📄 evolutionary biology

The Environmental Games

This paper introduces Pure Environmental Games (PEGs), a novel framework in evolutionary game theory that formally incorporates the environment as a distinct strategy to model parallel neutral and environmental selection dynamics, offering new insights into microbial persistence and regimes like r/K selection through the lens of environmental biotechnology.

Original authors: Marcus, A.

Published 2026-07-22

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Marcus, A.

Original paper licensed under CC BY 4.0 (https://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 ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed.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

Imagine the natural world as a giant, cosmic playground where every living thing is constantly playing a high-stakes game of survival. For billions of years, the "rules" of this game have been set by the environment itself—the temperature, the food, the water, and the space. Scientists have long tried to write down the math for how life evolves in this playground using a field called Evolutionary Game Theory. Think of this theory like a scoreboard that predicts who wins and who loses based on how different players interact with each other. Traditionally, the math focused almost entirely on the players bumping into one another: a lion hunting a gazelle, or two bacteria fighting for the same drop of sugar. In this old view, the environment was just the silent stage where the drama happened, not an active player in the game. But what if the stage itself could grab a controller and start playing? That's the big question this paper asks: What happens if we treat the environment not just as a backdrop, but as a real opponent with its own strategy?

The author of this paper, Andrew Marcus, introduces a brand new way of looking at these biological games, which he calls "Pure Environmental Games" (PEGs). Instead of just watching how bacteria fight each other, he invents a mathematical framework where the "Environment" is a player sitting at the table with its own moves. In this new game, the environment has a strategy, and the bacteria have to adapt to it. The paper suggests that by treating the environment as a strategy, we can better understand how life survives in extreme conditions, like deep in the ocean or inside a wastewater treatment plant. It turns out that sometimes, the best way to win isn't to fight your neighbor, but to partner with the very conditions that surround you.

The New Game: When the Room Becomes a Player

To understand this new idea, let's imagine a crowded dance floor. In the old way of thinking (traditional game theory), the dance floor is just a static room. The dancers (the bacteria) only care about who they bump into. If you're a fast dancer, you might push a slow dancer aside to get to the center. The math here focuses on those direct shoves and bumps. But the author says, "Wait a minute!" The room itself changes. The music gets faster, the lights get dimmer, or the floor gets slippery. These changes affect how well everyone dances, regardless of who they bump into.

In this paper, the author creates a new model where the "Room" (the environment) is actually a dancer too. He calls this the Pure Environmental Game. In this game, the environment has a strategy, and the bacteria have to play against it. The author sets up a scenario where the bacteria don't fight each other directly at all; instead, they only interact with the environment. It's like a video game where you aren't fighting other players, but you are trying to survive the level itself. The "score" for the bacteria isn't how many other bacteria they beat, but how well they can grow given the current state of the environment.

The Six Ways Life Plays the Game

The paper uses a specific example to show how this works: two types of tiny, single-celled organisms called Methanosarcina and Methanothrix. These are the "r-strategists" and "K-strategists" of the microbial world.

The r-strategist (Methanosarcina) is like a chaotic, fast-talking opportunist. It loves to grow super fast when there's a huge feast, but it's messy and can't handle it when things get tough.
The K-strategist (Methanothrix) is like a careful, slow-and-steady planner. It doesn't grow as fast, but it's incredibly efficient and can survive when food is scarce.

The author simulates what happens to these two players in a controlled environment (like a giant tank of water used to clean wastewater) and finds six distinct "regimes" or ways the game plays out, depending on how long the water stays in the tank and how much food is in it.

