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...

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...

The dynamics of a network of autocatalytically replicating species in a continuously stirred tank reactor can be described by a replicator equation in the limit of small flux rates.

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...