2005/01/31 by Kavita Jain, Joachim Krug · 5 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Gene Regulatory Network Analysis #cond-mat.dis-nn #q-bio.PE
paper · pdf · doi:10.1088/1742-5468/2005/04/p04008
published as J. Stat. Mech. (2005) P04008 · Figures in color; minor revisions in text
openalex publication_date 2005/04/20 · arxiv created 2005/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation–selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype jumps from one local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant subpopulations, to study the dynamics of this model and of a simpler one-dimensional model which ignores the geometry of the sequence space. We find that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness records , and exploit several results from the record theory for non-identically distributed random variables. The genotypes that contribute to the trajectory are those records that are not bypassed by superior records arising further away from the initial population. Several conjectures concerning the statistics of bypassing are extracted from numerical simulations. In particular, for the one-dimensional model, we propose a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size. The latter can be determined exactly in terms of the extremal properties of the fitness distribution.