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...

The effect of recombination on genotypes can be represented in the form of P-structures, i.e. a map from the set of pairs of genotypes to the power set of genotypes. The interpretation is that the P-structure maps the pair of parental genotypes to the set of recombinant genotypes which result...

The relationship of orthogonal functions associated with vertex transitive graphs and random walks on such graphs is investigated. We use this relations to characterize the exponentially decaying autocorrelation functions along random walks on isotropic random fields defined on vertex transitive...

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...