  We study the adaptation dynamics of an initially maladapted asexual
population with genotypes represented by binary sequences of length $L$. The
population evolves in a maximally rugged fitness landscape with a large number
of local optima. We find that whether the evolutionary trajectory is
deterministic or stochastic depends on the effective mutational distance
$d_{\mathrm{eff}}$ upto which the population can spread in genotype space. For
$d_{\mathrm{eff}}=L$, the deterministic quasispecies theory operates while for
$d_{\mathrm{eff}} < 1$, the evolution is completely stochastic. Between these
two limiting cases, the dynamics are described by a local quasispecies theory
below a crossover time $T_{\times}$ while above $T_{\times}$, the population
gets trapped at a local fitness peak and manages to find a better peak either
via stochastic tunneling or double mutations. In the stochastic regime
$d_\mathrm{eff} < 1$, we identify two subregimes associated with clonal
interference and uphill adaptive walks, respectively. We argue that our
findings are relevant to the interepretation of evolution experiments with
microbial populations.
