Abstract
An important question in the simulation of complex systems concerns the emergence of global behaviours and how to model them. Individual-based models (IBM), on one hand, are designed precisely for exploring emergent phenomena, but they must be simulated (sometimes extensively) in order to detect the behaviours that could emerge at the global level. Moreover, there are no “theories of IBM” that would allow modellers to make predictions about the long-term emerging behaviours they can observe. On the other hand, equation-based models (EBM), while not exploring the same causes of emergence, represent a useful tool for making predictions about global emerging behaviours of a system, especially in the long term. In this paper, we will explore the methodological issues that arise when attempting to derive an IBM from an existing EBM model in population dynamics, dedicated to exploring the dynamics of two competing populations in a “two-patch” environment.
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Dubreuil, E., Auger, P., Gaillard, J.M., Khaladi, M.: Effects of aggressive behaviour on age structured population dynamics. Ecological Modelling 193, 777–786 (2006)
Edelstein-Keshet, L.: Mathematical models in biology. Random house, New York (1989)
Fahse, L., Wissel, C., Grimm, V.: Reconciling classical and individual-based approaches in theoretical population ecology: a protocol for extracting population parameters from individual-based models. American Naturalist 152, 838–852 (1998)
Georiy, V.B., Goedecke, M.D., Yu, J.F., Epstein, S.M.: A hybrid epidemic model: Combining the advantages of agent-based and equation-based approaches. In: Proceeding of the 2007 Winter Simulation Conference (2007)
Murray, J.: Mathematical Biology. Springer, Heidelberg (1989)
Nguyen, N.D., Auger, P., de la Parra, R.B.: Effects of fast migrations on competitive coexistence (2008)
Auger, P., Pontier, D.: Fast Game Theory Coupled to Slow Population Dynamics: The case of Domestic Cat Populations. Mathematical Biosciences 148, 65–82 (1998)
Auger, P., Bravo de la Parra, R., Morand, S., Sanchez, E.: A predator-prey model with predators using hawk and dove tactics. Mathematical Biosciences 177, 185–200 (2002)
Auger, P., Bravo de la Parra, R., Poggiale, J.C., Sánchez, E., Nguyen Huu, T.: Aggregation of variables and applications to population dynamics. In: Magal, P., Ruan, S. (eds.) Structured Population Models in Biology and Epidemiology. Springer, Heidelberg (2008)
Auger, P., Kooi, B., Bravo de la Parra, R., Poggiale, J.-C.: Bifurcation Analysis of a Predator-prey Model with Predators using Hawk and Dove Tactics. Journal of Theoretical Biology 238, 597–607 (2006)
Amarasekare, N.R.M.: Spatical heternogeneity Source-Sink Dynamics and the Local coexistence of competing species. American Naturalist 158(6) (2001)
Amarasekare, P.: The role of density-dependent dispersal in source-sink dynamics. Journal of Theoretical Biology 226, 159–168 (2004)
Laubenbacher, R., Jarrah, A.S., Mortveit, H., Ravi, S.S.: A mathematical formalism for agent-based modeling, arXiv:08.01.0249v1 [cs. MA] (2007)
Law, R., Dieckmann, U.: Moment approximations of individual-based models (1999), http://www.iiasa.ac.at/Admin/PUB/Documents/IR-99-043.pdf
Hinckley, S., Hermann, A.J., Megrey, B.A.: Development of a spatially explicit, individual-based model of marine fish early life history. Marine Ecology Progress Series 139, 47–68 (1996)
Tilman, D.: Competition and biodiversity in spatially structured habitats. Ecology 75, 2–16 (1994)
Grimm, V., Steven, R.F.: Individual-based Modeling and Ecology. Princeton University Press, Princeton (2005)
Grim, V.: A standard protocol for describing individual-based and agents-based model. Ecological Modelling 198, 115–126 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, N.D., Drogoul, A., Auger, P. (2008). Methodological Steps and Issues When Deriving Individual Based-Models from Equation-Based Models: A Case Study in Population Dynamics. In: Bui, T.D., Ho, T.V., Ha, Q.T. (eds) Intelligent Agents and Multi-Agent Systems. PRIMA 2008. Lecture Notes in Computer Science(), vol 5357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89674-6_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-89674-6_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89673-9
Online ISBN: 978-3-540-89674-6
eBook Packages: Computer ScienceComputer Science (R0)