Entropic Equilibria Selection of Stationary Extrema in Finite Populations

TL;DR

This paper introduces an entropy-based measure to evaluate the stability of states in Markov processes, specifically applied to the Moran process, revealing how population parameters influence stationary extrema stability.

Contribution

It defines a novel entropy measure for Markov trajectories and applies it to analyze stability of stationary extrema in the Moran process with mutation.

Findings

Population size, mutation rate, and selection strength impact stability.

Entropy measure correlates with the likelihood of states being stable.

Method provides a new way to assess stability in evolutionary models.

Abstract

We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.