# American Institute of Mathematical Sciences

2004, 1(1): 131-145. doi: 10.3934/mbe.2004.1.131

## Coexistence in a metapopulation model with explicit local dynamics

 1 Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States 2 Department of Forestry and Natural Resources, Purdue University, West Lafayette, IN 47907, United States 3 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States 4 Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3

Received  February 2004 Revised  March 2004 Published  March 2004

Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We studied a metapopulation model that explicitly incorporates the local population dynamics of two competing species. The singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to more complex outcomes than simple patch models which do not include explicit local dynamics. We also discuss implications of the model for ecological systems in fragmented landscapes.
Citation: Zhilan Feng, Robert Swihart, Yingfei Yi, Huaiping Zhu. Coexistence in a metapopulation model with explicit local dynamics. Mathematical Biosciences & Engineering, 2004, 1 (1) : 131-145. doi: 10.3934/mbe.2004.1.131
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