Memoirs of the American Mathematical Society 2015; 87 pp; softcover Volume: 233 ISBN10: 1470409674 ISBN13: 9781470409678 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/233/1096
 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 \[\ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0,\] \[{\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].\] Table of Contents  Introduction
 The model
 Main results
 Coupling
 Normalized model
 Lumping
 Monotonicity
 Stochastic bounds
 Birth and death processes
 The neutral phase
 Synthesis
 Appendix on Markov chain
 Bibliography
 Index
