Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1997-02-11
Nonlinear Sciences
Adaptation and Self-Organizing Systems
4 pages, 3 figures, submitted to Phys. Rev. Lett
Scientific paper
10.1103/PhysRevLett.79.3298
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.
Aranson Igor
Tsimring Lev
Vinokur Valerii
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