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

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.