Advertisement

Methodological Steps and Issues When Deriving Individual Based-Models from Equation-Based Models: A Case Study in Population Dynamics

  • Ngoc Doanh Nguyen
  • Alexis Drogoul
  • Pierre Auger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5357)

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.

Keywords

Individual-based models Equation-based models Population dynamics Agent-based simulation Complex systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dubreuil, E., Auger, P., Gaillard, J.M., Khaladi, M.: Effects of aggressive behaviour on age structured population dynamics. Ecological Modelling 193, 777–786 (2006)CrossRefGoogle Scholar
  2. 2.
    Edelstein-Keshet, L.: Mathematical models in biology. Random house, New York (1989)zbMATHGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Murray, J.: Mathematical Biology. Springer, Heidelberg (1989)CrossRefzbMATHGoogle Scholar
  6. 6.
    Nguyen, N.D., Auger, P., de la Parra, R.B.: Effects of fast migrations on competitive coexistence (2008)Google Scholar
  7. 7.
    Auger, P., Pontier, D.: Fast Game Theory Coupled to Slow Population Dynamics: The case of Domestic Cat Populations. Mathematical Biosciences 148, 65–82 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Amarasekare, N.R.M.: Spatical heternogeneity Source-Sink Dynamics and the Local coexistence of competing species. American Naturalist 158(6) (2001)Google Scholar
  12. 12.
    Amarasekare, P.: The role of density-dependent dispersal in source-sink dynamics. Journal of Theoretical Biology 226, 159–168 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Laubenbacher, R., Jarrah, A.S., Mortveit, H., Ravi, S.S.: A mathematical formalism for agent-based modeling, arXiv:08.01.0249v1 [cs. MA] (2007)Google Scholar
  14. 14.
    Law, R., Dieckmann, U.: Moment approximations of individual-based models (1999), http://www.iiasa.ac.at/Admin/PUB/Documents/IR-99-043.pdf
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Tilman, D.: Competition and biodiversity in spatially structured habitats. Ecology 75, 2–16 (1994)CrossRefGoogle Scholar
  17. 17.
    Grimm, V., Steven, R.F.: Individual-based Modeling and Ecology. Princeton University Press, Princeton (2005)CrossRefzbMATHGoogle Scholar
  18. 18.
    Grim, V.: A standard protocol for describing individual-based and agents-based model. Ecological Modelling 198, 115–126 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ngoc Doanh Nguyen
    • 1
    • 2
  • Alexis Drogoul
    • 1
    • 2
  • Pierre Auger
    • 1
  1. 1.IRD, GEODES UR 079Bondy CedexFrance
  2. 2.MSI, IFI, Hanoi, VietnamHanoiVietnam

Personalised recommendations