Population Exploration on Genotype Networks in Genetic Programming

  • Ting Hu
  • Wolfgang Banzhaf
  • Jason H. Moore
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8672)


Redundant genotype-to-phenotype mappings are pervasive in evolutionary computation. Such redundancy allows populations to expand in neutral genotypic regions where mutations to a genotype do not alter the phenotypic outcome. Genotype networks have been proposed as a useful framework to characterize the distribution of neutrality among genotypes and phenotypes. In this study, we examine a simple Genetic Programming model that has a finite and compact genotype space by characterizing its genotype networks. We study the topology of individual genotype networks underlying unique phenotypes, investigate the genotypic properties as vertices in genotype networks, and discuss the correlation of these network properties with robustness and evolvability. Using GP simulations of a population, we demonstrate how an evolutionary population diffuses on genotype networks.


Genetic Programming Vertex Degree Single Point Mutation Closeness Centrality Neutral Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Lenski, R.E., Barrick, J.E., Ofria, C.: Balancing robustness and evolvability. PLoS Biology 4(12), e428 (2006)Google Scholar
  2. 2.
    van Nimwegen, E., Crutchfield, J.P., Huynen, M.A.: Neutral evolution of mutational robustness. Proceedings of the National Academy of Sciences 96(17), 9716–9720 (1999)CrossRefGoogle Scholar
  3. 3.
    Kirschner, M., Gerhart, J.: Evolvability. Proceedings of the National Academy of Sciences 95, 8420–8427 (1998)CrossRefGoogle Scholar
  4. 4.
    Pigliucci, M.: Is evolvability evolvable? Nature Review Genetics 9, 75–82 (2008)CrossRefGoogle Scholar
  5. 5.
    Wagner, A.: Robustness, evolvability, and neutrality. Federation of European Biochemical Societies Letters 579(8), 1772–1778 (2005)CrossRefGoogle Scholar
  6. 6.
    Masel, J., Trotter, M.V.: Robustness and evolvability. Trends in Genetics 26, 406–414 (2010)CrossRefGoogle Scholar
  7. 7.
    Draghi, J.A., Parsons, T.L., Wagner, G.P., Plotkin, J.B.: Mutational robustness can facilitate adaptation. Nature 463, 353–355 (2010)CrossRefGoogle Scholar
  8. 8.
    Landry, C.R., Lemos, B., Rifkin, S.A., Dickinson, W.J., Hartl, D.L.: Genetic properties influcing the evolvability of gene expression. Science 317, 118–121 (2007)CrossRefGoogle Scholar
  9. 9.
    McBride, R.C., Ogbunugafor, C.B., Turner, P.E.: Robustness promotes evolvability of thermotolerance in an RNA virus. BMC Evolutionary Biology 8, 231 (2008)CrossRefGoogle Scholar
  10. 10.
    de Visser, J.A.G.M., Hermission, J., Wagner, G.P., Meyers, L.A., Bagheri-Chaichian, H., et al.: Evolution and detection of genetic robustness. Evolution 57(9), 1959–1972 (2003)Google Scholar
  11. 11.
    Reidys, C., Stadler, P.F., Schuster, P.: Generic properties of combinatory maps: neutral networks of RNA secondary structures. Bulletin of Mathematical Biology 59(2), 339–397 (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
    Schuster, P., Fontana, W., Stadler, P.F., Hofacker, I.L.: From sequences to shapes and back: A case study in RNA secondary structures. Proceedings of The Royal Society B 255, 279–284 (1994)CrossRefGoogle Scholar
  13. 13.
    Wagner, A.: Robustness and evolvability: A paradox resolved. Proceedings of The Royal Society B 275(1630), 91–100 (2008)CrossRefGoogle Scholar
  14. 14.
    Ciliberti, S., Martin, O.C., Wagner, A.: Innovation and robustness in complex regulatory gene networks. Proceedings of the National Academy of Sciences 104(34), 13591–13596 (2007)CrossRefGoogle Scholar
  15. 15.
    Wilke, C.O.: Adaptive evolution on neutral networks. Bulletin of Mathematical Biology 63, 715–730 (2001)CrossRefGoogle Scholar
  16. 16.
    Cowperthwaite, M.C., Economo, E.P., Harcombe, W.R., Miller, E.L., Meyers, L.A.: The ascent of the abundant: How mutational networks constrain evolution. PLoS Computational Biology 4(7), e1000110 (2008)Google Scholar
  17. 17.
    Banzhaf, W.: Genotype-phenotype mapping and neutral variation - a case study in genetic programming. In: Davidor, Y., Schwefel, H.P., Manner, R. (eds.) PPSN 1994. LNCS, vol. 866, pp. 322–332. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  18. 18.
    Rothlauf, F., Goldberg, D.E.: Redundant representations in evolutionary computation. Evolutionary Computation 11(4), 381–415 (2003)CrossRefGoogle Scholar
  19. 19.
    Hu, T., Banzhaf, W.: Evolvability and speed of evolutionary algorithms in light of recent developments in biology. Journal of Artificial Evolution and Applications 568375 (2010)Google Scholar
  20. 20.
    Galvan-Lopez, E., Poli, R.: An empirical investigation of how and why neutrality affects evolutionary search. In: Cattolico, M. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1149–1156 (2006)Google Scholar
  21. 21.
    Hu, T., Banzhaf, W.: Neutrality and variability: Two sides of evolvability in linear genetic programming. In: Rothlauf, F. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference, pp. 963–970 (2009)Google Scholar
  22. 22.
    Soule, T.: Resilient individuals improve evolutionary search. Artificial Life 12, 17–34 (2006)CrossRefGoogle Scholar
  23. 23.
    Banzhaf, W., Leier, A.: Evolution on neutral networks in genetic programming. In: Yu, T., Riolo, R., Worzel, B. (eds.) Genetic Programming Theory and Practice III, pp. 207–221. Springer (2006)Google Scholar
  24. 24.
    Ebner, M., Shackleton, M., Shipman, R.: How neutral networks influence evolvability. Complexity 7(2), 19–33 (2002)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Hu, T., Payne, J.L., Banzhaf, W., Moore, J.H.: Evolutionary dynamics on multiple scales: A quantitative analysis of the interplay between genotype, phenotype, and fitness in linear genetic programming. Genetic Programming and Evolvable Machines 13, 305–337 (2012)CrossRefGoogle Scholar
  26. 26.
    Bavelas, A.: Communication patterns in task-oriented groups. Journal of the Acoustical Society of America 22, 725–730 (1950)CrossRefGoogle Scholar
  27. 27.
    Sabidussi, G.: The centrality index of a graph. Psychometrika 31(4), 581–603 (1966)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ting Hu
    • 1
  • Wolfgang Banzhaf
    • 2
  • Jason H. Moore
    • 1
  1. 1.Computational Genetics Laboratory, Geisel School of MedicineDartmouth CollegeLebanonUSA
  2. 2.Department of Computer ScienceMemorial UniversitySt. John’sCanada

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