Evolving Reaction Networks

Status: Core concept — formed Session 5 Connected to: Chemical Organization Theory, autopoiesis, multi-scale composition, computational irreducibility, ANT translation, trace→actor crossing, open-ended evolution Topic: How reaction networks that generate new reactions overcome the evolvability stall

The Problem: Fixed Networks Stall

Chemical Organization Theory (Dittrich & di Fenizio, 2007) describes organizations as attractors of a FIXED reaction network. Once the system converges to an organization, it stays there. Our sim03 is consistent with this: the system reached a fixed equilibrium by generation 1 and never changed for 3000 generations. (2026-07-27: "confirmed" was too strong. sim03's organization count is a structural property of a fixed, hand-authored network — identical at every sampled generation of every run — so the stall is guaranteed by the design rather than measured. The concentration equilibrium is a real result; the organizational stall is not an independent test. See ../simulations/REVIEW.md §4.) This is the same stall as EvoLoop, computational autopoiesis, and Echo — self-maintenance without evolution.

Vasas, Szathmáry & Santos (2010, PNAS) proved this formally: autocatalytic sets (a special case of COT organizations) lack evolvability. Compositional genomes ("composomes") cannot maintain heritable variation because replication of compositional information is too inaccurate. The system "cannot substantially depart from the asymptotic steady-state solution already built-in in the dynamical equations."

The Resolution: Rare Novel Reactions + Compartments

Vasas et al. (2012, "Evolution before genes," Biology Direct) found the way out:

1. Rare uncatalyzed reactions produce novel molecular species from the "shadow" (species that could exist but don't yet). Most disappear. But rarely, a novel species catalyzes its own production from existing molecules, forming a viable autocatalytic loop — a new core.

2. Autocatalytic cores are sets of connected autocatalytic loops. A core is the "genotype" — it can seed itself from any one member. The periphery (molecules catalyzed by the core) is the "phenotype."

3. Compartmentalization is required. Compartments filter harmful modifications and enable between-compartment selection. Without compartments, novel cores are diluted.

4. Multiple cores = multiple attractors. With only one core, there's one attractor and no selection. With multiple cores, there are multiple attractors with different growth rates — the basis for natural selection.

5. Heredity via core loss/gain. When a compartment divides, a core may be lost (segregation instability). When rare reactions occur, a core may be gained. This is mutation. Core → periphery is genotype → phenotype. This is heredity.

6. Two levels of autocatalysis: molecular (within compartments) and compartmental (division). The compartment reproduces; the core replicates.

Key Empirical Results (Vasas et al. 2012)

• In 460 simulation runs of 30,000 steps each, 5 runs showed persistent increase in non-food set mass due to novel viable loops.
• Novel cores produce selectable attractors — a 1% selective advantage is enough to shift population composition.
• Networks with inhibition had multiple attractors but they were NOT selectable (transitions were periodic/chaotic, overriding selection). Multiple attractors ≠ evolvability. Selectability requires attractors that are stable, heritable, and differentially fit.
• The original Farmer/Kauffman autocatalytic sets always had exactly ONE attractor — definitively not evolvable.

The "One Bit" Limitation

Vasas et al. note that a viable core constitutes approximately "one bit of heritable information." The number of possible selectable attractors is small, so autocatalytic networks "may not be able to sustain open-ended evolution." However, each novel core extends the "shadow" (adjacent possible), opening new possibilities for discovering further cores. This is "cooptive evolution" — stepwise expansion into the adjacent possible.

This connects directly to Kauffman's "adjacent possible" concept: the system explores the space of possible reactions by expanding into neighboring regions. Each new core opens new neighbors.

Connection to Fontana & Buss (1994)

Fontana & Buss ("The Arrival of the Fittest," SFI 1993) pioneered this approach using lambda calculus as the "chemistry." In their AlChemy system:

• Molecules are lambda expressions
• Reactions are lambda calculus operations (application, composition)
• New molecules appear as products of reactions
• The system explores an open-ended space of possible molecules

They found that the system produces "organizational transitions" — shifts between qualitatively different organizational regimes. This is the same phenomenon as Vasas's novel cores: the reaction network itself evolves, producing new organizations.

Key Fontana & Buss insight: "construction" (building new molecules from existing ones) is what enables open-endedness. A system that only "copies" (identity functions) stalls. A system that constructs novel molecules from existing ones explores the adjacent possible. Parasites and side-reactions are not bugs — they are the source of novelty.

