Dynamical mean-field theory: from ecosystems to reaction networks

Abstract

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The maintenance of diversity in large ecosystems is a longstanding puzzle, towards which recent progress has been made by the derivation of dynamical mean-field theories of random models. In particular, it has recently been shown that these random models have a chaotic phase in which abundances display wild fluctuations. When modest spatial structure is included, these fluctuations are stabilized and diversity is maintained. If and how these phenomena have parallels in biochemical reaction networks is currently unknown. Making this connection is of interest since life requires cooperation among a large number of molecular species. In this work, we find a reaction network whose large-scale behavior recovers the random Lotka-Volterra model recently considered in theoretical ecology. We clarify the assumptions necessary to derive its large-scale description, and reveal the underlying assumptions made on the noise to recover previous dynamical mean-field theories. Then, we show how local detailed balance and the positivity of reaction rates, which are key physical requirements of chemical reaction networks, provide obstructions towards the construction of an associated dynamical mean-field theory of biochemical reaction networks. Finally, we outline prospects and challenges for the future.

References in corpus (15)

• Fractal free energy landscapes in structural glasses
• Nonequilibrium Physics in Biology
• A collective phase in resource competition in a highly diverse ecosystem
• Stochastic population dynamics in spatially extended predator-prey systems
• Demographic noise can reverse the direction of deterministic selection
• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model
• Dynamics of interacting particle systems: stochastic process and field theory
• Rejuvenation and Memory Effects in a Structural Glass
• The complex chemical Langevin equation
• Field theories and exact stochastic equations for interacting particle systems
• Well-mixed Lotka-Volterra model with random strongly competitive interactions
• Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain
• Population Extinction on a Random Fitness Seascape

Cited by in corpus (10)

• Dimension of activity in random neural networks
• Macroscopic Stochastic Thermodynamics
• Path integrals and stochastic calculus
• Quantifying Rare Events in Stochastic Reaction-Diffusion Dynamics Using Tensor Networks
• Dynamical Theory for Adaptive Systems
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Universal Slow Dynamics of Chemical Reaction Networks
• Noise equals control
• Effective one-dimension reduction of multi-compartment complex systems dynamics
• Entangled criticality and irreversibility in random Markov dynamics