Finite-size scaling of the quasispecies model

We use finite-size scaling to study the critical behavior of the quasispecies 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 characteristics 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.