Evolution on a rugged landscape: Pinning and aging

Population dynamics on a rugged landscape is studied analytically and numerically. The dynamics of the population is described in terms of Langevin diffusion of a single particle in a specific random environment. The randomness in the mutation rate leads to population pinning and to a logarithmic slowdown of the evolution, resembling aging phenomenon in spin glass systems. Individual realizations of evolutionary behavior exhibit so-called punctuated equilibria, or long periods of stasis interrupted by rapid changes of fitness. 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.”