Max-Planck-Institut für Physik komplexer Systeme

International Workshop on 
Biological Evolution and Statistical Physics
May 10-14, 2000 

The Structure of Fitness Landscapes
Peter F. Stadler 
    Institute for Theoretical Chemistry and Structural Biology 
     Währingerstr. 17,  A-1090 Vienna 
studla@tbi.univie.ac.at

Landscapes are an important concept in molecular evolution, the physics of disordered systems, and combinatorial optimization. We understand a landscape as a real-valued function of a usually very large set of configurations: RNA sequences, spin configurations, or Travelling Salesman tours, together with a notion of ``nearness'' among configurations, which is derived e.g. from the genetic operators or search rules.

In order to understand the qualitative differences between relatively simple spin glasses or combinatorial optimization problems and realistic biological fitness landscape models, aggregate measures of ruggedness and neutrality are considered. Ruggedness, sometimes measured in terms of local optima or adaptive walks, is most easily quantified by means of correlation functions. Neutrality, albeit seemingly just the absence of ruggedness,
turns out to be an independent property of landscapes.

A Fourier transform-like formalism can be used to extract global information on a landscape and to compare different cost functions on the same configuration space or the same cost function as seen by different search operators. 

       
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