Raphael Cerf 
Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model [PDF ebook] 

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].$