Fluctuation Relations of Fitness and Information in Population Dynamics

TL;DR

This paper derives fluctuation relations linking fitness, information, and phenotype-switching strategies in populations, revealing how sensing and feedback influence evolutionary dynamics through an information-theoretic framework.

Contribution

It introduces a novel fluctuation relation framework for population fitness, incorporating sensing, feedback, and information-theoretic principles in phenotype-switching models.

Findings

Optimal switching strategies are characterized by path probability consistency.

Fitness loss satisfies fluctuation relations constraining its average and fluctuations.

Sensing-related fitness gains are quantified via multivariate mutual information.

Abstract

Phenotype-switching with and without sensing environment is a ubiquitous strategy of organisms to survive in fluctuating environment. Fitness of a population of organisms with phenotype-switching may be constrained and restricted by hidden relations as the entropy production in a thermal system with and without sensing and feedback is well-characterized via fluctuation relations (FRs) . In this work, we derive such FRs of fitness together with an underlying information-theoretic structure in selection. By using path-integral formulation of a multi-phenotype population dynamics, we clarify that the optimal switching strategy is characterized as a consistency condition for time-forward and backward path probabilities. Within the formulation, the selection is regarded as passive information compression, and the loss of fitness from the optimal strategy is shown to satisfy various FRs that constrain the average and fluctuation of the loss. These results are naturally extended to the situation that organisms can use an environmental signal by actively sensing the environment. FRs of fitness gain by sensing are derived in which the multivariate mutual information among the phenotype, the environment and the signal plays the role to quantify the relevant information in the signal for fitness gain.