 
@@ -121,15 +121,15 @@ 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, 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{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 the 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 the 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 tested here, what broke merging was conflicting conventions on shared circuitry, which is the thing to detect.
 
-\textbf{Continual learning at the population scale.} Within a single network, the discipline's remedies for forgetting are this framework's operators writ small. Rehearsal and replay of stored data (26, 27) is grounded inheritance within one lineage, and the replay fractions the field settled on empirically, on the order of 1\% for instruction tuning (45) and 5\% to 25\% by distribution-shift strength in continual pretraining (46), sit where the minimal model's operational threshold lies. \emph{Pseudo-rehearsal}, the replay of a network's own generated samples, proposed as a cure in 1995 (47) and revived as generative replay (48), is precisely the ungrounded null studied here: immigration from a drifting source, benign for one hop, compounding over generations, with verifier-filtering (29, 49) converting it back into grounding. Parameter isolation (50), including frozen-base adapters, which forget far less (51), is engineered decorrelation; complementary-learning-systems consolidation (52--54) is the periodic adapter-into-base merge; the recent turn to merging as a continual-learning mechanism (55--58) applies recombination within one lineage over time, where this paper applies it across lineages; and the observation that rare examples and long-tail knowledge are forgotten first (59--61) is tail extinction seen one model at a time. The mechanisms differ (forgetting is largely deterministic interference, collapse is sampling drift) but the victims and the remedies coincide, and to our knowledge no prior work carries population-genetic formalism into continual learning. Read into that field, the results offer: (i) an equilibrium theory for the replay ratio, with the 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, 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 (29, 47--49); (iii) \emph{pre-merge interference prediction with a mechanism}: where the current state of the art fits regressions over candidate metrics (44), 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 (62); 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.
+\textbf{Continual learning at the population scale.} Within a single network, the discipline's remedies for forgetting are this framework's operators writ small. Rehearsal and replay of stored data (26, 27) is grounded inheritance within one lineage, and the replay fractions the field settled on empirically, on the order of 1\% for instruction tuning (45) and 5\% to 25\% by distribution-shift strength in continual pretraining (46), sit where the minimal model's operational threshold lies. \emph{Pseudo-rehearsal}, the replay of a network's own generated samples, proposed as a cure in 1995 (47) and revived as generative replay (48), is precisely the ungrounded null studied here: immigration from a drifting source, benign for one hop, compounding over generations, with verifier-filtering (29, 49) converting it back into grounding. Parameter isolation (50), including frozen-base adapters, which forget far less (51), is engineered decorrelation; complementary-learning-systems consolidation (52--54) is the periodic adapter-into-base merge; the recent turn to merging as a continual-learning mechanism (55--58) applies recombination within one lineage over time, where this paper applies it across lineages; and the observation that rare examples and long-tail knowledge are forgotten first (59--61) is tail extinction seen one model at a time. The mechanisms differ (forgetting is largely deterministic interference, collapse is sampling drift) but the victims and the remedies coincide, and to my knowledge no prior work carries population-genetic formalism into continual learning. Read into that field, the results offer: (i) an equilibrium theory for the replay ratio, with the 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, 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 (29, 47--49); (iii) \emph{pre-merge interference prediction with a mechanism}: where the current state of the art fits regressions over candidate metrics (44), 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 I note the standing objection that apparent forgetting can be skewed task-inference over latent capability rather than erasure (62); the irreversibility results here 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.
 
-\textbf{What is borrowed and what is ours.} The collapse-as-drift diagnosis is established prior work (21--25); so are the empirical facts that merges can beat parents, that decorrelated parents merge better, and that naive averaging loses to interference-aware or routed merges (4, 63, 64), that model populations can climb (5, 8--10), and that merge success admits ML-native predictors (44, 65), correlational where this framework supplies mechanism; the reading of sex as an algorithm for mixability in the theory of computation (66) anticipated the transfer before model merging existed. Ours is the framework-level synthesis --- inheritance, diversity, and compatibility as managed quantities --- together with: the conservation law for blending inheritance and its operator boundaries; the per-item grounding floor; the society ablation with its complementary failure modes; model speciation as a named, tested question, with the coordinate-versus-functional decomposition under permutation-and-rescaling alignment and the emergent null that bounds it; and the controlled predictive test with its controls. We claim the framework generated these measurements and experiments; we do not claim their outcomes validate a uniquely population-genetic mechanism, and one refinement it proposed was not supported.
+\textbf{What is borrowed and what is new.} The collapse-as-drift diagnosis is established prior work (21--25); so are the empirical facts that merges can beat parents, that decorrelated parents merge better, and that naive averaging loses to interference-aware or routed merges (4, 63, 64), that model populations can climb (5, 8--10), and that merge success admits ML-native predictors (44, 65), correlational where this framework supplies mechanism; the reading of sex as an algorithm for mixability in the theory of computation (66) anticipated the transfer before model merging existed. New here is the framework-level synthesis --- inheritance, diversity, and compatibility as managed quantities --- together with: the conservation law for blending inheritance and its operator boundaries; the per-item grounding floor; the society ablation with its complementary failure modes; model speciation as a named, tested question, with the coordinate-versus-functional decomposition under permutation-and-rescaling alignment and the emergent null that bounds it; and the controlled predictive test with its controls. I claim the framework generated these measurements and experiments; I do not claim that their outcomes validate a uniquely population-genetic mechanism, and one refinement it proposed was not supported.
 
