🧬 biology

Evolutionary Systems Thinking -- From Equilibrium Models to Open-Ended Adaptive Dynamics

This paper proposes Stability-Driven Assembly (SDA), a non-equilibrium framework that treats evolutionary dynamics as a core system-thinking problem where endogenous selection emerges from the differential persistence of stochastic patterns, thereby demonstrating why traditional equilibrium models fail to capture open-ended evolution and highlighting the need for co-evolving structural and dynamic approaches in economics and policy.

Original authors: Dan Adler

Published 2026-02-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dan Adler

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Big Idea: Why "Evolution" is Often Just a Fancy Word for "Adjustment"

Imagine you are watching a video game.

The Old Way (Equilibrium Models): Most economic and policy models today are like a game where the rules are hard-coded. The characters can move around, get richer, or get poorer, but they can never invent a new weapon, change the map, or create a new type of character. They just bounce around inside a fixed box, eventually settling into a predictable pattern. The paper calls this "equilibrium-seeking." It's like a ball rolling down a hill until it stops at the bottom.
The Problem: We often say things like "the market evolved" or "technology evolved." But if the model can't create new things, it's not really evolution. It's just adaptation within a cage.

The Paper's Solution:
Dan Adler argues that we need to stop treating "evolution" as a biological metaphor (genes, babies, DNA) and start treating it as a physics problem about stability.

He introduces a concept called Stability-Driven Assembly (SDA). Here is how it works, using a simple analogy.

The Analogy: The "Lego City" of Ideas

Imagine a giant, chaotic room where people are constantly throwing Lego bricks together to build random structures.

The Chaos: Every minute, people grab two random structures and smash them together to make something new.
The Filter (Stability): Some of these new creations are wobbly and fall apart immediately. Others are sturdy and stay standing for a long time.
The Accumulation: The wobbly ones disappear. The sturdy ones stay in the room.
The Feedback Loop: Because the sturdy ones are still there, they are more likely to get picked up and smashed into new combinations next time. The wobbly ones are gone, so they can't be used.

The Magic:
Over time, the room fills up with only the sturdiest, most complex structures.

Did anyone design them? No.
Did they reproduce? No (they didn't make babies).
Did they have a "fitness score"? No.
Why did they win? Simply because they didn't fall apart.

In this system, survival of the fittest becomes survival of the most stable. The "fittest" structures win not because they are "better" in a moral sense, but because they stick around long enough to be used again and again.

Why This Changes How We Think

The paper argues that most of our current models (in economics, policy, and business) are like a River in a Fixed Channel.

The water (the economy) can flow fast or slow.
It can flood or dry up.
But the banks of the river never change. The river can never decide to dig a new channel.

SDA is like a River that Can Dig Its Own Banks.
In Adler's model, the water itself changes the shape of the riverbed. If a certain pattern of water flow is stable, it carves a deeper channel, making it even more likely that future water will follow that path.

Old Model: The river finds the lowest point and stops.
New Model (SDA): The river keeps carving, creating canyons, waterfalls, and new paths that didn't exist before. This is Open-Ended Evolution.

What This Means for Real Life

1. For Business and Economics

We often think companies succeed because they are "smart" or "optimized."

The Paper says: Companies often succeed simply because they are durable. A business model that doesn't collapse under pressure stays in the market longer. Because it stays longer, it gets more customers, more partners, and more attention. It becomes the "standard" not because it was the best design, but because it didn't die out quickly.
The Lesson: Don't just try to optimize for today's profit. Build things that are resilient enough to survive the next decade. The survivors will naturally shape the future market.

2. For Policy Makers

Policymakers usually try to pick a "perfect" outcome (like a specific tax rate) and assume the system will settle there.

The Paper says: You can't just pick a destination. You have to shape the landscape of survival.
Instead of asking, "What is the optimal policy?", ask: "Which policies create structures that can survive and grow on their own?"
If you make a rule that helps a bad idea survive just a little longer, that bad idea might eventually dominate the whole system. If you help a good idea survive, it will naturally take over.

3. For Artificial Intelligence (AI)

Current AI is often trained to find the "best" answer to a specific problem.

The Paper suggests: We should build AI systems that act like this Lego room. Let them generate millions of random ideas, let the unstable ones fail, and let the stable ones keep interacting to create new things we couldn't have imagined. This leads to true creativity, not just optimization.

The Takeaway

Evolution isn't about "survival of the fittest" in a biological sense; it's about "survival of the stickiest."

If you want to understand how complex systems (like the economy, culture, or technology) change over time, stop looking for a master plan or a fixed goal. Instead, look at what sticks around. The things that persist, even by accident, will eventually become the foundation for everything that comes next.

The paper is a call to stop building models that assume the future is just a slightly different version of the present. We need models that allow the future to invent itself by keeping the things that work and letting the things that don't fall away.

1. Problem Statement

The paper identifies a fundamental disconnect between the descriptive use of "evolution" in economics, policy, and technology studies and the mechanistic limitations of current system dynamics (SD) models.

