MachineSex/paper/pnas/main.md

# The evolution of sex for artificial intelligence: a population-genetic framework for multigenerational model populations

**Giorgio F. Gilestro** — Department of Life Sciences, Imperial College London. giorgio@gilest.ro

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## 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? 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.

## 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. 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.

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## 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).
Weight-space *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.

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
same sampling accident by which rare surnames vanish from small villages and rare alleles (gene
variants) drift out of island populations with no selection against them. 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 —
the point at which diverged lineages can no longer produce working offspring, biology's boundary
between species — carried as one framework from closed forms to trained networks to 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: *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.

## The minimal model, and where its exactness ends

Knowledge is modelled as a distribution `p_t` over `K` discrete items (capabilities, facts, modes of
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, population genetics' canonical model of neutral
evolution, in which each new generation is a random sample of size `n` from the previous one and
every statistical property of drift follows from that one step. Diversity throughout this paper is
*heterozygosity*, `H = 1 − Σ p_i²`: the probability that two random draws differ (one minus a
collision probability), high when many items share the mass, zero at total collapse. The identity is
exploited 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 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 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 *asexual reproduction*, and sustained loss under it carries the defining consequence
of *Muller's ratchet* (28), the mechanism by which lineages that never recombine decay irreversibly —
the reason non-recombining genomes such as the Y chromosome have shed most of their ancestral genes.
Once every copy of a rare capability is gone from all parents and sources, no recombination can
rebuild it: each such loss is a click of the ratchet, and remedies must act while copies still
survive somewhere (a consequence-level correspondence; the minimal model lacks the ratchet's
recurrent-mutation driver).

**Table 1.** The dictionary. Each biological term is introduced in the section that develops it; 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.

| Population genetics | Model populations | Support |
|---|---|---|
| Genetic drift in a finite population | Training on finite samples of model output | Exact (minimal model); signs in trained nets; diagnosis conceded to prior work |
| Immigration from a fixed source | Grounding with verified real data | Exact equilibrium; signs in RNN/MLP/VAE/MNIST |
| Muller's ratchet (asexual decay) | Irreversible arm of model collapse | Correspondence, scoped: applies to unrecoverable loss |
| Recombination / sexual reproduction | Model merging | Empirical at 0.5B–7B |
| Fisher–Muller effect | Merged specialists exceed every parent | Analytic model; replicated in LLMs |
| Outbreeding depression under epistasis | Merging entangled skills harms offspring | Analytic model (NK landscapes); hypothesis at LLM scale |
| Mating systems / population structure | Who merges with whom (breadth of the parent pool) | Analytic model; hypothesis for real populations |
| Reproductive isolation (BDM incompatibilities) | Merge failure from functional conflict | Empirical (MLP + LLM tiers, conflict-associated); emergent form not observed |
| Selection on a fitness function | Verifier-anchored selection ("reality that can say no") | Analytic model (complementary with recombination and diversity in the tested society) |

## Results

### 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). Immigration is what conservation managers prescribe when a fragmented reserve loses
diversity, and its striking property there is how little is needed — the field's rule of thumb is
that one migrant per generation holds an isolated population's diversity (32). The same economy
appears here: 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 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). 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 `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
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 `∝ 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 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 ~10% grounding holds all thirty (the trained model needs roughly twice the exact-operator
fraction, the measured price of the estimator bias).

*(FIG:fig1)*

### Recombination: a conservation law, its operators, and offspring that exceed every parent

The largest returns from the transfer concern merging. *Blending inheritance* — offspring as the
average of their parents — is the failure mode at the root of population genetics' founding
controversy: the swamping argument pressed in Jenkin's 1867 review of *The Origin of Species*, that
under blending a rare advantageous variant is diluted toward the common type faster than selection
can multiply it (33), an objection dissolved only by Mendel's particulate inheritance, in which
discrete variants pass through generations undiluted. Refitting a child model to the mean of its
parents' output distributions is blending inheritance, and the proposition below is Jenkin's dilution
made exact. **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
`n·p/K ≪ 1`, where per-item survival is first-order in sampled mass, expected *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 *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, *weight averaging* (a nonlinear network's weight-mean does not compute its parents'
output-mean) and *routing among intact specialists* (34) (different storage and inference budgets from a
single child), are its empirical cousins, and the measured bridge is a *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 *Fisher–Muller effect* (35, 36), the classical account of why sex speeds
adaptation: in an asexual population, beneficial variants arising in different individuals can only
compete until all but one lineage is lost, whereas recombination assembles them in one offspring,
producing a *genotype* (an individual's combination of variants, one at each *locus*, or position)
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 (37) 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).