-\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{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 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 (43) 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.
+\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.
 
 \section*{Materials and Methods}
 

paper/pnas/main.md

@@ -10,7 +10,7 @@ Artificial intelligence increasingly consists of populations of models rather th
 Models are fine-tuned from common ancestors, trained on data that earlier models generated, and
 combined by weight merging. These practices couple model generations the way reproduction couples
 biological generations, and they raise the same question: how does a population retain and
-accumulate abilities over time? We transfer the population genetics of sexual reproduction to this
+accumulate abilities over time? I transfer the population genetics of sexual reproduction to this
 setting and test it in simulations, small neural networks, and language models. The framework
 recasts continual learning at the population scale and yields design rules: how much real data
 retraining requires, when to combine models, when to keep them separate, and how to anticipate a
@@ -20,20 +20,20 @@ failed combination before making it.
 
 AI development increasingly resembles a population process. Models are specialised, retrained on
 model output, and recombined by weight merging, and the practice is described in evolutionary
-vocabulary with little use of evolutionary theory. We treat multigenerational model populations as
-systems whose inheritance, diversity, and compatibility must be managed, and we transfer the
+vocabulary with little use of evolutionary theory. I treat multigenerational model populations as
+systems whose inheritance, diversity, and compatibility must be managed, and transfer the
 quantitative framework of the evolution of sex. Its starting point, that training on model output is
 genetic drift and model collapse its signature, is by now established from several independent
-directions; we develop the structure that follows from it. In a minimal
+directions; I develop the structure that follows from it. In a minimal
 inheritance model that is exactly Wright–Fisher, and measurably Wright–Fisher plus estimator bias in
-trained networks, we derive and test remedies. Grounding acts as immigration: a real-data fraction
+trained networks, I derive and test remedies. Grounding acts as immigration: a real-data fraction
 far below one retained most equilibrium diversity, with a per-capability observation floor that
 makes the rarest knowledge expensive under unstratified sampling. Refitting a child to the mean of
 its parents' output distributions cancels the multi-parent gain to first order in the rare-item
 regime; union-preserving operators realise it. Merged language-model specialists exceeded every
 parent in replicated experiments. Blind recombination fails on rugged task landscapes; screening
 candidate offspring restores the gain. The optimal mating breadth narrows as skills entangle.
-Finally, we introduce model speciation: a merge barrier remaining after permutation-and-rescaling
+Finally, I introduce model speciation: a merge barrier remaining after permutation-and-rescaling
 alignment tracks functional conflict, isolation did not emerge from compatible specialisation, and
 in a controlled test pre-merge functional disagreement predicted merge damage while weight-geometry
 baselines showed no detectable association.
@@ -61,7 +61,7 @@ machine-generated or machine-translated text (14, 15), and the stock of human te
 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 we
+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.
@@ -89,7 +89,7 @@ when should specialists be kept separate rather than consolidated? In practice t
 convention and by trial-and-error search. They are also, recognisably, machine learning's oldest
 problem at a new scale: *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, we will argue, prices these decisions. Table 1 summarises the
+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.
 
