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The Topology of Evolutionary Biology
by
Peter F. Stadler
University Leipzig
The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a non-graphical structure of the combinatorial search spaces. Central notions in evolutionary biology are intrinsically topological. This claim is maybe most obvious for the discontinuities associated with punctuated equilibria.
We explore a framework based on generalized topological spaces (defined in terms of a subset of Kuratowski's closure axioms) and show that concepts of immediate biological interest correspond to natural properties of the topology of the underlying spaces. While the topological structure of genotype space is defined by well-known genetic operators, phenotype space inherits its structure from genotype space by virture of the 'genotype-phenotype map' that encapsulates the processes of development and morphogenesis.
The concepts of a 'phenotypic character' and a notion of homology in the spirit of Lewontin's definition as quasi-independent variational units can be derived rigorously from the topological framework.
Date received: September 29, 2004
Copyright © 2004 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capf-03.