Expansion of the master equation for a biomolecular selection model (Q1063543)

A stochastic model based on Eigen and Schuster's theory of biomolecular self-replication [\textit{M. Eigen}, Self-organization of matter and the evolution of biological macromolecules. Naturwiss. 58, 465-523 (1971); \textit{M. Eigen} and \textit{P. Schuster}, The hypercycle: A principle of natural self-organization. Springer (1979)] is studied by treating the master equation with the system-size expansion technique. The steady- state results are found to be in good agreement with the previous results and with those derived from the principle of detailed balancing. Multispecies competition and co-existence are studied carefully with the conclusions that a stable steady state is predicted for the former and a metastable state for the latter. The stochastic selection processes are also analyzed and discussed.