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 of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is . He deals only with the sharp peak landscape: the replication rate is for the master sequence and for the other sequences. He studies the equilibrium distribution of the process in the regime where

For the discovery time, there is no miracle: before discovering the master
sequence, the process is likely to explore a significant portion of the genotype
space, hence the discovery time should be of order card{A,T,G,C }l = 4l. These
simple heuristics indicate that the persistence time depends on the selection drift,
while the discovery time depends on the spatial entropy. Suppose that we send
m, l to ∞ simultaneously. If the discovery time is much larger than the persistence
time, then the ...