We build on the deterministic population genetics formulation of the quasispecies model [Phys. Rev. E, 54, 4048 (1996)] to propose an analytical framework to investigate the quasispecies evolution of finite populations. In particular, we focus on the dependence of the error threshold on the population size and find that, for large populations, the replication accuracy at the threshold increases linearly with the reciprocal of the population size.