# A Stochastic Version of the Eigen Model

@article{Musso2011ASV, title={A Stochastic Version of the Eigen Model}, author={Fabio Musso}, journal={Bulletin of Mathematical Biology}, year={2011}, volume={73}, pages={151-180} }

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…

## 14 Citations

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The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small selective advantage, rapid evolvability, increased information capacity, and selection against parasitic branches.

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- Computer Science
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The result is the twin brother of the corresponding result for the Moran model, and it relies on the Freidlin-Wentzell theory of random perturbations of dynamical systems.

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