  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 $L \to
\infty$, 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
\left [ \left (Q - Q_c) N^{1/2} \right ] $, where $f_a$ is an $a$-dependent
scaling function.