The Washout (Regime I): Imagine the water flowing through the tank so fast that the bacteria get flushed out before they can even eat. In this scenario, the environment is so harsh that the bacteria lose immediately. The environment wins, and the biological players are wiped out. The paper notes that in this state, the environment is a "strict Nash equilibrium," meaning it's so strong that no bacteria can invade it.
The r-Domination (Regime II): If the water stays in the tank long enough and there's plenty of food, the fast-talking Methanosarcina takes over. It grows so quickly that it crowds out the slower Methanothrix. The environment allows the "r-strategist" to win.
The K-Domination (Regime IV): If the water stays in the tank for a very long time and the food is scarce, the careful Methanothrix wins. It's so good at surviving on very little that it pushes the fast-growers out. The environment now favors the "K-strategist."
The Neutral Zone (Regime III): There is a very specific, narrow moment where the conditions are just right that both types of bacteria have the exact same chance of surviving. In this "environmentally neutral selection" zone, the environment doesn't pick a winner. It's like a coin toss; who wins depends on random luck, not on who is better at the game.
The Minimum Energy (Regime V): As the system gets even more extreme, the bacteria reach a point where they are surviving on the absolute bare minimum of energy. They are barely hanging on, maintaining a tiny, stable existence. The paper calculates that for Methanothrix, this minimum energy dissipation rate is 1.4 × 10⁻¹¹ kJ cell⁻¹ y⁻¹. It's a state of extreme efficiency.
The Persistence (Regime VI): This is the most fascinating finding. Below that minimum energy line, the bacteria should theoretically die out (extinction). But the paper suggests they don't just vanish instantly. Instead, they enter a state of "persistence." They shut down their metabolism to the bare minimum, almost like hitting "pause" on a video game. They can survive for thousands or even millions of years in this dormant state, waiting for the environment to change so they can wake up again. The paper notes that deep-ocean microorganisms might do this, reducing their energy use to as low as 10⁻¹⁵ kJ cell⁻¹ y⁻¹.

Why This Matters

The author isn't claiming to have solved the mystery of life, but he is offering a new tool to look at it. By treating the environment as a player, we can see that life isn't just about fighting your neighbors; it's about forming a partnership with the world around you. The paper suggests that in a closed system (like a sealed tank or perhaps even the deep ocean), life persists by "partnering" with the environmental strategy. This connects to a famous idea by physicist Erwin Schrödinger, who said that life feeds on "negative entropy" (order) to stay alive.

The paper uses these ideas to explain why certain bacteria survive in wastewater treatment plants and how they might survive in extreme environments on Earth. It shows that "persistence" is a real, dynamic regime where life buys time, waiting for the game to change. The author emphasizes that this is a "modular" approach, meaning scientists can plug in different environmental rules to see how different life forms would react.

In short, this paper invites us to stop thinking of the environment as a silent stage and start seeing it as the most important player in the game of life. Whether it's a fast-growing bacterium in a feast or a dormant microbe in the deep ocean, the rules of the game are written by the environment itself. And sometimes, the best strategy isn't to win the fight, but to survive the game long enough to play again.

Technical Summary: The Environmental Games

Problem Statement
For over 4 billion years, the environment has acted as a primary driver of evolutionary selection by presenting biological entities with opportunities and challenges. However, in the framework of Evolutionary Game Theory (EGT), the environment has not been formally introduced as a strategy. Traditional EGT relies on the replicator equation, where the "game" is defined strictly by direct interaction coefficients between biological entities. While eco-evolutionary models have attempted to incorporate environmental feedback, they typically do so by modifying these direct interaction coefficients rather than creating a distinct environmental game. This approach creates a difficulty in mapping games to EGT classifications when intrinsic growth rate differentials exist, as the selection baseline is altered by environmental conditions rather than just direct competition.

Methodology
The author proposes a new framework called Pure Environmental Games (PEGs) to formally introduce the environment as a strategy within EGT. The methodology proceeds in two conceptual steps:

Derivation of an Ideal Lotka-Volterra Model (LVM): The direct-interaction submatrix is set to null (zero), creating a limiting case of neutral selection where deterministic selection continues solely via intrinsic growth rates.
Definition of PEGs: The payoffs that biological strategies derive from an "environmental strategy" are set to the net specific accumulation rates ( $\mu_{a,i}(E)$ ), which are parameterized by the environmental state.

