Landscapes and Their Correlation Functions

Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive constant) eigenfuctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.