Peter Schuster (Vienna):

Complexity in Evolutionary Processes

Abstract:

Darwin's principle of evolution by natural selection is readily casted into a mathematical formalism. Molecular biology revealed the mechanism of mutation and provides the basis for a kinetic theory of evolution that models correct reproduction and mutation as parallel chemical reaction channels. A result of the kinetic theory is the existence of a phase transition in evolution occurring at a critical mutation rate, which represents a localization threshold for the population in sequence space. Occurrence and nature of such phase transitions depend critically on fitness landscapes. The fitness landscape being tantamount to a mapping from sequence or genotype space into phenotype space is identified as the true source of complexity in evolution. Modeling evolution as a stochastic process is discussed and neutrality with respect to selection is shown to provide a major challenge for understanding evolutionary processes

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