Abstract
A new formalism, Grid Systems, aimed at modelling population dynamics is presented. The formalism is inspired by concepts of Membrane Computing (P Systems) and spatiality dynamics of Cellular Automata. The semantics of Grid Systems describes how stochasticity is exploited for reaction duration as well as reaction selection. Grid Systems perform reactions in maximally parallel manner, imitating natural processes. Environmental events that change population behaviour can be defined in Grid Systems as rewrite rules.
A population model of a species of mosquitoes, Aedes albopictus, is presented. The model considers three types of external events: temperature change, rainfall, and desiccation. The events change the behaviour of the species directly or indirectly. Each individual in the population can move around in the ecosystem. The simulation of the model was performed by using a semantics based tool.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Rio Declaration on Environment and Development. United Nations Conference on Environment and Development (UNCED), Rio de Janeiro, Brazil (1992)
Adamatzky, A.: Identification of Cellular Automata. Taylor and Francis, London (1994)
Barbuti, R., Caravagna, G., Maggiolo-Schettini, A., Milazzo, P., Pardini, G.: The calculus of looping sequences. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 387–423. Springer, Heidelberg (2008)
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)
Basuki, T.A., Cerone, A., Barbuti, R., Maggiolo-Schettini, A., Milazzo, P.: Modelling the dynamics of an aedes albopictus population. In: Proceedings of Application of Membrane Computing, Concurrency and Agent-based Modelling in Population Biology (2010)
Cardelli, L., Gardner, P.: Processes in space. In: Ferreira, F., Löwe, B., Mayordomo, E. (eds.) CiE 2010. LNCS, vol. 6158, pp. 78–87. Springer, Heidelberg (2010)
Cardona, M., Colomer, M.A., Perez-Jimenez, M.J., Sanuy, D., Margalida, A.: A P system modeling an ecosystem related to the bearded vulture. In: Proceedings of Sixth Brainstowming Week on Membrane Computing, pp. 52–66 (2008)
Chaloupka, M.: Stochastic simulation modelling of southern great barrier reef green turtle population dynamics. Ecol. Model. 148, 79–109 (2001)
Dematté, L., Priami, C., Romanel, A.: The BlenX language: a tutorial. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 313–365. Springer, Heidelberg (2008)
Focks, D.A., Daniels, E., Haile, D.G., Keesling, J.E.: A simulation model of the epidemiology of urban dengue fever: literature analysis, model development, preliminary validation, and samples of simulation results. Am. J. Trop. Med. Hyg. 53, 489–506 (1995)
Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. 104, 1876–1889 (2000)
Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)
Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001)
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)
Hawley, W.A.: The biology of aedes albopictus. J. Am. Mosq. Control Assoc. 4, 1–39 (1988)
John, M., Ewald, R., Uhrmacher, A.M.: A spatial extension to the \(\pi \)-calculus. Electron. Notes Theoret. Comput. Sci. 194, 133–148 (2009)
Kahramanoğullari, O., Jordan, F., Lynch, J.: CoSBiLab LIME: a language interface for stochastic dynamical modelling in ecology. Environ. Model Softw. 26, 685–687 (2011)
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)
Lanotte, R., Tini, S.: Probabilistic bisimulation as a congruence. ACM Trans. Comput. Log. 10(2), 1 (2009)
Li, H., Petzold, L.: Logarithmic Direct Method for Discrete Stochastics Simulation of Chemically Reacting Systems. Technical report, University of California Santa Barbara (2006)
Milazzo, P.: Qualitative and quantitative formal modeling of biological systems. Ph.D. thesis, Università di Pisa (2007)
Milner, R.: Communication and mobile systems: the \(\pi \)-calculus. In: Proceeding of the Pacific Symposium on Biocomputing, pp. 459–470 (2001)
Moreno, D.H.R., Federico, P., Canziani, G.A.: Population dynamics models base on cellular automata that includes habitat quality indices defined through remote sensing. In: ISRSE RM (2001)
Pardini, G.: Formal modelling and simulation of biological systems with spatiality. Ph.D. thesis, Università di Pisa (2011)
Pineda-Krch, M.: Gillespie SSA: implementing the stochastic simulation algorithm in R. J. Stat. Softw. 25, 1–18 (2008)
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)
Păun, G.: Twenty six research topics about spiking neural P systems. In: Proceeding of Sixth Brainstowming Week on Membrane Computing (2008)
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)
Tini, S.: Non-expansive epsilon-bisimulations for probabilistic processes. Theor. Comput. Sci. 411(22–24), 2202–2222 (2010)
Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)
Acknowledgments
This work has been supported partly by UNU-IIST and partly 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).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barbuti, R., Cerone, A., Maggiolo-Schettini, A., Milazzo, P., Setiawan, S. (2014). Modelling Population Dynamics Using Grid Systems. In: Cerone, A., et al. Information Technology and Open Source: Applications for Education, Innovation, and Sustainability. SEFM 2012. Lecture Notes in Computer Science(), vol 7991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54338-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-54338-8_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54337-1
Online ISBN: 978-3-642-54338-8
eBook Packages: Computer ScienceComputer Science (R0)