Dynamical Theory for Adaptive Systems

Abstract

The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) to analyse nonequilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness.

30 pages and 2 figures

References in corpus (7)

• Adaptive Coevolutionary Networks: A Review
• Evolutionary dimension reduction in phenotypic space
• Nature of the Volcano Transition in the Fully Disordered Kuramoto Model
• A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation
• Dynamically selected steady states and criticality in non-reciprocal networks
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Coalescence of limit cycles in the presence of noise

Cited by in corpus (3)

• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Irreversibility in Non-reciprocal Chaotic Systems
• Zero-temperature dynamics of the spherical model with non-reciprocal interactions