Finite-size scaling of the quasiespecies model

TL;DR

This paper applies finite-size scaling to analyze the critical behavior of the quasiespecies model, revealing universal properties and threshold sharpness in molecular evolution dynamics.

Contribution

It demonstrates the use of finite-size scaling to characterize the critical phenomena and universal behavior in the quasiespecies model.

Findings

Threshold sharpness persists over a range of Q near Q_c

Universal forms observed in normalized Hamming distance

Scaled fluctuations follow universal patterns in the critical region

Abstract

We use finite-size scaling to investigate the critical behavior of the quasiespecies 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 characteristic 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.