We present a method for approximating a fitness landscapes as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with P-ary interactions can be computed. We show an application to RNA free...

Correlation functions are important characteristics of (fitness) landscapes. We use the fourier expansion of landscapes in order to characterize the set of all the possible autocorrelation functions on highly symmetric graphs, as well as the isotropic random fields on such graphs. A canonical...

A class of autocatalytic reaction networks based on template dependent replication and specific catalysis is considered. Trimolecular "elementary strps" of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and...

We consider the kinetics of an autocatalytic reaction network in which replication and catalytic action is separated by a translation step. We find that the behavior of such a system is closely related to second order replicator equations, which describe the kinetic of autocatalytic reaction...

Novel species are introduced into a network of interacting replicators either (i) as mutants of members of the network or (ii) as unrelated immigrants. We consider the meta-population dynamics of such a system. In the first case, the appearance of mutants leads to a slow growth of the replicator...

In many cases fitness landscapes are obtained as particular instances of random fields by assigning a large number of random parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of...

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the...

We cast some classes of fitness landscapes as problems in spectral analysis on various Cayley graphs. In particular, landscapes derived from RNA folding are realized on Hamming graphs and analyzed in terms of Walsh transforms; assignment problems are interpreted as functions on the symmetric...

We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an

Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of replicator type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems---$n= 2, 3 $, and 4---are discussed and complete...