The number of local optima is an important characteristic of a landscape. It appears to depend on the pair-correlation of the landscape as well as on its deviations from statistical isotropy. We use Tanaka and Edward's XY Hamiltonian as an example for an investigation of the relationships...

In this contribution we consider the effect of a class of ``averaging operators'' on isotropic fitness landscapes. Explicit expressions for the correlation function of the averaged landscapes are derived. A new class of tuneably rugged landscapes, obtained by iterated smoothing of the random...

Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying configuration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be...

The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a ``fitness'' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by...

The interplay of ruggedness and neutrality in fitness landscapes plays an important role in explaining the dynamics of evolutionary adaptation. While various measures of ruggedness (correlation functions, adaptive walks, or the density of local optima) are reasonably well understood, and models...

Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every directed graph with a Hamiltonian circuit there is a choice of rate constants such that the system is...

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...

The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical...

RNA and protein molecules were found to be both templates for replication and specific catalysts for biochemical reactions. RNA molecules, although very difficult to obtain via plausible synthetic pathways under prebiotic conditions, are the only candidates for early replicons. Only they are...