A Deterministic Size-Structured Metapopulation Model

John Val , Jana Verboom , J.(Hans) A.J. Metz
1 Institute of Evolutionary and Ecological Sciences,Department of Theoretical Biology
Leiden University, Kaiserstraat 63,NL-2311 GP, Leiden, the Netherlands.
2 Institute for Forestry and Nature Research (IBN),
P.O. Box 23, 6700 AA Wageningen, the Netherlands

February 26, 1997

Abstract:

A metapopulation model is presented for species which can reach high population densities per patch, and for which migration is such a frequent event that it influences local patch dynamics. Depending on the local dynamics chosen and the way patch extinction is modeled, there can exist stable and bi-stable situations. The model is compared to winking-patch models and single population models, favoring the latter as representatives of metapopulation dynamics. Although empty patches cannot exist in the model unless they are inhabitable, results comparable to those for the winking-patch models do exist. Single population models appear to be excellent predictors in studying the possible presence of a metapopulation.

• Introduction
• The model
  • A partial differential equation at the metapopulation level.
  • A Stieltjes renewal equation at the metapopulation level.
• Steady states and stability
• Specific growth dynamics
• Model comparison
  • Winking patches
  • Single population
• Discussion
• Acknowledgements
• References
• Numerical methods
• Characteristic equations for the steady states.
• Partial derivatives with respect to D
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