A stochastic version of the Eigen model.

We exhibit a stochastic discrete time model that produces the Eigen model (Naturwissenschaften 58:465-523, 1971) in the deterministic and continuous time limits. The model is based on the competition among individuals differing in terms of fecundity but with the same viability. We explicitly write down the Markov matrix of the discrete time stochastic model in the two species case and compute the master sequence concentration numerically for various values of the total population. We also obtain the master equation of the model and perform a Van Kampen expansion. The results obtained in the two species case are compared with those coming from the Eigen model. Finally, we comment on the range of applicability of the various approaches described, when the number of species is larger than two.