Error Threshold of Fully Random Eigen Model

TL;DR

This paper investigates how random fluctuations in fitness and mutation rate parameters affect the error threshold in the Eigen model, revealing a crossover region instead of a sharp phase transition, with implications for antiviral strategies.

Contribution

It introduces a fully random Eigen model with Gaussian-distributed parameters, showing the error threshold becomes a smooth crossover influenced mainly by mutation rate fluctuations.

Findings

Error threshold appears as a crossover region, not a sharp transition.

Increased fluctuation strength smooths the crossover region.

Mutation rate randomization significantly alters the error threshold.

Abstract

Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two important parameters in the Eigen model, the fitness and mutation rate, are treated as Gaussian distributed random variables simultaneously to examine the property of the error threshold. Numerical simulation results show that the error threshold in the fully random model appears as a crossover region instead of a phase transition point, and as the fluctuation strength increases the crossover region becomes smoother and smoother. Furthermore, it is shown that the randomization of the mutation rate plays a dominant role in changing the error threshold in the fully random model, which is consistent with the existing experimental data. The implication of the threshold change due to the randomization for antiviral strategies is discussed.