Error threshold in finite populations

TL;DR

This paper introduces an analytical framework for studying finite population quasispecies evolution, revealing how the error threshold depends on population size and providing exact solutions in the deterministic limit.

Contribution

It presents a simple analytical model that neglects linkage disequilibrium to analyze the error threshold in finite populations, especially under a sharp-peak landscape.

Findings

Error threshold increases linearly with the reciprocal of population size for large populations.

The model yields exact steady-state solutions in the deterministic limit.

Population composition is a random combination of molecules at equilibrium.

Abstract

A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage disequilibrium at the population level is neglected. In particular, for the single-sharp-peak replication landscape we investigate the dependence of the error threshold on the population size and find that the replication accuracy at threshold increases linearly with the reciprocal of the population size for sufficiently large populations. Furthermore, in the deterministic limit our formulation yields the exact steady-state of the quasispecies model, indicating then the population composition is a random combination of the molecules.