Synthesis of random libraries of polynucleotide sequences has become a standard procedure of biotechnology; in combination with amplification methods such as the polymerase chain reaction (PCR) [1] this allows for selection experiments in which large pools of sequences are screened for a...

Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of structure. Two classes of biopolymers, RNA molecules and proteins are considered in detail. A general...

A class of autocatalytic reaction networks based on template dependent ligation and higher order catalysis is analyzed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The over-all dynamics...

A particular class of ordinary differential equations (ODE) describing catalyzed, template-induced, and erroneous replication is investigated. The ODEs can be split into a replicator part accounting for the correct replication and a mutation term accounting for all miscopying processes. The set...

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.

We explore the dynamics of a model of two-party competition under spatial voting. the parties are allowed to {\it incrementally} adapt their platforms by following the voting gradient imposed by the preferences of the electorate and platform of the opposition. The emphasis in this model is on...

Random graph theory is used to model relationships between sequences and secondary structure of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of...

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...

The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from four different unequal crossover models in the context of pretopological spaces. We show that all four...

A new mathematical representaion is proposed for the configuration space structure induced by recombination which we called "P-structure." It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes"...