Sex has risks and, for AI, an unfair advantage, both quantified on Kauffman's NK fitness landscapes
(38), the standard model of *epistasis*, biology's term for interaction between genes: the fitness
contribution of a variant depends on which variants occupy the other loci, much as a component's
value in an ML system depends on the components around it. Each of the landscape's `N` sites
interacts with `K` others (the model's eponymous parameters), and raising that interaction count
tunes the landscape from smooth and additive to rugged and many-peaked (Fig. 3). When skills are entangled, blind recombination produces offspring *below* their parents,
worsening with ruggedness, and the optimal recombination rate shrinks as entanglement grows. Biology
knows this failure as *outbreeding depression*, the reason conservation practice warns against
crossing locally adapted populations: in the textbook case, an ibex herd in the Tatra Mountains
restocked with animals from Turkey and Sinai produced fertile hybrids that bore their young in the
coldest month of winter, and the herd died out (39). But an engineered population can do what biology cannot: recombine unbounded
parents, choose complementary mates, and *screen many candidate offspring against a verifier before
keeping one*. This directed sex converts the outbreeding catastrophe into a reliable gain in the
model (tracking or exceeding the best parent at every ruggedness) and replicates as a sign in language
models: bred-and-screened merges beat the a-priori blend in every seed on headroom tasks, including
one seed where the blend failed catastrophically and selection was immune (Fig. 6A). Finally,
population *structure* is itself a knob: sweeping the mate-pool breadth from monogamous (repeated
local pairings) to promiscuous (*panmixia*: any model may merge with any other) against ruggedness,
wide mixing maximises the population mean while
monotonically destroying diversity, and the best *champion* shifts from wide breadth on smooth
landscapes to intermediate breadth on rugged ones (Fig. 3C), the mating-system phenomenon known to
structured-population search, mapped onto merging populations.

*(FIG:fig2)*

*(FIG:fig3)*

### 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 *grounded inheritance*: external samples added to the reproduction process (the
data channel). In the society model, grounding is *grounded evaluation*: selection weights true
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 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 (40)) 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 *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.

*(FIG:fig4)*

### The limit of sex: model speciation

Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become
separate species (*reproductive isolation*) through Bateson–Dobzhansky–Muller incompatibilities (41, 42):
changes harmless on their own genetic background but deleterious in combination — the mechanism behind
the mule's sterility and the inviability of many between-species crosses, in which two genomes that
each work perfectly cannot run in the same cell. 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 *count* snowballs quadratically with divergence
(42). 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 (43);
richer symmetry groups remove more (44), with known failures beyond the shared-data regime (45). 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
(residual ≈ 0.001, the aligned merge performing at parent level): coordinate, not functional; two
networks trained on *conflicting* label maps have a barrier the same alignment leaves largely
unchanged (0.502 → 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 → 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 *structure around it*: which divergences
generate conflict, and what moves the cliff.

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
catastrophically-forgetting specialists (parents ≈ 0.50, merge ≈ 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 *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→12 epochs (cf. the merging literature's expert-duration effect; 46) 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.

*(FIG:fig5)*

### 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 × 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 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
divergence with zero conflict). Before merging, six predictors are computed: *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 (47), LoRA-delta cosine and distance, and a cross-task performance
baseline. The pre-registered outcome is the merge penalty against oracle parent potential (the analogue of
*hybrid load*, the fitness a hybrid loses relative to what its parents' genes could jointly supply),
also reported against best- and mean-parent references because the predictor
ordering is sensitive to that choice.

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
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 ρ stable at +0.37 to +0.53 in each seed alone,
geometry ≈ 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 (ρ = +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 *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.

*(FIG:fig6)*

**Table 2.** Headline quantitative results with sample sizes, uncertainty, and outcome definitions
(full per-experiment tables and falsifier status in SI Appendix and per-experiment documentation).

| Result | Setting / n | Outcome definition | Headline |
|---|---|---|---|
| Closed-form validation | Analytic tier; standing tests | Simulated vs closed-form H-decay, immigration equilibrium, multi-teacher union | Agreement < 0.5% |
| Grounding retention | Minimal model; 18+ replicates per point | Fraction of equilibrium diversity retained at grounding g (operational threshold) | g ≈ 0.05 retained ≥95% (tested setting); smooth in g |
| MNIST collapse & rescue | Conv-VAE, 4 replicates; frozen oracle (98.5% mode acc.) | Mode support / forward-KL over generations | Dry: 30→1 modes; 10% grounding: 30/30 held |
| Fisher–Muller in LLMs | 5 seeds (0.5B), fixed tests; single 7B run | Merged vs best-specialist accuracy (overall; worst family) | Ties 0.647±0.027 vs 0.592±0.009; 7B 0.87 vs 0.77 |
| Union vs blend (headroom) | 3 seeds (0.5B hard); single 7B-hard run | Paired per-seed ordering, routing vs weight-average | Routing > blend in 3/3 seeds; one catastrophic blend failure avoided |
| Speciation decomposition | MLPs, 3 replicates | LMC error barrier residual after permutation+rescaling alignment | Same-task 0.001; conflict 0.497 (naive 0.502) |
| Emergent isolation | MLPs 4 reps to 6.4× base training; LLM 1→12 epochs | Residual barrier; merged vs parent accuracy | 0.000 everywhere; merge rescues parents (≈0.955 vs ≈0.50) |
| Predictive test | 13 conditions × 3 seeds (0.5B) | Merge penalty vs oracle parent potential (pre-registered; ±: clustered 95% CI) | Functional ρ +0.45/+0.46, CI excl. 0; LOCO ρ ≈ 0.4; geometry n.s.; paired differences n.s. |

