Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model

The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of cardinality $\kappa$. The mutation probability per locus is $q$. He deals only with the sharp peak landscape: the replication rate is $\sigma>1$ for the master sequence and $1$ for the other sequences. He studies the equilibrium distribution of the process in the regime where $\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,$${\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].$