Finite-size scaling of the quasiespecies model

Abstract

We use finite-size scaling to investigate the critical behavior of the quasiespecies model of molecular evolution in the single-sharp-peak replication landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where Q is the probability of exact replication of a molecule of length L and a is the selective advantage of the master string. We investigate the sharpness of the threshold and find that its characteristic persist across a range of Q of order L^(-1) about Q_c. Furthermore, using the data collapsing method we show that the normalized mean Hamming distance between the master string and the entire population, as well as the properly scaled fluctuations around this mean value, follow universal forms in the critical region.