Random matrices and localization in the quasispecies theory

TL;DR

This paper explores the connections between localization theory, random matrices, and the quasispecies model to better understand evolutionary dynamics in asexual organisms, revealing power-law distributions in evolutionary jump times.

Contribution

It uncovers overlooked relations between localization, random matrices, and the quasispecies model, providing new insights into the model's dynamics.

Findings

Distribution of times between evolutionary jumps follows a power law

Results align with recent findings in the shell model

Provides a new theoretical framework for studying quasispecies dynamics

Abstract

The quasispecies model of biological evolution for asexual organisms such as bacteria and viruses has attracted considerable attention of biological physicists. Many variants of the model have been proposed and subsequently solved using the methods of statistical physics. In this paper I will put forward important but largely overlooked relations between localization theory, random matrices, and the quasispecies model. These relations will help me to study the dynamics of this model. In particular, I will show that the distribution of times between evolutionary jumps in the genotype space follows a power law, in agreement with recent findings in the shell model - a simplified version of the quasispecies model.