Replicator equations and the principle of minimal production of information

TL;DR

This paper demonstrates that solutions to a broad class of replicator equations inherently minimize information production over time, linking system dynamics to principles like minimum discrimination information and maximum entropy.

Contribution

It establishes that replicator equations naturally derive the Kullback principle and maximum entropy principle from their dynamics, rather than assuming them a priori.

Findings

Solutions minimize information production under constraints

Explicit computation of constraints at each time point

Applications to biological and demographic models

Abstract

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the production of information under time-dependent constraints, which, in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle of minimum discrimination information, as well as the maximum entropy principle, for systems governed by the replicator equations can be derived from the system dynamics rather than postulated. Applications to the Malthusian inhomogeneous models, global demography, and the Eigen quasispecies equation are given.