Mathematical Model of Proportion Control and Fluctuation Characteristic in Termite Caste Differentiation
Yusuke Ikemoto*, Kuniaki Kawabata**, Toru Miura***,
and Hajime Asama*
*RACE, The University of Tokyo, 5-1-5 Kashiwano-ha, Kashiwa, 277-8568, Japan
**RIKEN, 2-1 Hirosawa, Wako, Saitama, Japan
***Graduate School of Environmental Science, Hokkaido University, Sapporo 060-0810, Japan
Self-organization of hierarchy of system has been focused in task allocation of distributed autonomous systems and network analysis. It is important to realize the mechanism of hierarchy generation for implementation in artificial systems. In order to know the principle, we try to model the control of caste differentiations in the termite ecology. Equations of evolution are created, using both of biological data and assumptions obtained by mathematical analysis. In addition, the model is validated by computer simulations. In this study, we propose that the probability migration of individuals and modulations of fluctuation are operated as a differentiation control strategy.
-  H. Asama, T. Arai, T. Fukuda, and T. Hasegawa (Eds.), “Distributed Autonomous Robotic Systems 5,” Springer, ISBN 4-431-70339-X, 2002.
-  T. Mizuguchi and M. Sano, “Proportion Regulation of Biological Cells in Globally Coupled Nonlinear Systems,” Physical Review Letters, 75, pp. 966-969, 1995.
-  H. Sakaguchi, “Domain-size Control by Global Feedback in Bistable Systems,” Rhysical Review E, 64, 047101, 2001.
-  T. Mizuguchi, K. Sugawara, H. Nishimori, T. Tao, T. Kazama, H. Nakagawa, Y. Hayakawa, and M. Sano, “Collective Dynamics of Active Elements: Task Allocation and Pheromone Trailing,” qbio., PE, 0408019, 2004.
-  E. Bonabeau, G. Theraulaz, and J. Deneubourg, “Mathematical model of self-organizing hierarchies in animal societies,” Bulletin of Mathematical Biology, 58(4), pp. 661-717, 1996.
-  T. Miura and T. Matsumoto, “Worker polymorphism and division of labor in the foraging behavior of the black marching termite Hospitalitermes medioflavus,” on Borneo Island, Naturwissenschaften, 82, pp. 564-567, 1995.
-  T. Miura and T. Matsumoto, “Ergatoid reproductives in Nasutitermes takasagoensis (Isoptera: Termitidae),” Sociobiol., 27, pp. 223-238, 1996.
-  T. Miura, Y. Roisin, and T. Matsumoto, “Developmental pathways and polyethism of neuter castes in the processional nasute termite Hospitalitermes medioflavus (Isoptera, Termitidae),” Zoological Science, 15, pp. 843-848, 1998.
-  E. M. Miller, “Caste differentiation in the lower termites,” Biology of Termites, Vol.I (K. Krishna and F. M. Weesner, Eds.), Academic Press, New York, pp. 283-310, 1969.
-  C. Noirot, “Formation of castes in the higher terimtes,” Biology of Termites, Vol.I. (K. Krishna and F. M. Weesner, Eds.), Academic Press, New York, pp. 311-350, 1969.
-  Y. Roisin, “Diversity and evolution of caste patterns,” Termites: Evolution, Sociality, Symbioses, Ecology, (T. Abe, D. E. Bignell, and M. Higashi, Eds.), Dordrecht, The Netherlands, Kluwer Academic Publishers, 2000 (in press).
-  T. Miura, A. Kamikouchi, M. Sawata, H. Takeuchi, S. Natori, T. Kubo, and T. Matsumoto, “Soldier caste-specific gene expression in the mandibular glands of Hodotermopsis japonica (Isoptera: Termopsidae),” Proc. of the National Academy of Sciences, USA, 96, pp. 13874-13879, 1999.
-  T. Miura and T. Matsumoto, “Soldier morphogenesis in a nasute termite: discovery of a disk-like structure forming a soldier nasus,” Proc. R. Soc. Lond., B, 267, pp. 1185-1189, 2000.
-  S. Sameshima, T. Miura, and T. Matsumoto, “Wing Disc Development during Caste Differentiation in the Ant Pheidole Megacephala (Hymenoptera: Formicidae),” Evolution and Development, 6, pp. 336-341, 2004.
-  R. W. Howard and M. I. Haverty, “Termites and juvenile hormone analogues: A review of methodology and observed effects,” Sociobiol., 4, pp. 269-278, 1979.
-  R. Howard and M. I. Haverty, “Seasonal variation in caste proportions of field colonies of Reticulitermes flavipes (Kollar),” Environ. Entomol., 10, pp. 546-549, 1981.
-  W. D. Hamilton, “The genetic theory of social behaviour,” I, II. J. Theor. Biol., 7, pp. 1-52, 1964.
-  M. Lüscher, “Social control of polymorphism in termites,” Insect Polymorphism (J. S. Kennedy, Ed.), Roy. Entomol. Soc., London., pp. 57-67, 1961.
-  G. D. Prestwich, “Chemical systematics of termite exocrine secretions,” Annu. Rev. Ecol. Syst., 14, pp. 287-311, 1983.
-  G. Henderson, “Primer pheromones and possible soldier caste influence on the evolution of sociality in lower termites,” Pheromone Communication in Social Insects - Ants, Wasps, Bees and Termites (R. K. Vander Meer, M. D. Breed, M. L. Winston and K. E. Espelie, Eds.), Westview Press, Boulder., pp. 314-330, 1998.
-  P. Lefeuve and C. Bordereau, “Soldier formation regulated by a primer pheromone from the soldier frontal gland in a higher termite,” Nasutitermes lujae, Proc. Natl. Acad. Sci., USA, 81, pp. 7665-7668, 1984.
-  M. Lüscher, “Hormonal control of caste differentiation in termites,” Ann. New York Acad. Sci., 89, pp. 549-563, 1960.
-  H. F. Nijhout and D. E. Wheeler, “Juvenile hormone and the physiological basis of insect polymorphisms,” Quart. Rev. Biol., 57, pp. 109-133, 1982.
-  J. A. Harvey, L. S. Corley, and M. R. Strand, “Competition induces adaptive shifts in caste ratios of a polyembryonic wasp,” Nature, 406, pp. 183-186, Letters to Editor, 2003.
-  D. M. Gordon, “Soldier production under threat,” Nature, 379, pp. 583-584, News and Views, 1996.
-  L. Passera, E. Roncin, B. Kaufmann, and L. Keller, “Increased soldier production in ant colonies exposed to intraspecific competition,” Nature, 379, pp. 630-631, Letters to Editor, 1996.
-  T. Miura, “Developmental regulation of caste-specific characters in social-insect polyphenism,” Evolution and Development, 7, pp. 122-129, 2005.
-  C. Noirot, “Caste differentiation in Isoptera: basic features, role of pheromones,” Ethol. Ecol. Evolution Special, Issue 1, pp. 3-7, 1991
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.
Copyright© 2007 by Fuji Technology Press Ltd. and Japan Society of Mechanical Engineers. All right reserved.