Dynamical properties of quasispecies model on correlated fitness landscapes

Abstract

In a broad sense, evolution happens in galaxies, languages, political systems and in many other systems. The biological evolution refers to the populations and not to individuals and the changes must be passed on to the next generation. We study the evolution of asexual organisms like bacteria and virus. An experiment [1] that studied the evolution of starving E. coli has shown that the fitness (for example, cell volume) of the population increases in steps as shown in Fig. 1. We are interested in the modeling of a system that exhibits such evolutionary dynamics. Our study is at sequence level where the sequence could be a combination of amino acids as in the case of protein molecules, nucleotide bases of RNA molecules etc. For simplicity, we take the sequence σ = {σ1, σ2, ..., σL} as the string of binary digits 0 and 1 where L is the length of the sequence. Each sequence is assigned a fitness value Fσ which defines the number of offspring produced by sequence σ. The fitness can also represent the replication (copying itself) rate of genome or the binding rate of enzyme. We consider the situation in which initially a low fitness sequence is most populated (leader).