Abstract
We present a simplified version of a previously presented model (Camazine et al. (1990)) that generates the characteristic pattern of honey, pollen and brood which develops on combs in honey bee colonies. We demonstrate that the formation of a band of pollen surrounding the brood area is dependent on the assumed form of the honey and pollen removal terms, and that a significant pollen band arises as the parameter controlling the rate of pollen input passes through a bifurcation value. The persistence of the pollen band after a temporary increase in pollen input can be predicted from the model. We also determine conditions on the parameters which ensure the accumulation of honey in the periphery and demonstrate that, although there is an important qualitative difference between the simplified and complete models, an analysis of the simplified version helps us understand many biological aspects of the more complex complete model.
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References
Belic, M. R., Skarka, V., Deneubourg, J. L., Lax, M.: Mathematical model of honeycomb construction. J. Math. Biol. 24, 437–449 (1986)
Camazine, S.: Self-organizing pattern formation on the combs of honey bee colonies. Behav. Ecol. Sociobiol. 28, 61–76 (1991)
Camazine, S., Sneyd, J., Jenkins, M. J., Murray, J. D.: A mathematical model of self-organized pattern formation on the combs of honey bee colonies. J. Theor. Biol. 147, 553–571 (1990)
Deneubourg, J. L., Aron, G., Goss, S., Pasteels, J. M.: The self-organizing exploratory pattern of the Argentine ant. J. Insect Behav. 3, 159–168 (1990)
Deneubourg, J. L., Goss, S., Franks, N., Pasteels, J. M.: The blind leading the blind: modelling chemically mediated army ant raid patterns. J. Insect Behav. 2, 719–725 (1989)
Goss, S., Deneubourg, J. L.: The self-organising clock pattern of Messor pergandei (Formicidae, Myrmicinae). Insectes Soc. 36, 137–150 (1989)
Goss, S., Aron, S., Deneubourg, J. L., Pasteels, J. M.: Self-organized shortcuts in the Argentine ant. Naturwissenschaften 76, 579–581 (1989)
Heinrich, B.: The mechanisms and energetics of honeybee swarm temperature regulation. J. Exp. Biol. 91, 25–55 (1981)
Omholt, S. W.: Thermoregulation in the winter cluster of the honeybee, Apis mellifera. J. Theor. Biol. 128, 219–231 (1987)
Pasteels, J. M., Deneubourg, J. L., Goss, S.: Self-organization mechanisms in ant societies (I): trail recruitment to newly discovered food sources. In: Pasteels J. M., Deneoubourg J. L. (eds.) From individual to collective behavior in social insects, pp. 155–176. Basel: Birkhäuser 1987
Seeley, T. D.: The ecology of temperate and tropical honey bee societies. Am. Sci. 71, 264 (1983)
Seeley, T. D., Morse R. A.: The nest of the honey bee (Apis mellifera L.). Insects Soc. 23, 495 (1976)
Seeley, T. D., Camazine, S., Sneyd, J.: Collective decision-making in honey bees: how colonies choose among nectar sources. Behav. Ecol. Sociobiol. (in press)
Winston, M.: The biology of the honey bee. Cambridge: Harvard University Press 1987
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Jenkins, M.J., Sneyd, J., Camazine, S. et al. On a simplified model for pattern formation in honey bee colonies. J. Math. Biol. 30, 281–306 (1992). https://doi.org/10.1007/BF00176152
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DOI: https://doi.org/10.1007/BF00176152