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The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations

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Abstract

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation R <1 but greater than a lower critical value R * . We show that the metapopulation will persist independently of its initial status if R > 1.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, FL, 32611-8105, USA

    Maia Martcheva

  2. Zoology Department, University of Florida, 620B Bartram Hall, Box 118525, Gainesville, FL, 32611-8525, USA

    Benjamin M. Bolker

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  1. Maia Martcheva
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  2. Benjamin M. Bolker
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Correspondence to Maia Martcheva.

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Martcheva, M., Bolker, B.M. The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations. Bull. Math. Biol. 69, 135–156 (2007). https://doi.org/10.1007/s11538-006-9075-y

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  • DOI: https://doi.org/10.1007/s11538-006-9075-y

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