American Institute of Mathematical Sciences

Advanced
2005, 2(4): 833-868. doi: 10.3934/mbe.2005.2.833

Edge-linked dynamics and the scale-dependence of competitive

Robert Stephen Cantrell 1, , Chris Cosner 1, and  William F. Fagan 2,

1. 

Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States
2. 

Department of Biology, University of Maryland, College Park, MD 20742, United States

Received  April 2005 Revised  October 2005 Published  October 2005

Empirical data for several ecological systems suggest that how resource availability scales with patch geometry may influence the outcome of species interactions. To study this process, we assume a pseudoequilibrium to reduce the dimensionality of a two-consumer-two-resource model in which different resources are available in the interior of a patch versus at the edge. We analyze the resulting two species competition model to understand how the outcome of competition between consumers changes as the size of the patch changes, paying particular attention to the differential scaling of interior and edge-linked allochthonous resources as a function of patch size. We characterize conditions on patch size and parameters under which competitive exclusion, coexistence, and a reversal in competitive dominance occur. We find that the degree of exclusivity in the use of edge versus interior habitats influences the potential for transitions in competitive outcomes, but that differences in resource quality between interior and edge habitats can, depending on the scenario, have either qualitative or quantitative influences on the transitions. The work highlights the importance of patch size to understanding species interactions and demonstrates that competitive dominance can be a scale- dependent trait.
Keywords: allochthonous resources, habitat fragmentation, metapopulation dynamics, habitat edges, patch size, edge e®ects, spatial subsidies., domain size.
Mathematics Subject Classification: 92D40, 34D2.
Citation: Robert Stephen Cantrell, Chris Cosner, William F. Fagan. Edge-linked dynamics and the scale-dependence of competitive. Mathematical Biosciences & Engineering, 2005, 2 (4) : 833-868. doi: 10.3934/mbe.2005.2.833
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