Acta Biologica Hungarica

, Volume 63, Supplement 2, pp 75–79 | Cite as

Mathematical Analysis of the Honeybee Waggle Dance

  • R. OkadaEmail author
  • H. Ikeno
  • T. Kimura
  • Mizue Ohashi
  • H. Aonuma
  • E. Ito


A honeybee informs her nestmates of the location of a flower by doing a waggle dance. The waggle dance encodes both the direction of and distance to the flower from the hive. To reveal how the waggle dance benefits the colony, we created a Markov model of bee foraging behavior and performed simulation experiments by incorporating the biological parameters that we obtained from our own observations of real bees as well as from the literature. When two feeders were each placed 400 m away from the hive in different directions, a virtual colony in which honeybees danced and correctly transferred information (a normal, real bee colony) made significantly greater numbers of successful visits to the feeders compared to a colony with inaccurate information transfer. Howerer, when five feeders were each located 400 m from the hive, the inaccurate information transfer colony performed better than the normal colony. These results suggest that dancing’s ability to communicate accurate information depends on the number of feeders. Furthermore, because non-dancing colonies always made significantly fewer visits than those two colonies, we concluded that dancing behavior is beneficial for hives’ ability to visit food sources.


Insect waggle dance Markov model simulation social behavior 


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  1. 1.
    Beekman, M., Lew, J. B. (2008) Foraging in honeybees - when does it pay to dance? Behav. Ecol. 19, 255–262.CrossRefGoogle Scholar
  2. 2.
    Camazine, S., Sneyd, J. (1991) A model of collective nectar source selection by honeybee: Self-organization through simple rules. J. Theor. Biol. 149, 547–571.CrossRefGoogle Scholar
  3. 3.
    de Vries, H., Biesmeijer, J. C. (1998) Modelling collective foraging by means of individual behaviour rules in honey-bees. Behav. Ecol. Sociobiol 44, 109–124.CrossRefGoogle Scholar
  4. 4.
    Dornhaus, A., Kliigl, F., Oechslein, C., Puppe, F., Chittka, L. (2006) Benefits of recruitment in honey bees: effects of ecology and colony size in an individual-based simulation model. Behav. Ecol. 17, 336–344.CrossRefGoogle Scholar
  5. 5.
    Gould, J. M., Gould, C. G. (1988) The honey bee. Scientific American Library, New York.Google Scholar
  6. 6.
    Michelsen, A. (1993) The transfer of information in the dance language of honeybees: progress and problems. J. Comp. Physiol. 173, 135–141.CrossRefGoogle Scholar
  7. 7.
    Menzel, R., Greggers, U., Smith, A., Berger, S., Brandt, R., Brunke, S., Bundrock, G., Hiilse, S., Pliiimpe, T., Schaupp, F., Schiittler, E., Stach, S., Stindt, J. Stollhoff N., Watzl, S. (2005) Honey bees navigate according to a map-like spatial memory. Proc. Natl. Acad. Sci. USA 102, 3040–3045.CrossRefGoogle Scholar
  8. 8.
    Okada, R., Ikeno, H., Kimura, T., Ohashi, M., Aonuma, H., Ito, E. (2010) Markov model of honeybee social behavior. Information 13, 1115–1130.Google Scholar
  9. 9.
    Okada, R., Ikeno, H., Aonuma, H., Ito, E. (2008) Biological insights into robotics: honeybee foraging behavior by waggle dance. Adv. Robotics 22, 1665–1681.CrossRefGoogle Scholar
  10. 10.
    Okada, R., Ikeno, H., Sasayama, N., Aonuma, H., Kurabayashi, D., Ito, E. (2008) The dance of the honeybee: how do they dance to transfer the food information effectively? Acta Biol. Hung. 59 (Suppl), 157–162.CrossRefGoogle Scholar
  11. 11.
    Otani, T. (1985) An ethological study of adult female honeybees within the hive. Ph.D. Thesis, Hokkaido Univ.Google Scholar
  12. 12.
    Reliey, J. R., Greggers, U., Smith, A. D., Reynolds, D. R., Menzel, R. (2005) The flight paths of honeybees recruited by the waggle dance. Nature 435, 205–207.CrossRefGoogle Scholar
  13. 13.
    Sumpter, D. J. T., Pratt, S. C. (2003) A modelling framework for understanding social insect foraging. Behav. Ecol. Sociobiol. 53, 131–144.Google Scholar
  14. 14.
    von Frisch, K. (1993) The dance language and orientation of bees. Harvard University Press, Cambridge, MA, USA.CrossRefGoogle Scholar

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© Akadémiai Kiadó, Budapest 2012

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • R. Okada
    • 1
    Email author
  • H. Ikeno
    • 2
  • T. Kimura
    • 2
  • Mizue Ohashi
    • 2
  • H. Aonuma
    • 3
  • E. Ito
    • 1
  1. 1.Kagawa School of Pharmaceutical SciencesTokushima Bunri UniversitySanuki, KagawaJapan
  2. 2.School of Human Science and EnvironmentUniversity of HyogoHimeji, HyogoJapan
  3. 3.Research Institute for Electronic ScienceHokkaido UniversitySapporo, HokkaidoJapan

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