Abstract
Seasonal migration is the long-distance movement of a large number of animals belonging to one or more species that occurs on a seasonal basis. It is an important phenomenon that often has a major impact on one or more ecosystem(s). It is not fully understood how this population dynamics phenomenon emerges from the behaviours and interactions of a large number of animals. We propose an approach to the modelling of seasonal migration in which dynamics is stochastically modelled using rewriting systems, and spatiality is approximated by a grid of cells. We apply our approach to the migration of a wildebeest species in the Serengeti National Park, Tanzania. Our model relies on the observations that wildebeest migration is driven by the search for grazing areas and water resources, and animals tend to follow movements of other animals. Moreover, we assume the existence of dynamic guiding paths. These paths could either be representations of the individual or communal memory of wildebeests, or physical tracks marking the land. Movement is modelled by rewritings between adjacent cells, driven by the conditions in the origin and destination cells. As conditions we consider number of animals, grass availability, and dynamic paths. Paths are initialised with the patterns of movements observed in reality, but dynamically change depending on variation of movement caused by other conditions. This methodology has been implemented in a simulator that visualises grass availability as well as population movement.
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Adamatzky, A.: Identification of Cellular Automata. Taylor and Francis, London (1994)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Cerone, A., Setiawan, S.: Modelling population dynamics using grid systems. In: MoKMaSD 2012. LNCS, vol. 7991, pp. 172–189. Springer, Heidelberg (2014)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Pardini, G., Rama, A.: A process calculus for molecular interaction maps. In: Membrane Computing and Biologically Inspired Process Calculi (MeCBIC), pp. 35–49 (2009)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: Compositional semantics and behavioral equivalences for p systems. Theor. Comput. Sci. 395(1), 77–100 (2008)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: A p systems flat form preserving step-by-step behaviour. Fundam. Inform. 87(1), 1–34 (2008)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: An overview on operational semantics in membrane computing. Int. J. Found. Comput. Sci. 22(1), 119–131 (2011)
Boone, R.B., Thirgood, S.J., Hopcraft, J.G.C.: Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology 87(8), 1987–1994 (2006)
Durier, V., Graham, P., Collett, T.S.: Snapshot memories and landmark guidance in wood ants. Curr. Biol., Elsevier Science Ltd. 13, 1614–1618 (2003)
Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)
Goss, P.J., Peccoud, J.: Quantitative modeling of stochastic system in molecular biology by using Petri Nets. J. Bioinform. Comput. Biol. 95, 6750–6755 (1990)
Holdo, R.M., Holt, R.D., Fryxell, J.M.: Opposing rainfall and plant nutritional gradients best explain the wildebeest migration in the Serengeti. Am. Nat. 173, 431–445 (2009)
Kaupp, U.B., Kashikar, N.D., Weyand, I.: Mechanism of sperm chemotaxis. Ann. Rev. Physiol. 70, 93–117 (2008)
Kohn, K.W., Aladjem, M.I., Weinstein, J.N., Pommier, Y.: Molecule interaction maps of bioregularity networks: a general rubric for systems biology. Mol. Biol. Cell 17, 1–13 (2005)
Lohmann, K.J., Putman, N.F., Lohmann, C.M.F.: Geomagnetic imprinting: a unifying hypothesis of long-distance natal homing in salmon and sea turtles. Proc. Nat. Acad. Sci. 105(49), 19096–19101 (2008)
Milazzo, P.: Qualitative and quantitative formal modeling of biological systems. Ph.D thesis, Università di Pisa (2007)
Pardini, G.: Formal modelling and simulation of biological systems with spatiality. Ph.D thesis, Università di Pisa (2011)
Priami, C., Regev, A., Silverman, W., Shapiro, E.Y.: Application of a stochastic name-passing calculus to representation and simulation a molecular processes. Inf. Process. Lett. 80, 25–31 (2001)
Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (2000)
Regev, A., Silverman, W., Shapiro, E.Y.: Representation and simulation of biochemical processes using the \(\pi \)-calculus process algebra. In: Proceeding of the Pacific Symposium on Biocomputing, pp. 459–470 (2001)
Reynolds, C.W.: Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. 21(4), 25–34 (1987)
Rojas, R.: Neural Networks - A Systematic Introduction. Springer, Berlin (1996)
Rozenberg, G., Bck, T., Kok, J.: Handbook of Natural Computing. Springer, Heidelberg (2012)
Acknowledgments
This work has been supported by Macao Science and Technology Development Fund, File No. 07/2009/A3, in the context of the EAE project. Suryana Setiawan is supported by a PhD scholarship under I-MHERE Project of the Faculty of Computer Science, University of Indonesia (IBRD Loan No. 4789-IND & IDA Credit No. 4077-IND, Ministry of Education and Culture, Republic of Indonesia).
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Setiawan, S., Cerone, A. (2014). Stochastic Modelling of Seasonal Migration Using Rewriting Systems with Spatiality. In: Counsell, S., Núñez, M. (eds) Software Engineering and Formal Methods. SEFM 2013. Lecture Notes in Computer Science(), vol 8368. Springer, Cham. https://doi.org/10.1007/978-3-319-05032-4_23
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DOI: https://doi.org/10.1007/978-3-319-05032-4_23
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