Complex Dynamics of Molecular Evolutionary Processes

Evolution is an extreme complex dynamical phenomenon which has to be partitioned into simpler systems for an adequate description. Peter Schuster suggested a partition of evolutionary dynamics into three such subsystems 35]: Population Dynamics Population Support Dynamics Genotype{Phenotype Mapping In this paper we present an adequate description of all three systems and a structural and dynamical characterisation of their combination. Describing genotype{phenotype relations by RNA sequence{structure maps is the most delicate part in this approach. Such a relation plays a central role in evolution, because genetic mutation acts upon genotype but selection operates on phenotypes. The set of all sequences which map into a particular structure is modelled as random graph in sequence-space. Population-support dynamics by means of a catalytic network is realized as a (large) random digraph and secondary structures as vertex set. Studying a population of catalytic RNA-molecules exploring and utilising a large catalytic network shows signiicantly diierent behavior compared to a deterministic description: hypercycles are able to coexist and survive resp. a parasite with superior catalytic support. A switching between diierent dynamical organisations of the network can be reported. Evolutionary dynamics in its full capability of describing interacting evolving species provides a powerful tool for molecular evolutionary biology. Not only evolutionary experiments yield better models but also these models are capable for the design of optimal experimental strategies. This synthesis between theoretical model and experimental setup is the key of a comprehensive and complete description of molecular evolution.