Finite-size scaling of the error threshold transition in finite populations

The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model exhibits a first-order transition at Q = Q(c) = 1/a, where Q is the probability of exact replication of a molecule of length L --> infinity, and a is the selective advantage of the master string. For sufficiently large population size, N, we show that in the critical region the characteristic time for the vanishing of the master strings from the population is described very well by the scaling assumption tau = N(1/2)f(a)[(Q - Q(c))N-1/2], where f(a) is an a-dependent scaling function.