Evolution of Molecular Phenotypes { APhysicist ' s View of Darwin ' s Principle ?

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 diieren-tial 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 ow reactor. The approach towards a predeened structure is monitored and reconstructed in terms of a relay series being an uninterrupted sequence of phenotypes from initial stucture to target. Analysis of the molecular shapes in the relay series provides the basis for a novel deenition of continuity in evolution. Discontinuities can be identiied as major changes in molecular structures. Evolution of asexually replicating individuals in the sense of Darwin's principle is characterized by the interplay of two processes which have counteracting innuences on heterogeneity of populations: (i) Mutations increase diversity of genotypes, and (ii) selection decreases diversity of phenotypes. 3 In sexually reproducing populations recombination acts as an additional process increasing diversity. It is important to realize that variation and selection operate on diierent manifestations of the individual, genotype and phenotype, respectively. At a rst glance, decoupling, or more precisely uncorrelatedness of the targets for mutation and selection may seem to be a disadvantage: 3 The genotype is understood as the polynucleotide sequence that carries the genetic information of the organism, DNA, or RNA in the case of several families of viruses. The phenotype is the adult organism which enters the reproductive phase and determines thereby tness commonly understood as the number of progeny transferred into the next generation.