The Paradox of the Plankton: Oscillations and Chaos in Multispecies Evolution

  • Jeffrey Horn
  • James Cattron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2723)


Two theoretical ecologists have recently discovered that even under the simplest models of competition, three species are sufficient to generate permanent oscillations, and five species can generate chaos (Huisman & Weissing, 2001). We can show that these results carry over into genetic algorithm (GA) resource sharing after making one minor change in the “usual” sharing methods. We also bring together previous, scattered results showing oscillatory and chaotic behavior in the “usual” GA sharing methods themselves. Thus one could argue that oscillations and chaos are fairly easy to generate once individuals are allowed to influence each other, even if such interactions are extremely simple, natural, and indirect, as they are under resource sharing. We suggest that great care be taken before assuming that any particular implementation of resource sharing leads to a unique and stable equilibrium.


Genetic Algorithm Resource Sharing Chaotic Behavior Tournament Selection Evolutionary Game Theory 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Booker, L. B. (1989). Triggered rule discovery in classifier systems. In J. D. Schaffer, (Ed.), Proceedings of the Third International Conference on Genetic Algorithms. (ICGA 3). San Mateo, CA: Morgan Kaufmann. 265–274.Google Scholar
  2. Ficici, S. G., Melnik, O., & Pollack, J. B. (2000). A game-theoretic investigation of selection methods used in evolutionary algorithms. In A. Zalzala, et al (Ed.s), Proceedings of the 2000 Congress on Evolutionary Computation. IEEE Press.Google Scholar
  3. Horn, J. (1997). The Nature of Niching: Genetic Algorithms and the Evolution of Optimal, Cooperative Populations. Ph.D. thesis, University of Illinois at Urbana-Champaign, (UMI Dissertation Services, No. 9812622).Google Scholar
  4. Horn, J., Goldberg, D. E., & Deb, K. (1994). Implicit niching in a learning classifier system: nature’s way. Evolutionary Computation, 2(1). 37–66.CrossRefGoogle Scholar
  5. Huberman, B. A. (1988). The ecology of computation. In B. A. Huberman (Ed.), The Ecology of Computation. Amsterdam, Holland: Elsevier Science Publishers B. V. 1–4.Google Scholar
  6. Huisman, J., & Weissing, F. J. (1999). Biodiversity of plankton by species oscillations and chaos. Nature, 402. November 25, 1999, 407–410.CrossRefGoogle Scholar
  7. Huisman, J., & Weissing, F. J. (2001). Biological conditions for oscillations and chaos generated by multispecies competition. Ecology, 82(10). 2001, 2682–2695.CrossRefGoogle Scholar
  8. Juillé, H., & Pollack, J. B. (1998). Coevolving the “ideal” trainer: application to the discovery of cellular automata rules. In J. R. Koza, et. al., (Ed.s), Genetic Programming 1998. San Francisco, CA: Morgan Kaufmann. 519–527.Google Scholar
  9. McCallum, R. A., & Spackman, K. A. (1990). Using genetic algorithms to learn disjunctive rules from examples. In B. W. Porter & R. J. Mooney, (Ed.s), Machine Learning: Proceedings of the Seventh International Conference. Palo Alto, CA: Morgan Kaufmann. 149–152.Google Scholar
  10. Oei, C. K., Goldberg, D. E., & Chang, S. (1991) Tournament selection, niching, and the preservation of diversity. IlliGAL Report No. 91011. Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL. December, 1991.Google Scholar
  11. Rosin, C. D., & Belew, R. K. (1997). New methods for competitive coevolution. Evolutionary Computation, 5(1). Spring, 1997, 1–29.CrossRefGoogle Scholar
  12. Smith, R. E., Forrest, S., & Perelson, A. S. (1993). Searching for diverse, cooperative populations with genetic algorithms. Evolutionary Computation, 1(2). 127–150.CrossRefGoogle Scholar
  13. Watson, R.A., & Pollack, J.B. (2001). Coevolutionary dynamics in a minimal substrate. In L. Spector, et. al. (Ed.s), Proceedings of the 2001 Genetic and Evolutionary Computation Conference, Morgan Kaufmann.Google Scholar
  14. Werfel, J., Mitchell, M., & Crutchfield, J. P. (1999). Resource sharing and coevolution in evolving cellular automata. IEEE Transactions on Evolutionary Computation, 4(4). November, 2000, 388–393.Google Scholar
  15. Wilson, S. W. (1994). ZCS: A zeroth level classifier system. Evolutionary Computation, 2(1). 1–18.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jeffrey Horn
    • 1
  • James Cattron
    • 1
  1. 1.Department of Mathematics and Computer ScienceNorthern Michigan UniversityMarquetteUSA

Personalised recommendations