LANDSCAPES AND THEIR CORRELATION-FUNCTIONS

Fitness landscapes are an important concept in molecular evolution. Ma ny important examples of landscapes in physics and combinatorial optim ization, which are widely used as model landscapes in simulations of m olecular evolution and adaptation, are ''elementary'', i.e., they are (up to an additive constant) eigenfunctions of a graph Laplacian. It i s shown that elementary landscapes are characterized by their correlat ion functions. The correlation functions are in turn uniquely determin ed by the geometry of the underlying configuration space and the neare st neighbor correlation of the elementary landscape. Two types of corr elation functions are investigated here: the correlation of a time ser ies sampled along a random walk on the landscape and the correlation f unction with respect to a partition of the set of all vertex pairs.