The Gap: While terms like "evolving firms" or "evolving markets" are common, standard SD models rely on fixed state spaces, static transition rules, and equilibrium-seeking dynamics.
The Limitation: These models can simulate adaptation within predefined structures but cannot explain the endogenous emergence of new structures, strategies, or categories. They treat evolution as a metaphor rather than a dynamical process.
The Core Issue: Equilibrium-constrained models assume the "landscape" of possibilities is fixed. In true evolutionary systems, the landscape itself must co-evolve with the population, a feature absent in traditional stock-and-flow or standard agent-based models (ABMs) that lack population-level feedback on interaction rules.

2. Methodology: Stability-Driven Assembly (SDA)

The author introduces Stability-Driven Assembly (SDA) as a minimal, non-equilibrium framework to model evolutionary dynamics without biological prerequisites (genes, replication, or predefined fitness functions).

Core Mechanism: SDA operates on the principle that differential persistence drives selection.
- Stochastic Assembly: New patterns (motifs) are generated through random interactions between existing elements.
- Differential Persistence: Each generated pattern is assigned a "lifetime" based on its stability. Unstable patterns decay immediately; stable patterns persist longer.
- Feedback Loop: Because longer-lived patterns remain in the population longer, they accumulate in higher frequencies. Consequently, they are sampled more frequently for future interactions.
Mathematical Formulation:
- The system is modeled as a Fokker–Planck equation where the drift term is functional (dependent on the entire population distribution $P$ ) rather than a fixed external field.
- Equation (1): $\frac{\partial P(x, t)}{\partial t} = -\nabla \cdot [A[P](x, t) P(x, t)] + D\nabla^2 P(x, t)$ $\frac{\partial P ( x , t )}{\partial t} = - \nabla \cdot [A [P] (x, t) P (x, t)] + D \nabla^{2} P (x, t)$
  - The Drift term ( $A[P]$ ) represents the endogenous bias toward stable regions, emerging from the population's composition.
  - The Diffusion term ( $D$ ) represents stochastic creation (novelty).
- This creates a nonlinear, history-dependent, non-equilibrium system where the "fitness" of a pattern is an emergent property of its stability and frequency, not an externally imposed value.
Algorithmic Implementation:
1. Initialize population with base elements.
2. Remove expired patterns (decay).
3. Replenish base elements (open system).
4. Sample two patterns from the current population (probability proportional to frequency).
5. Generate a new pattern via combination/recombination.
6. Assign a lifetime based on stability and add to the population.

3. Key Contributions

Decoupling Evolution from Replication: The paper demonstrates that "fitness-proportional sampling" (a hallmark of genetic algorithms) can emerge solely from stability-weighted sampling. Selection does not require genes, replication, or inheritance; it requires only that stable patterns accumulate and bias future interactions.
Critique of Equilibrium Models: It formally argues that equilibrium-constrained models (even when simulated numerically) are structurally incapable of open-ended evolution because they fix the transition rules and state space, preventing the "landscape" from changing in response to the population.
Reinterpretation of Agent-Based Models (ABMs): The author argues that many ABMs fail to capture true evolution because they treat population statistics as outputs rather than causal states. In SDA, the population distribution is a dynamical variable that actively reshapes the rules of future interaction.
Extension of System Dynamics: The paper proposes a new paradigm for stock-and-flow modeling where "stocks" represent populations of patterns with dynamic identities, and "flows" represent stochastic interactions and decay, allowing the model structure itself to evolve.

4. Results

Simulation Evidence: Using a minimal symbolic SDA system, the author simulated the evolution of pattern distributions.
- Control Group (No Persistence Bias): The system exhibited high Shannon entropy, representing a broad, random exploration of the pattern space with no convergence.
- SDA Group (With Persistence Bias): The system showed a steady decrease in Shannon entropy. Probability mass accumulated on a small subset of long-lived motifs.
Emergent Order: This entropy reduction demonstrated that order and selection can emerge spontaneously in a non-equilibrium system driven purely by differential persistence, without any external optimization function or fitness landscape.
Natural Genetic Algorithm (SDA/GA): The simulation confirmed that SDA functions as a "natural genetic algorithm" where stability acts as the selection pressure, driving the system toward structured, persistent configurations.

5. Significance and Implications

For System Dynamics: The paper calls for a shift from modeling systems as seeking equilibrium to modeling them as open-ended adaptive systems. It suggests that to model complex change, the model's structure (stocks, flows, rules) must be allowed to co-evolve with the population.
For Economics and Policy:
- Policy Design: Policy should move from "optimization" (trying to engineer a specific outcome) to "resilience engineering" (shaping the persistence landscape). Policies that alter survival rates or turnover can have outsized, path-dependent effects by reshaping which organizational forms accumulate.
- Industry Ecosystems: The framework explains how industry structures (e.g., supply chains, partnerships) emerge not through central design, but through the differential persistence of viable configurations that attract further interaction.
For AI and Agent-Based Modeling: The paper suggests that future evolutionary models should integrate AI agents that can modify their internal representations. However, the critical requirement remains the coupling of persistence to population-level bias; without this feedback, even sophisticated learning agents will converge to fixed equilibria rather than exhibiting open-ended evolution.

Conclusion:
The paper posits that evolution is not merely a biological metaphor but a general dynamical class arising from persistence-weighted feedback. By adopting Stability-Driven Assembly, researchers can model systems where structure and dynamics co-evolve, offering a more accurate framework for understanding complex adaptive systems in economics, technology, and policy than traditional equilibrium-based approaches.