Edge-linked dynamics and the scale-dependence of competitive

  • Received: 01 April 2005 Accepted: 29 June 2018 Published: 01 October 2005
  • MSC : 92D40, 34D20.

  • 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.

    Citation: Robert Stephen Cantrell, Chris Cosner, William F. Fagan. Edge-linked dynamics and the scale-dependence of competitive[J]. Mathematical Biosciences and Engineering, 2005, 2(4): 833-868. doi: 10.3934/mbe.2005.2.833

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  • 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.


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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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