Theory for Adaptive Systems: Collective Robustness of Genotype-Phenotype Evolution

The investigation of mutually coupled 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 biological evolution and learning. We develop a general theory for such dynamics by extending dynamical mean field theory. We then apply our framework to biological systems whose fate is determined by the evolution of genotype-phenotype relationship. Here phenotypic evolution is shaped by stochastic gene-expression fast dynamics and is coupled to selection-based slow changes of genotypes encoding the network of gene regulations. We find dynamically robust patterns of phenotypes can be achieved under an intermediate level of external noise where the genotype-phenotype relation evolves in such a way that results in intrinsic out-of-equilibrium fluctuations of phenotypes even in the absence of that noise.