Abstract
The chemical mass recruitment of ants with a fixed rate of workers and scouts is described by a set of differential equations which can be reduced to one delayed first order equation. The model allows the description of the time-development of the quality of a food source. It depends on the proportion of workers and scouts in the population whether there remains a threshold quantity which is not worth exploiting. The more intensive the trail-laying efforts the more rapid and exhaustive the exploitation. The number of ants on the trail from the nest to the source will be maximal, if the trail-laying efforts are in equilibrium with the evaporating effects of the trail-pheromone.
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References
Bessert, W. H., Wilson, E. O.: The analysis of olfactory communication among animals. J. Theoret. Biol. 5, 443–469 (1963)
Jaffe, K.: Theoretical analysis of the communication system for chemical mass recruitment in ants. J. Theoret. Biol. 84, 589–609 (1980)
Jaffe, K., Howse, P. E.: The mass recruitment system of the leaf cutting ant Atta cephalotes (L). Animal Behav. 27, 930–939 (1979)
Okubo, A.: Diffusion and ecological problems: Mathematical models. Berlin —Heidelberg —New York: Springer 1980
Weyer, J.: Diffusionsphänomene bei der chemischen Kommunikation zwischen Insekten, to appear in: Conference Volume “Mathematische Modellierung” (Ed. F. Wille). B. G. Teubner Verlag, Stuttgart
Wilson, E. O.: Chemical communication among workers of the fire ant Solenopsis saevissima. Animal Behav. 10, 134–164 (1962)
Wilson, E. O.: The insect societies. London: The Belknap Press of Harvard University Press 1979
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Weyer, J. A mathematical model for chemical mass recruitment of ants. J. Math. Biology 21, 307–315 (1985). https://doi.org/10.1007/BF00276229
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DOI: https://doi.org/10.1007/BF00276229