  Evolutionary adaptation is the process that increases the fit of a population
to the fitness landscape it inhabits. As a consequence, evolutionary dynamics
is shaped, constrained, and channeled, by that fitness landscape. Much work has
been expended to understand the evolutionary dynamics of adapting populations,
but much less is known about the structure of the landscapes. Here, we study
the global and local structure of complex fitness landscapes of interacting
loci that describe protein folds or sets of interacting genes forming pathways
or modules. We find that in these landscapes, high peaks are more likely to be
found near other high peaks, corroborating Kauffman's "Massif Central"
hypothesis. We study the clusters of peaks as a function of the ruggedness of
the landscape and find that this clustering allows peaks to form interconnected
networks. These networks undergo a percolation phase transition as a function
of minimum peak height, which indicates that evolutionary trajectories that
take no more than two mutations to shift from peak to peak can span the entire
genetic space. These networks have implications for evolution in rugged
landscapes, allowing adaptation to proceed after a local fitness peak has been
ascended.
