Punctuated equilibrium in statistical models of generalized coevolutionary resilience: How sudden ecosystem transitions can entrain both phenotype expression and Darwinian selection

Abstract

We argue, using a mathematical model based on asymptotic limit theorems of probability theory, that mesoscale ecosystem resilience shifts can entrain punctuated events of gene expression and other cognitive phenomena on more rapid time scales, and, in part through such means, slower changes induced by selection pressures, triggering punctuated equilibrium Darwinian evolutionary transitions on geologic time scales. The model reduces ecosystem, cognitive, and Darwinian genetic dynamics to a least common denominator of information sources interacting by crosstalk at markedly different rates. Pettini's 'topological hypothesis', via a homology between information source uncertainty and free energy density, generates a statistical model of sudden coevolutionary phase transition based on the Rate Distortion and Shannon-McMillan Theorems of information theory which links all three levels. Holling's (1992) extended keystone hypothesis regarding the particular role of mesoscale phenomena in entraining both slower and faster dynamical structures produces the result. A main theme is the necessity of a 'cognitive paradigm' for gene expression, mirroring I. Cohen's cognitive paradigm for immune function.