A stochastic version of the Eigen model

Abstract

We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model describes the competition among individuals differing for reproductive capability but equivalent as survivors. We explicitly write down the Markov matrix of the stochastic model in the two species case and compute numerically the master sequence concentration for various values of the total population. Finally we compare our results with those obtained with Eigen model and with Nowak and Schuster birth and death model.