Non-equilibrium time dynamics of genetic evolution

TL;DR

This paper develops a generalized master equation for genetic evolution in diploid organisms, analyzing non-equilibrium dynamics, timescales, and entropy production, providing new insights into evolutionary processes from a statistical mechanics perspective.

Contribution

It introduces a comprehensive continuous-time master equation for genotype evolution considering multiple processes and solves key cases analytically, advancing understanding of non-equilibrium evolutionary dynamics.

Findings

Entropy production peaks during evolution towards viable genotypes.

Steady states are confirmed stable via Glansdorff-Prigogine criterion.

Timescales of evolution are analytically characterized.

Abstract

Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, examination of the time-dependent non-equilibrium dynamics has been less studied. In this paper we first derive a generalized master equation in the genotype space for diploid organisms incorporating the processes of selection, mutation, recombination, and reproduction. The master equation is defined in terms of continuous time and can handle an arbitrary number of gene loci and alleles, and can be defined in terms of an absolute population or probabilities. We examine and analytically solve several prototypical cases which illustrate the interplay of the various processes and discuss the timescales of their evolution. The entropy production during the evolution towards steady state is calculated and we find that it agrees with predictions from non-equilibrium statistical mechanics where it is large when the population distribution evolves towards a more viable genotype. The stability of the non-equilibrium steady state is confirmed using the Glansdorff-Prigogine criterion.