Asymptotic behavior of Eigen's quasispecies model
Joseba Dalmau

TL;DR
This paper analyzes the long-term behavior of Eigen's quasispecies model as genotype length increases and mutation rates decrease, establishing convergence results for both continuous and discrete-time versions.
Contribution
It introduces a limiting infinite system of differential equations and proves convergence of trajectories and equilibria, extending the model to a discrete-time Moran version.
Findings
Convergence of trajectories in the asymptotic regime
Convergence of equilibrium solutions
Extension to a Moran discrete-time model
Abstract
We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove the convergence of the trajectories, as well as the convergence of the equilibrium solutions. We give the analogous results for a discrete-time version of Eigen's model, which coincides with a model proposed by Moran.
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Taxonomy
TopicsEvolution and Genetic Dynamics · Evolutionary Game Theory and Cooperation · Mathematical and Theoretical Epidemiology and Ecology Models
