Dynamical Theory for Adaptive Systems
arXiv:2306.01403 · doi:10.1088/1742-5468/ad8223
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.
arXiv comment30 pages and 2 figures
References in corpus (42)
- Adaptive Coevolutionary Networks: A Review
- Transition to chaos in random neuronal networks
- Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics
- Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems
- From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics
- Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
- Pluripotency, differentiation, and reprogramming: A gene expression dynamics model with epigenetic feedback regulation
- Optimal sequence memory in driven random networks
- Intrinsically-generated fluctuating activity in excitatory-inhibitory networks
- Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks
- Path Integral Approach to Random Neural Networks
- Path integral methods for the dynamics of stochastic and disordered systems
- Realization of Waddington's Metaphor: Potential Landscape, Quasi-potential, A-type Integral and Beyond
- Formation of Dominant Mode by Evolution in Biological Systems
- How single neuron properties shape chaotic dynamics and signal transmission in random neural networks
- Dimension of activity in random neural networks
- Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
- Evolutionary dimension reduction in phenotypic space
- Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks
- Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks
- Statistical Mechanics of Recurrent Neural Networks II. Dynamics
- Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
- Homeorhesis in Waddington's Landscape by Epigenetic Feedback Regulation
- Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
- Path-integral approach to the dynamics in sparse random network
- Breakdown of random-matrix universality in persistent Lotka--Volterra communities
- Dynamical mean-field theory: from ecosystems to reaction networks
- Artificial selection of communities drives the emergence of structured interactions
- Aging by near-extinctions in many-variable interacting populations
- Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution
- Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings
- Dimensional reduction in evolving spin-glass model: correlation of phenotypic responses to environmental and mutational changes
- 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
- Dynamics of random replicators with Hebbian interactions
- Dynamically selected steady states and criticality in non-reciprocal networks
- Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
- Slowly evolving geometry in recurrent neural networks I: extreme dilution regime
- Coalescence of limit cycles in the presence of noise
- Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models
- Double-replica theory for evolution of genotype-phenotype interrelationship
- Spin-glass model with partially annealed asymmetric bonds