Joseba Dalmau

Convergence of a Moran model to Eigen's quasispecies model

We prove that a Moran model converges in probability to Eigens quasispecies model in the infinite population limit. We show further that the invariant probability measure of the Moran model converges to the unique stationary solution of Eigens quasispecies model.

Quasispecies on Class-Dependent Fitness Landscapes

We study Eigen’s quasispecies model in the asymptotic regime where the length of the genotypes goes to

Asymptotic Behavior of Eigen’s Quasispecies Model

\infty

The distribution of the quasispecies for a Moran model on the sharp peak landscape

∞ and the mutation probability goes to 0. We give several explicit formulas for the stationary solutions of the limiting system of differential equations.

The distribution of the quasispecies for the Wright–Fisher model on the sharp peak landscape

We consider the classical Wright–Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies.

The quasispecies distribution

We study Eigen’s quasispecies model in the asymptotic regime where the length of the genotypes goes to

Galton-Watson and branching process representations of the normalized Perron-Frobenius eigenvector

\infty