In this framework, the general payoff matrix is divided into two parts: the direct interaction submatrix (traditional EGT) and the intrinsic growth submatrix (the environmental game). By setting the direct interactions to null, PEGs describe a neutral selection game operating in parallel to an environmental game. The environmental strategy ( $S_0$ ) and its frequency ( $x_0$ ) are introduced, with biological strategies sharing the same local environment.

To validate and illustrate these concepts, the paper utilizes Environmental Biotechnology as a collection of instances for PEGs. Specifically, it models the competition between two acetoclastic methanogens, Methanosarcina (an r-strategist) and Methanothrix (a K-strategist), within an idealized chemostat. The simulations solve mass and energy conservation laws, incorporating microbial kinetics and thermodynamics to determine net specific accumulation rates based on the solids residence time ( $\theta_x$ ) and influent substrate concentration ( $S_0$ ).

Key Contributions and Results
The paper identifies six distinct dynamic regimes within the r/K selection game operating under the PEG framework:

Regime I (Washout): When the solids residence time is below a critical minimum ( $\theta_x < [\theta_{min}^x]_{lim}$ ), the net accumulation rate is negative for all biological strategies. The environmental strategy acts as a strict Nash equilibrium, resisting invasion.
Regimes II and IV (r/K Selection): When $\theta_x$ $θ_{x}$ allows for growth, the environment is no longer a strict Nash equilibrium, allowing biological strategies to invade.
- Regime II: r-strategists (Methanosarcina) dominate when $\theta_x$ is low but above the washout threshold, as they can establish a steady presence and outcompete K-strategists.
- Regime IV: K-strategists (Methanothrix) dominate when $\theta_x$ is high, as they are better adapted to stable, low-substrate environments.
Regime III (Environmentally Neutral Selection): Occurs at a critical residence time ( $\theta_x = \theta_{crit}^x$ ) where the steady-state substrate concentrations for both strategists are equal ( $S^*_r = S^*_K$ ). Here, deterministic environmental selection dynamics no longer dictate a unique outcome, and neutral drift may occur.
Regime V ( $S^*_{min}$ ): As $\theta_x$ approaches infinity, the substrate concentration asymptotically approaches a minimum ( $S^*_{min}$ ) required to sustain steady-state biomass. This regime represents the thermodynamic boundary for sustaining life, with a calculated minimum energy dissipation rate for Methanothrix of $1.4 \times 10^{-11}$ kJ cell $^{-1}$ y $^{-1}$ .
Regime VI (Persistence): Below $S^*_{min$ , microorganisms enter a state of slow extinction or "persistence." By reducing metabolic activity to maintenance requirements, organisms can survive for extended periods (thousands to millions of years), as observed in deep-ocean sediments. This regime is described as a new dynamic state under extinction.

The analysis demonstrates that the environmental strategy resists invasion when it is a strict Nash equilibrium (i.e., when biological net accumulation rates are negative). Conversely, when biological strategies can invade, the environment selects for them based on their ability to lower the steady-state substrate concentration below that of competitors.

Significance
The paper claims that PEGs provide a template for identifying regimes of environmental selection within an environmental game, such as the r/K selection game. By formally introducing the environment as a strategy, the framework:

Recruits over a century of accumulated knowledge from Environmental Biotechnology (specifically principles of environmental selection and conservation laws) into evolutionary games.
Makes system boundaries explicit, linking the dynamics to mass exchange parameters like $\theta_x$ .
Aligns with Schrödinger's concept of life feeding on negative entropy; in a closed system (infinite $\theta_x$ ), persistence is achieved by minimizing energy dissipation through interaction with the environmental strategy.
Offers a modular approach where physical nuances (thermodynamics, kinetics) can be applied to traditional EGT concepts.

The author positions this work as a foundation for cross-disciplinary conversations between EGT, Environmental Biotechnology, and Microbial Ecology, rather than a source of novel predictive claims. The framework suggests that persistence may help explain phenomena such as the resurgence of measles or the resilience of antibiotic resistance genes, where extinction is not immediately observable.

The New Game: When the Room Becomes a Player

The Six Ways Life Plays the Game

Why This Matters

Technical Summary: The Environmental Games

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