  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
$\sigma^\ast(t)$, and we study the statistical properties of the evolutionary
trajectory which $\sigma^\ast(t)$ 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.