## 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 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
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. *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. *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 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 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
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 (48) and 5% to 25% by distribution-shift strength in
continual pretraining (49), sit where the minimal model's operational threshold lies.
*Pseudo-rehearsal*, the replay of a network's own generated samples, proposed as a cure in 1995 (50)
and revived as generative replay (51), is precisely the ungrounded null studied here: immigration from
a drifting source, benign for one hop, compounding over generations, with verifier-filtering (29, 52)
converting it back into grounding. Parameter isolation (53), including frozen-base adapters, which forget far
less (54), is engineered decorrelation; complementary-learning-systems consolidation (55–57) is the periodic
adapter-into-base merge; the recent turn to merging as a continual-learning mechanism (58–61) 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 (62–64) 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 `1 − e^{−m·p}` law) rather than by
average loss, testable against published replay sweeps; (ii) a *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, 50–52); (iii) *pre-merge interference
prediction with a mechanism*: where the current state of the art fits regressions over candidate
metrics (47), 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 *decision rule for the consolidate-versus-stay-modular question* that currently
splits the field's practice (keep adapters separate vs merge them; 57–61): union-preserving operators
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 I note the standing objection that apparent forgetting can be
skewed task-inference over latent capability rather than erasure (65); 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 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, 66, 67), that model populations can
climb (5, 8–10), and that merge success admits ML-native predictors (47, 68), correlational where this framework
supplies mechanism; the reading of sex as an algorithm for mixability in the theory of computation
(69) 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.

**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
*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 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.

**Creative diversity.** Collapse is not confined to facts and skills. Homogenisation of *style* is
already measurable: models trained on model output lose lexical and syntactic diversity across
generations (70), writing produced with model assistance is individually better but collectively less
diverse than writing produced without it (71, 72), and the house styles of the large assistants are
recognisable enough that their tics serve as signatures. In this framework these are the same
phenomenon at a different locus. A voice is a distribution over rare stylistic variants, exactly the
tail that drift erases first and that blending inheritance averages into a common register. The
remedies transfer unchanged, though they are untested here: grounding on stylistically diverse human
sources, decorrelated lineages maintained as distinct voices rather than merged into one,
union-preserving recombination over blending, and selection that rewards being different as well as
being good. Whether these preserve measured stylistic diversity at scale is an open experiment that
the framework specifies.

**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 (46) 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.

## Materials and Methods

**Analytic tier.** Pure NumPy/SciPy Wright–Fisher simulator over `K`-item distributions (knowledge as
`p_t`; Zipf-tailed truth `p*`; drift–grounding–refit generations), extended with a learning kernel
(smoothing/sharpening refit), multi-locus genotypes on additive and Kauffman NK landscapes, n-parent
crossover, and finite-population society loops. All parameters live in per-experiment YAML configs;
every run derives all randomness from one master seed (`SeedSequence.spawn`) and is bitwise
reproducible; scientific-validation tests assert the closed forms (heterozygosity decay, immigration
equilibrium, closed-form union) to <0.5% and run in CI with 151 further correctness tests.

**Neural tier.** Trained-network experiments realise the same abstractions with an exact oracle:
histogram/RNN/MLP/VAE generators on a synthetic mode universe (the histogram model reduces the harness
exactly to the analytic tier — the bridge gate), and a convolutional VAE on MNIST with a frozen CNN
oracle (98.5% mode accuracy; confusion matrix recorded as the measurement floor). Speciation
experiments fork no-BatchNorm MLPs (784–512–512–10) from a shared base, weight-average, and measure
linear-mode-connectivity error barriers before and after alignment; alignment composes deterministic
Git Re-Basin permutation matching with exact per-unit scale canonicalisation (the unit symmetry
group of this class, as the alignment search space; control recovery does not establish global
optimality), gated by exact recovery of a permuted-and-rescaled copy.

**Language-model tier.** LoRA specialists (rank 16) on procedurally generated task families with an
exact-match verifier, on frozen Qwen2.5-Instruct bases (0.5B on one 16 GB GPU; 7B on one L40S).
Operators: weight-space merges (soup/TIES via adapter arithmetic), per-input routing, and
Dirichlet-sampled offspring populations screened on held-out validation splits. Multi-seed protocols
fix the test sets and vary the training seed. The predictive test computes all predictors pre-merge
(generation confidence from token log-probabilities; base-model gradient cosines; exact r-space
LoRA-delta geometry) and evaluates merges on held-out tests; robust statistics (condition-clustered
bootstrap, paired predictor contrasts, leave-one-condition-out prediction, multi-reference outcomes)
are produced by a committed script. Statistical, per-seed reproducibility is documented for GPU tiers.

**Data and code availability.** All code, configs, seeds, results artifacts (with content hashes),
figures, and a one-command reproduction script will be deposited openly (repository + archived DOI) on
publication; every figure in this paper regenerates from committed artifacts without re-simulation.

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