Evolutionary dynamics of the most populated genotype on rugged fitness landscapes

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.

arXiv commentMinor changes. To appear in Phys Rev E

References in corpus (11)

• Error Thresholds on Dynamic Fittness-Landscapes
• Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer
• Breaking records in the evolutionary race
• Quasispecies Theory for Multiple-Peak Fitness Landscapes
• Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes
• Statistics of Lead Changes in Popularity-Driven Systems
• Log-Poisson statistics and full aging in glassy systems
• Evolutionary trajectories in rugged fitness landscapes
• Punctuated evolution for the quasispecies model
• Universal Extremal Statistics in a Freely Expanding Jepsen Gas
• Leadership Statistics in Random Structures

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• Evolutionary dynamics on strongly correlated fitness landscapes
• Mutation-selection dynamics and error threshold in an evolutionary model for Turing Machines
• Evolutionary adaptation is facilitated by the presence of lethal genotypes
• Adaptation dynamics of the quasispecies model