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 ℓ over an alphabet of cardinality κ. The mutation probability per locus is q. He deals only with the sharp peak landscape: the replication rate is σ>1 for the master sequence and 1 for the other sequences. He studies the equilibrium distribution of the process in the regime whereℓ→ ∞,m→ ∞,q→0,ℓq→a∈]0, ∞[,mℓ→α∈[0, ∞].