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We consider finite population size effects for Crow-Kimura and Eigenquasispecies models with single peak fitness landscape. We formulate accuratelythe iteration procedure for the finite population models, then deriveHamilton-Jacobi equation (HJE) to describe the dynamic of the probabilitydistribution. The steady state solution of HJE gives the variance of the meanfitness. Our results are useful for understanding population sizes of virus inwhich the infinite population models can give reliable results for thebiological evolution problems.

Finite population size effects in quasispecies models with single-peak fitness landscape