Finite population size effects in quasispecies models with single-peak fitness landscape

TL;DR

This paper investigates how finite population sizes influence quasispecies models with a single-peak fitness landscape, deriving equations to understand the dynamics and variance in mean fitness, aiding viral population analysis.

Contribution

It formulates an accurate iteration procedure and derives a Hamilton-Jacobi equation to describe finite population effects in quasispecies models with a single-peak landscape.

Findings

Derived Hamilton-Jacobi equation for finite populations

Provided variance estimates of mean fitness

Clarified applicability limits of infinite population models

Abstract

We consider finite population size effects for Crow-Kimura and Eigen quasispecies models with single peak fitness landscape. We formulate accurately the iteration procedure for the finite population models, then derive Hamilton-Jacobi equation (HJE) to describe the dynamic of the probability distribution. The steady state solution of HJE gives the variance of the mean fitness. Our results are useful for understanding population sizes of virus in which the infinite population models can give reliable results for the biological evolution problems.