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 L angevin diffusion of a single particle in a specific random environmen t. The randomness in the mutation rate leads to population pinning and to a logarithmic slowdown of the evolution, resembling aging phenomen on in spin glass systems. Individual realizations of evolutionary beha vior exhibit so-called punctuated equilibria, or long periods of stasi s interrupted by rapid changes of fitness. In contrast, the randomness in the replication rate turns out to be irrelevant for evolution in t he long-time limit as it is smoothed out by increasing ''evolution tem perature.''