Evolutionary dynamics of the most populated genotype on rugged fitness landscapes

TL;DR

This paper investigates how the most populated genotype in an evolving asexual population on rugged fitness landscapes changes over time, comparing models and deriving exact properties of these jumps.

Contribution

It introduces a simplified shell model to analyze genotype dynamics and provides exact calculations for jump properties in infinite populations, with preliminary results for finite populations.

Findings

Match between quasispecies and shell model for fit genotypes at short times

Exact calculation of jump properties in infinite populations

Finite population simulations show jump distribution decays as t^{-2}

Abstract

We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from a fitness peak to a better one during the process of adaptation. This is done using the dynamics of the shell model which is a simplified version of the quasispecies model for infinite populations and standard Wright-Fisher dynamics for large finite populations. We show that the population fraction of a genotype obtained within the quasispecies model and the shell model match for fit genotypes and at short times, but the dynamics of the two models are identical for questions related to the most populated genotype. We calculate exactly several properties of the jumps in infinite populations some of which were obtained numerically in previous works. We also present our preliminary simulation results for finite populations. In particular, we measure the jump distribution in time and find that it decays as $t^{-2}$ as in the quasispecies problem.