RNA Shape Space Topology


Jan Cupal, Stefan Kopp, Peter F. Stadler

Submitted to Alife

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which of one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.

Keywords: Genotype-Phenotype Map - RNA Folding - Finite Topological Space - Continuity in Evolution.

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