Relevance to Our Project

Evolving networks ↔ H7 (Trace→Actor Crossing)

The "rare novel reaction" that produces a new viable core IS the trace→actor crossing. In COT terms:

• Existing resources are "traces" (accumulated products of reactions)
• A novel reaction among existing resources produces a new self-maintaining set (organization)
• The new organization is a new "actor" at a new level
• The crossing from "trace" to "actor" is the appearance of a novel viable core

This makes H7 mechanistically concrete: the trace→actor crossing occurs when a rare novel reaction produces a viable autocatalytic core from existing resources.

Evolving networks ↔ H8 (Computational Irreducibility)

You cannot predict which novel cores will appear — you must simulate. The space of possible reactions is too large to enumerate, and the conditions for viability (closure + self-maintenance) depend on the entire network state. This is computational irreducibility at the level of the reaction network. The system must be run to know what it will produce.

Evolving networks ↔ ANT Translation (H2)

The appearance of a novel core is ANT's "enrollment" — a new collective forms from existing actors and begins to act as one. The core's periphery is the "mobilization" — the new collective acts on its environment (catalyzing peripheral molecules). The loss of a core at division is "disenrollment" — the collective dissolves.

Evolving networks ↔ Multi-scale composition (H1)

Two levels of autocatalysis (molecular + compartmental) IS multi-scale composition. The molecular level (reactions within a compartment) and the compartmental level (division, selection between compartments) have different rules. The molecular level produces novelty (new cores); the compartmental level selects among them. This is the cross-scale interaction we've been looking for — and it emerges naturally from the reaction network + compartment structure.

Evolving networks ↔ Holland's Signals and Boundaries

Holland (2012) argued that CAS are built from co-evolving signals and boundaries. In Vasas's model:

• Boundaries = compartment membranes (filter, contain)
• Signals = catalytic activities (molecules that enable reactions)
• Co-evolution = the boundary (compartment) determines which signals (cores) persist; the signals (cores) determine the compartment's fitness (growth rate)

Holland's framework and Vasas's model arrive at the same structure from different directions. Holland from CAS theory; Vasas from origin-of-life chemistry. Our project from ANT + computational irreducibility. Three independent paths converging on: evolving signal/boundary hierarchies = multi-scale composition.

Criticisms

1. The "one bit" problem

Vasas et al. acknowledge that autocatalytic cores carry ~1 bit of heritable information. Open-ended evolution requires unlimited heritable information (Taylor 2012). The gap between "evolvable" and "open-ended" is enormous.

2. Chemical realism

All models use abstract "chemistry" (random catalysis probabilities). Real chemistry has structure-dependent catalysis (sequence → fold → function). The probability of viable cores in real chemistry may be much lower.

3. The supracriticality problem

For novel cores to appear at appreciable rates, the catalytic probability P must be above a threshold. In real peptide chemistry, P is likely too low. The models require "unrealistically high" catalytic probabilities.

4. No spatial structure

Vasas's model has no spatial structure — compartments are well-mixed. Multi-scale composition in real systems involves spatial structure (termite mounds, embryos, ecosystems). The compartment is a spatial boundary, but within it, everything mixes.

5. Open-endedness not demonstrated

Vasas shows limited evolvability (selection between 2-3 attractors). No demonstration of open-ended evolution (unbounded novelty). The system eventually exhausts the adjacent possible for a given food set.

Empirical Evidence

• Vasas et al. (2012): 5/460 runs showed persistent complexity increase via novel viable loops
• Fontana & Buss (1994): organizational transitions in lambda calculus chemistry
• Bagley, Farmer & Fontana (1992): supracritical growth above catalytic threshold
• Hordijk & Steel (2018): RAF sets as special case of COT organizations

No empirical evidence for open-ended evolution in evolving reaction networks. The evidence supports limited evolvability, not open-endedness.

Cross-References

• [[concepts/chemical-organization-theory]] — COT describes fixed networks; evolving networks extend it
• [[concepts/autopoiesis]] — Cores are autocatalytic = self-producing
• [[concepts/multi-scale-composition]] — Two-level autocatalysis = multi-scale
• [[concepts/signals-and-boundaries]] — Holland's framework converges with Vasas
• [[concepts/open-ended-evolution]] — The "one bit" limitation
• Vasas et al. (2012) — "Evolution before genes"
• Fontana & Buss (1994) — "The Arrival of the Fittest"
• Holland (2012) — "Signals and Boundaries"