Punctuated Equilibrium in Statistical Models of Generalized Coevolutionary Resilience: How Sudden Ecosystem Transitions Can Entrain Both Phenotype Expression and Darwinian Selection

Abstract

We argue that mesoscale ecosystem resilience shifts akin to sudden phase transitions in physical systems can entrain similarly punctuated events of gene expression on more rapid time scales, and, in part through such means, slower changes induced by selection pressure, triggering punctuated equilibrium Darwinian evolutionary transitions on geologic time scales. The approach reduces ecosystem, gene expression, and Darwinian genetic dynamics to a least common denominator of information sources interacting by crosstalk at markedly differing rates. Pettini's `topological hypothesis', via a homology between information source uncertainty and free energy density, generates a regression-like class of statistical models of sudden coevolutionary phase transition based on the Rate Distortion and Shannon-McMillan Theorems of information theory which links all three levels. A mathematical treatment of Holling's 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 approach to immune function. Invocation of the necessary conditions imposed by the asymptotic limit theorems of communication theory enables us to penetrate one layer more deeply before needing to impose an empirically-derived phenomenological system of `Onsager relation' recursive coevolutionary stochastic differential equations. Extending the development to second order via a large deviations argument permits modeling the influence of human cultural structures on ecosystems as `farming'.