  We consider the adaptation dynamics of an asexual population that walks
uphill on a rugged fitness landscape which is endowed with large number of
local fitness peaks. We work in a parameter regime where only those mutants
that are single mutation away are accessible, as a result of which the
population eventually gets trapped at a local fitness maximum and the adaptive
walk terminates. We study how the number of adaptive steps taken by the
population before reaching a local fitness peak depends on the initial fitness
of the population, the extreme value distribution of the beneficial mutations
and correlations amongst the fitnesses. Assuming that the relative fitness
difference between successive steps is small, we analytically calculate the
average walk length for both uncorrelated and correlated fitnesses in all
extreme value domains for a given initial fitness. We present numerical results
for the model where the fitness differences can be large, and find that the
walk length behavior differs from that in the former model in the Fr\'echet
domain of extreme value theory. We also discuss the relevance of our results to
microbial experiments.
