  We consider finite population size effects for Crow-Kimura and Eigen
quasispecies models with single peak fitness landscape. We formulate accurately
the iteration procedure for the finite population models, then derive
Hamilton-Jacobi equation (HJE) to describe the dynamic of the probability
distribution. The steady state solution of HJE gives the variance of the mean
fitness. Our results are useful for understanding population sizes of virus in
which the infinite population models can give reliable results for the
biological evolution problems.
