Universal constraint on nonlinear population dynamics

TL;DR

This paper establishes a universal information-theoretical constraint on nonlinear population dynamics, generalizing Fisher's theorem and predicting bounds on relaxation speeds near bifurcations across biological systems.

Contribution

It introduces a universal constraint applicable to diverse nonlinear population models, linking information theory with dynamical systems in biology.

Findings

Verified the constraint in evolutionary, epidemiological, and ecological models.

Derived bounds on relaxation speeds near bifurcation points.

Connected bifurcation types with universal dynamical limits.

Abstract

Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics has remained a challenge. Here, we derive a universal information-theoretical constraint on a broad class of nonlinear dynamical systems represented as population dynamics. The constraint is interpreted as a generalization of Fisher's fundamental theorem of natural selection. Furthermore, the constraint indicates nontrivial bounds for the speed of critical relaxation around bifurcation points, which we argue are universally determined only by the type of bifurcation. Our theory is verified for an evolutionary model and an epidemiological model, which exhibit the transcritical bifurcation, as well as for an ecological model, which undergoes limit-cycle oscillation. This work paves a way to predict biological dynamics in light of information theory, by providing fundamental relations in nonequilibrium statistical mechanics of nonlinear systems.