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
