Abstract
We present an algorithm for allocating individual ants to tasks that relies solely on task change being caused by the unavailability of work. We prove that such an algorithm will allocate the correct number of individuals to each job. Furthermore, we can demonstrate that if such an algorithm is used then an age structure emerges over the ants performing the various tasks. This matches closely with the weak temporal structure over tasks that is observed in Sendova-Franks and Franks (1993. Division of labour in ants nests within highly variable environments. (A study of temporal polyethism: experimental).Bull. math. Biol. 55, 75–96).
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Literature
Baeten, J., J. Bergstra and J. Klop. 1986. Syntax and defining equations for an interrupt mechanism in process algebra.Fundamenta Informatica IX, 127–168.
Calabi, P. 1988.Behavioural Flexibility in Hymenoptra: A Reexamination of the Concept of Caste, Advances in Myrmecology Leiden: E. J. Brill.
van Glabbek, R., S. A. Smolka, B. Steffen and C. Tofts. 1990. Reactive, Generative and Stratified Models of Probabilistic Processes, proceedings LICS.
Hoare, C. A. R. 1985.Communicating Sequential Processes. New York: Prentice-Hall.
Hölldobler, B. and E. O. Wilson. 1990.The Ants. Harvard: Belknap Press of Harvard University Press.
Keilson, J. 1979.Markov Chain Models—Rarity and exponentiality, Applied Mathematical Sciences 28. New York: Springer Verlag.
Larsen, K. G. and A. Skou. 1989. Bisimulation through probabilistic testing. Proceedings POPL.
Milner, R. 1983. Calculi for synchrony and asynchrony.Theor. comput. Sci. 25(3); 267–310.
Milner, R. 1990.Communication and Concurrency. New York: Prentice Hall.
Oster, G. F. and E. O. Wilson. 1978. Caste and ecology in social insects. Princeton, NJ: Princeton University Press.
Porter, S. D. and C. D. Jorgensen. 1981. Foragers of the harvester ant.Pogonomyrex owyheei: a disposable caste?Behav. Ecol. Sociobiol. 9, 247–256.
Plotkin, G. D. 1981. A structured approach to operational semantics. Technical report Daimi Fn-19, Computer Science Department, Aarhus University.
Sendova-Franks, A. B. and N. R. Franks. 1993. Division of labour in ants nests within highly variable environments. (A study of temporal polyethism: experimental.).Bull. Math. Biol. 55, 75–96.
Smolka, S., B. Steffen and C. Tofts. 1990. Probability+restriction→priority. Unpublished notes.
Tofts, C. 1990a.A Synchronous Calculus of Relative Frequency, CONCUR '90. New York: Springer Verlag, LNCS 458
Tofts, C. 1990b. The Autosynchronisation ofLeptothorax Acervorum (Fabricius) described in WSCCS, LFCS-Report Number 128.
Tofts, C. 1991. Task Allocation in Monomorphic Ant Species, LFCS Report Number 143. LFCS reports can be obtained by writing to The Department of Computer Science, James Clerk Maxwell Building, King's Building, University of Edinburgh, Mayfield Road, Edinburgh, U.K.
Tofts, C. 1992. Describing social insect behaviour using process algebra. Trans. Sim., in press.
Tofts, C. and N. R. Franks. 1992. Doing the right thing: ants, bees and naked mole rats.TREE 7, 346–349.
Tofts, C., M. J. Hatcher, and N. R. Franks. 1992. Autosynchronisation in the antLeptothorax Acervorum, theory, testability and experiment.J. theor. Biol. 157, 71–82.
Wilson, E. O. and B. Hölldobler. 1988. Dense heterachies and mass communication as the basis of organisation in ant colonies.TREE 3, 65–67.
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Tofts, C. Algorithms for task allocation in ants. (A study of temporal polyethism: Theory). Bltn Mathcal Biology 55, 891–918 (1993). https://doi.org/10.1007/BF02460691
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DOI: https://doi.org/10.1007/BF02460691