Expansion of an error threshold for a finite population in the Moran model

TL;DR

This paper introduces a refined definition of the error threshold in finite populations within the Moran model, accounting for population size effects on the stability of master sequences using probabilistic bounds and explicit lifetime formulas.

Contribution

It provides a new finite-population correction to the error threshold in the Moran model, using bounds and lifetime estimates of master sequences.

Findings

The correction term scales as 1/√(ℓm) after the main logarithmic term.

Explicit formulas for the lifetime of master sequences are derived and expanded.

The approach bounds the number of master sequences using birth-death chains.

Abstract

We propose a new definition for the error threshold of a population evolving through mutation and selection. We compute the correction term due to the finiteness of the population by estimating the lifetime of master sequences. Our technique consists in bounding from above and below the number of master sequences in the Moran model, by birth and death chains. The expectation of this lifetime is then computed with the help of explicit formulas which are in turn expanded with Laplace method. The first term after $\ln(\sigma)/\ell$ is computed, it scales as $1/\sqrt(\ell m)$, where $\ell$ is the genome size and $m$ is the number of individuals in the population.