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

¹ Institute of Physics, Academia Sinica - Nankang, Taipei 11529, Taiwan
² A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation - 2 Alikhanian Brothers St., Yerevan 375036, Armenia
³ National Center for Theoretical Sciences: Physics Division, National Taiwan University - Taipei 106, Taiwan
⁴ Department of Physics & Astronomy, Rice University - Houston, TX 77005-1892, USA

^a saakian@phys.sinica.edu.tw
^b huck@phys.sinica.edu.tw

Received: 5 December 2011
Accepted: 2 March 2012

Abstract

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 the 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 the population sizes of viruses in which the infinite population models can give reliable results for biological evolution problems.