Evolution on a Rugged Landscape:Pinning and Aging

Abstract

Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank equation which allows us to describe the dynamics of the population in terms of thermo-activated Langevin diffusion of a single particle in a specific random potential. We found that the randomness in the mutation rate leads to pinning of the population and on average to a logarithmic slowdown of the evolution, resembling aging phenomenon in spin glass systems. In contrast, the randomness in the replication rate turns out to be irrelevant for evolution in the long-time limit as it is smoothed out by increasing ``evolution temperature''. The analytic results are in a good agreement with numerical simulations.

4 pages, 3 figures, submitted to Phys. Rev. Lett

References in corpus (1)

• Evolution on a smooth landscape

Cited by in corpus (4)

• Evolution dynamics in terraced NK landscapes
• Evolutionary dynamics on rugged fitness landscapes: exact dynamics and information theoretical aspects
• One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers
• Instanton approach to the Langevin motion of a particle in a random potential