Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

TL;DR

This paper provides an exact analytical solution to a simplified time-dependent quasispecies model in a rugged fitness landscape, confirming previous numerical conjectures about genotype dominance changes.

Contribution

It introduces a novel mapping of the evolutionary dynamics onto a random flux model, enabling exact solutions and insights into genotype change statistics.

Findings

Exact statistics of genotype dominance changes obtained

Confirmation of previous numerical conjectures

Asymptotic behavior characterized by a random walk

Abstract

A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The statistics of the number of changes of the dominant genotype from a finite set of genotypes are exactly obtained confirming existing conjectures based on numerics.