Error Threshold of Fully Random Eigen Model

• Published in: arXiv.org
• Main Authors: Duo-Fang, Li, Tian-Guang Cao, Jin-Peng, Geng, Li-Hua, Qiao, Jian-Zhong, Gu, Zhan, Yong
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.06.2015
• Subjects: Biological activity; Biological evolution; Computer simulation; Crossovers; Errors; Fitness; Mathematical models; Mutation; Parameters; Phase transitions; Physical properties; Quantitative Biology - Populations and Evolution; Random variables; Randomization; Transition points; Variations
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1506.00344

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.