On a simplified model for pattern formation in honey bee colonies |
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Authors: | Michael J Jenkins James Sneyd Scott Camazine J D Murray |
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Institution: | (1) Centre for Mathematical Biology, Mathematical Institute, 24–29 St. Giles, OX1 3LB Oxford, UK;(2) Department of Biomathematics, UCLA School of Medicine, 10833 Le Cenre Ave, 90024 Los Angeles, CA, USA;(3) Section of Neurobiology and Behavior, Cornell University, Mudd Hall, 14853 Ithaca, NY, USA;(4) Department of Applied Mathematics FS-20, University of Washington, 98195 Seattle, WA, USA |
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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.
Corresponding author |
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Keywords: | Insect societies Honey bees Mathematical model Pattern formation Self-organisation |
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