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

Details Finite-size scaling of the error threshold transition in finite population Finite-size scaling of the error threshold transition in finite population

1998-09-15

arxiv.org/abs/cond-mat/9809209v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 ps figures. submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/32/1/001

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.

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