Average Fitness Differences on NK Landscapes

  • Wim HordijkEmail author
  • Stuart A. Kauffman
  • Peter F. Stadler
Original Article


The average fitness difference between adjacent sites in a fitness landscape is an important descriptor that impacts in particular the dynamics of selection/mutation processes on the landscape. Of particular interest is its connection to the error threshold phenomenon. We show here that this parameter is intimately tied to the ruggedness through the landscape’s amplitude spectrum. For the NK model, a surprisingly simple analytical estimate explains simulation data with high precision.


NK model Fitness landscapes Elementary landscape Graph Laplacian Error threshold 



WH thanks the Institute for Advanced Study, Amsterdam, for financial support through a fellowship. Discussions with Bärbel M. R. Stadler are gratefully acknowledged.

Supplementary material


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.SmartAnalytiX.comLausanneSwitzerland
  2. 2.Institute for Systems BiologySeattleUSA
  3. 3.Bioinformatics Group, Department of Computer ScienceLeipzig UniversityLeipzigGermany
  4. 4.Interdisciplinary Center of BioinformaticsLeipzig UniversityLeipzigGermany
  5. 5.German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-LeipzigLeipzig UniversityLeipzigGermany
  6. 6.Competence Center for Scalable Data Services and SolutionsLeipzig UniversityLeipzigGermany
  7. 7.Leipzig Research Center for Civilization DiseasesLeipzig UniversityLeipzigGermany
  8. 8.Max Planck Institute for Mathematics in the ScienceLeipzigGermany
  9. 9.University of ViennaInstitute for Theoretical ChemistryViennaAustria
  10. 10.Facultad de CienciasUniversidad Nacional de ColombiaBogotáColombia

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