Summary: The power of Darwinian evolution is based on the dichotomy of genotype and phenotype with the former being the object under variation and the latter constituting the target of selection. Only the simplest case of an evolutionary process, the optimization of RNA molecules in vitro, where phenotypes are understood as RNA structures, can be handled explicitly. We derive a model based on differential equations with stochastic terms which includes unfolding of genotypes to yield phenotypes as well as the evaluation of the latter. The relations between genotypes and phenotypes are understood as mappings from sequence space into shape space, the space of molecular structures. Generic properties of this map are derived and analyzed for RNA secondary structures as an example. The optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of a relay series being an uninterrupted sequence of phenotypes from initial structure to target. Analysis of the molecular shapes in the relay series provides the basis for a novel definition of continuity in evolution. Discontinuities can be identified as major changes in molecular structures.
For the entire collection see [Zbl 0942.00072].