Random matrices and localization in the quasispecies theory

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.Comment: 13 pages, 8 figures, presented at the 23rd Marian Smoluchowski Symposium on Statistical Physics - Random Matrices, Statistical Physics and Information Theory, 26-30 September 2010, Krakow, Poland. Small changes, one reference adde