@@ -99,19 +99,19 @@ Knowledge is modelled as a distribution `p_t` over `K` discrete items (capabilit
 behaviour), with a fixed true distribution `p*` whose rare tail carries the knowledge most at risk.
 One generation is: *draw `n` samples from the parent's distribution, optionally mix in `m` verified
 real samples ("grounding", `g = m/(n+m)`), and refit the child*. In this minimal inheritance model the
-resampling step *is* the Wright–Fisher process: the same equations, which we exploit as an
-engineering gate: our simulator reproduces the classical closed forms (heterozygosity decay
+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
 `E[H_t] = H_0(1 − 1/n)^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 we measured it rather than assumed it. Real training adds
+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 *opposite, architecture-specific* directions: a smoothing recurrent
 network resists collapse (keeping spurious variants alive), while a sharpening image generator
 accelerates it. A one-parameter *learning kernel* (a smoothing knob and a sharpening knob on the
 refit) reproduces both. Throughout, a real learner is therefore treated as Wright–Fisher *plus a signed, measurable
 estimator bias*, and the drift signs (rare-first loss; the grounding response)
-survived that bias in every architecture we tested, including a convolutional VAE retrained on its own
+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 *asexual reproduction*, and sustained loss under it carries the defining consequence
@@ -141,9 +141,9 @@ known limits is SI Appendix, Table S1.
 ### Grounding is immigration: cheap, with a floor
 
 In the minimal model, grounding from a fixed real source is *immigration* into a drifting population
-(29–31), and the equilibrium diversity has a closed form our simulator matches exactly. That equilibrium is
+(29–31), and the equilibrium diversity has a closed form the simulator matches exactly. That equilibrium is
 *smooth* in the grounding fraction (there is no phase transition in aggregate diversity), so the
-practical number is an operational threshold, and we define it as such: under the tested population
+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
@@ -155,7 +155,7 @@ accordingly, and with distinct consequences for continuous retention, stationary
 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 `∝ 1/p`; targeted
 or stratified sampling changes that cost, and recombination can recover rare capabilities *that are
-still retained across complementary parents* (next section). In trained networks the *sign* of the grounding response transfers everywhere we
+still retained across complementary parents* (next section). In trained networks the *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
@@ -166,7 +166,7 @@ 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. We begin with a result about the most common
+The largest returns from the transfer concern merging. I begin with a result about the most common
 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
@@ -224,7 +224,7 @@ data channel). In the society model, grounding is *grounded evaluation*: selecti
 fitness against conformity to the population's own consensus, `g`·true-fitness + (1−g)·conformity,
 the analogue of scoring models by the crowd's approval (the fitness channel). These are related design
 ideas, since both couple the lineage to a non-drifting external signal, but they are different operators,
-and we name them separately. In the tested society (a finite agent population on a rugged NK
+and I name them separately. In the tested society (a finite agent population on a rugged NK
 landscape), a four-arm ablation separates the failure modes: the full system (grounded evaluation +
 directed recombination + diversity-preserving selection (37)) climbs to near the global optimum while
 keeping its specialists; removing grounded evaluation converges the population confidently on an unfit
@@ -241,16 +241,16 @@ language-model scale this composed loop remains unbuilt; it is the paper's large
 Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become
 separate species (*reproductive isolation*) through Bateson–Dobzhansky–Muller incompatibilities (38, 39):
 changes harmless on their own background but deleterious in combination. A merged model is exactly the
-exposed hybrid. We built the analytic model (Fig. 5A): hybrid fitness tracks the parents while
+exposed hybrid. I built the analytic model (Fig. 5A): hybrid fitness tracks the parents while
 compatible, then peels off and crashes below the ancestor; the isolation cliff arrives earlier the
 denser the incompatibilities; and the incompatibility *count* snowballs quadratically with divergence
-(39). We note that a super-linear count does not by itself entail a sharp performance cliff without
+(39). Note that a super-linear count does not by itself entail a sharp performance cliff without
 the count-to-effect-size link, which the analytic model supplies under its assumptions and any neural
 test must establish separately.
 
 In trained networks, the claim must survive a known alternative: merge barriers between independently
 trained networks are famously *coordinate artefacts*, removable by re-aligning hidden units (40);
-richer symmetry groups remove more (41), with known failures beyond the shared-data regime (42). We therefore aligned under the composition of
+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 *same* task have a barrier that this alignment removes essentially entirely
@@ -266,7 +266,7 @@ Proposition S2), with the framework's role being the *structure around it*: whic
 generate conflict, and what moves the cliff.
 
 The strongest constraint comes from the pre-registered *emergent test*: true BDM incompatibilities are
-emergent (each lineage's changes harmless alone), so we let children diverge with *no conflicting
+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
 catastrophically-forgetting specialists (parents ≈ 0.50, merge ≈ 0.955, a sustained Fisher–Muller
@@ -285,7 +285,7 @@ on shared circuitry, not divergence per se.
 
