Asymptotic Behavior of Eigen’s Quasispecies Model
We study Eigen’s quasispecies model in the asymptotic regime where the length of the genotypes goes to \(\infty \) and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove convergence of trajectories, as well as convergence of the equilibrium solutions. We give analogous results for a discrete-time version of Eigen’s model, which coincides with a model proposed by Moran.
KeywordsEigen’s model Long-chain regime Class-dependent Mutation-selection equilibrium
This work was supported by a public grant as part of the Investissement d’avenir Project, Reference ANR-11-LABX-0056-LMH, LabEx LMH. The author wishes to thank Michel Benaïm and Raphaël Cerf for the valuable discussion that contributed to improve the article. The author is also grateful for the comments of an anonymous referee, as well as of the Associate Editor, which helped to improve the presentation and readability of the article.