Tempo and mode in quasispecies evolution

Abstract

Evolutionary dynamics in an uncorrelated rugged fitness landscape is studied in the framework of Eigen's molecular quasispecies model. We consider the case of strong selection, which is analogous to the zero temperature limit in the equivalent problem of directed polymers in random media. In this limit the population is always localized at a single temporary master sequence $σ^\ast(t)$, and we study the statistical properties of the evolutionary trajectory which $σ^\ast(t)$ traces out in sequence space. Numerical results for binary sequences of length N=10 and exponential and uniform fitness distributions are presented. Evolution proceeds by intermittent jumps between local fitness maxima, where high lying maxima are visited more frequently by the trajectories. The probability distribution for the total time $T$ required to reach the global maximum shows a $T^{-2}$-tail, which is argued to be universal and to derive from near-degenerate fitness maxima. The total number of jumps along any given trajectory is always small, much smaller than predicted by the statistics of records for random long-ranged evolutionary jumps.