FINITE-SIZE-SCALING OF THE QUASI-SPECIES MODEL

We use finite-size scaling to study the critical behavior of the quasi species model of molecular evolution in the single-sharp-peak replicat ion landscape. This model exhibits a sharp threshold phenomenon at Q=Q (c)= 1/a, where Q is the probability of exact replication of a molecul e of length L, and a is the selective advantage of the master string. We investigate the sharpness of the threshold and find that its charac teristics persist across a range of Q of order L-1 about Q(c). Further more, using the data collapsing method, we show that the normalized me an Hamming distance between the master string and the entire populatio n, as well as the properly scaled fluctuations around this mean value, follow universal forms in the critical region.