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Distinguishing the effects of dilution and restricted movement on the intra-nest transmission of honey-bee queen pheromones

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Abstract

This paper develops a simple model for the movement of a non-volatile pheromone through a honey-bee hive. The model is specifically developed for a pheromone produced by the queen which is thought to regulate colony swarming. Although the model begins as a system of partial integro-differential equations, it is in the end reduced to a system of linear, first-order partial differential equations for the average pheromone level per worker, the pheromone level of the hive substrate, and the pheromone level of the queen. Analysis of this system shows that both colony size and hive area have independent effects on the average pheromone levels of the workers, but that worker congestion can have an even stronger effect on the pheromone distribution. These results establish a relationship between colony size, hive area, worker crowding, and queen-pheromone transmission.

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References

  • Gradshtyen, I. S. and I. M. Ryzhik (1980). Table of Integrals, Series, and Products, Academic Press, New York.

    Google Scholar 

  • Jäger, E. and L. A. Segel (1992). On the ditribution of dominance in populations of social organisms. SIAM J. Appl. Math. 52, 1442–1468.

    Article  MathSciNet  Google Scholar 

  • Naumann, K., M. L. Winston, K. N. Slessor, G. D. Prestwich and F. X. Webster (1991). Production and transmission of honey bee queen (Apis mellifera L) mandibular gland pheromone. Behav. Ecol. Sociobio. 29, 321.

    Article  Google Scholar 

  • Naumann, K., M. L. Winston, and K. N. Slessor (1993). Movement of honey bee (Apis mellifera L) queen mandibular gland pheromone in populous and unpopulous colonies. J. Insect Behav. 6, 211.

    Article  Google Scholar 

  • Seeley, T. D. (1979). Queen substance dispersal by messenger workers in honeybee colonies. Behav. Ecol. Sociobio. 5, 391.

    Article  Google Scholar 

  • Seeley, T. D. and R. D. Fell (1981). Queen substance production in the honeybee (Apis mellifera). J. Kansas Entomol. Soc. 54, 192.

    Google Scholar 

  • Watmough, J. (1996). PhD thesis, University of British Columbia, Canada.

  • Watmough, J. (1997). A general model of pheromone transmission within honey bee hives. J. Theor. Bio. 189, 159–170.

    Article  Google Scholar 

  • Winston, M. L. (1987). The Biology of the Honeybee, Cambridge: Harvard University Press.

    Google Scholar 

  • Winston, M. L. and O. R. Taylor (1980). Factors preceeding queen rearing in the Africanized honeybee (Apis mellifera). Insectes Sociaux 27, 289.

    Article  Google Scholar 

  • Winston, M. L., H. A. Higo, S. J. Colley, T. Pankiw, and K. N. Slessor (1991). The role of queen mandibular pheromone and colony congestion in honey bee (Apis mellifera L.) reproductive swarming (Hymenoptera: Apidae). J. Insect Behav. 4, 649.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biology, Viginia Polytechnic Institute and State University, Blackburg, Virginia, 24061, USA

    James Watmough

  2. Department of Biology, Simon Fraser University, Burnaby, B.C., V5A 1S6, USA

    Mark Winston

  3. Department of Chemistry, Simon Fraser University, Burnaby, B.C., V5A 1S6, USA

    Keith Slessor

Authors
  1. James Watmough
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  2. Mark Winston
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  3. Keith Slessor
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Correspondence to James Watmough.

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Watmough, J., Winston, M. & Slessor, K. Distinguishing the effects of dilution and restricted movement on the intra-nest transmission of honey-bee queen pheromones. Bull. Math. Biol. 60, 307–327 (1998). https://doi.org/10.1006/bulm.1997.0006

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  • DOI: https://doi.org/10.1006/bulm.1997.0006

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