 The framework's prediction-level claim was put to a designed test (Fig. 6C). Thirty-nine parent pairs
 (13 conditions × 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 *across* conditions we
+so inference is condition-clustered, and because shared seeds also couple rows *across* conditions I
 report per-seed and leave-one-seed-out sensitivity alongside) span three axes decorrelated by construction: *conflict*
 (contradictory conventions on shared prompts, private budgets fixed), *compatible overlap* (the same
 shared prompts under the same convention — overlap and volume without conflict), and *duration* (weight
@@ -335,7 +335,7 @@ 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, answering the four decisions posed in the Introduction. *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 the 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
@@ -345,9 +345,9 @@ the operator to entanglement*: merge freely when skills are additive; sparingly,
 selection, when they entangle; and expect the champion-optimal mating breadth to narrow as landscapes
 roughen. *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. *Before merging,
-measure functional conflict* — cheap, pre-merge, and in our controlled setting predictive where the
+measure functional conflict* — cheap, pre-merge, and in the controlled setting predictive where the
 tested weight-distance baselines were not; and *do not treat divergence or specialisation alone as
-evidence of incompatibility* — in every regime we tested, what broke merging was conflicting
+evidence of incompatibility* — in every regime tested here, what broke merging was conflicting
 conventions on shared circuitry, which is the thing to detect.
 
 **Continual learning at the population scale.** Within a single network, the discipline's remedies
@@ -364,7 +364,7 @@ adapter-into-base merge; the recent turn to merging as a continual-learning mech
 recombination within one lineage over time, where this paper applies it across lineages; and the
 observation that rare examples and long-tail knowledge are forgotten first (59–61) is tail extinction
 seen one model at a time. The mechanisms differ (forgetting is largely deterministic interference,
-collapse is sampling drift) but the victims and the remedies coincide, and to our knowledge no prior
+collapse is sampling drift) but the victims and the remedies coincide, and to my knowledge no prior
 work carries population-genetic formalism into continual learning. Read into that field, the results
 offer: (i) an equilibrium theory for the replay ratio, with the sharper prediction that the required
 fraction is set by the rarest capability one refuses to lose (the `1 − e^{−m·p}` law) rather than by
@@ -379,23 +379,23 @@ splits the field's practice (keep adapters separate vs merge them; 54–58): uni
 where headroom exists, fusion where the base composes, consolidation as the slow-store step; and (v)
 *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 (62); our irreversibility results
+irreversible. On that last point I note the standing objection that apparent forgetting can be
+skewed task-inference over latent capability rather than erasure (62); the irreversibility results here
 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.
 
-**What is borrowed and what is ours.** The collapse-as-drift diagnosis is established prior work
+**What is borrowed and what is new.** The collapse-as-drift diagnosis is established prior work
 (21–25); so are the empirical facts that merges can beat parents, that decorrelated parents merge better, and that
 naive averaging loses to interference-aware or routed merges (4, 63, 64), that model populations can
 climb (5, 8–10), and that merge success admits ML-native predictors (44, 65), correlational where this framework
 supplies mechanism; the reading of sex as an algorithm for mixability in the theory of computation
-(66) anticipated the transfer before model merging existed. Ours is the framework-level
+(66) anticipated the transfer before model merging existed. New here is the framework-level
 synthesis — inheritance, diversity, and compatibility as managed quantities — together with: the
 conservation law for blending inheritance and its operator boundaries; the per-item grounding floor;
 the society ablation with its complementary failure modes; model speciation as a named, tested question, with the
 coordinate-versus-functional decomposition under permutation-and-rescaling alignment and the emergent
-null that bounds it; and the controlled predictive test with its controls. We claim the framework generated
-these measurements and experiments; we do not claim their outcomes validate a uniquely
+null that bounds it; and the controlled predictive test with its controls. I claim the framework generated
+these measurements and experiments; I do not claim that their outcomes validate a uniquely
 population-genetic mechanism, and one refinement it proposed was not supported.
 
 **Limits and open problems.** The demonstrations are deliberately small: exact where small is a virtue,
@@ -405,9 +405,9 @@ built at language-model scale. The predictive test's next bars, in order of valu
 *unfamiliar* conflict structures and real task pairs; a demonstrably better *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
+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 we pose but do not solve. What biology receives in return is a new model
+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.
@@ -418,11 +418,11 @@ development is consolidating around exactly the operators studied here: syntheti
 (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
+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 our small-scale null does not rule out, then lineages will begin to
+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.