  Fitness landscapes are genotype to fitness mappings commonly used in
evolutionary biology and computer science which are closely related to spin
glass models. In this paper, we study the NK model for fitness landscapes where
the interaction scheme between genes can be explicitly defined. The focus is on
how this scheme influences the overall shape of the landscape. Our main tool
for the analysis are adaptive walks, an idealized dynamics by which the
population moves uphill in fitness and terminates at a local fitness maximum.
We use three different types of walks and investigate how their length (the
number of steps required to reach a local peak) and height (the fitness at the
endpoint of the walk) depend on the dimensionality and structure of the
landscape. We find that the distribution of local maxima over the landscape is
particularly sensitive to the choice of interaction pattern. Most quantities
that we measure are simply correlated to the rank of the scheme, which is equal
to the number of nonzero coefficients in the expansion of the fitness landscape
in terms of Walsh functions.
