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Number of Source Patches Required for Population Persistence in a Source–Sink Metapopulation with Explicit Movement

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Abstract

We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Brief numerical considerations follow.

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Acknowledgements

JA and SK’s work is supported in part by NSERC. NB was supported by the Inria BIOCORE research team. The authors acknowledge comments by Matts Gyllenberg that helped tie this work with the existing literature. The authors thank an anonymous referee for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada

    Julien Arino, Nicolas Bajeux & Steve Kirkland

  2. Université Côte d’Azur, Inria BIOCORE Team, INRA, Sophia Antipolis, France

    Nicolas Bajeux

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  1. Julien Arino
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  2. Nicolas Bajeux
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  3. Steve Kirkland
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Correspondence to Julien Arino.

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Arino, J., Bajeux, N. & Kirkland, S. Number of Source Patches Required for Population Persistence in a Source–Sink Metapopulation with Explicit Movement. Bull Math Biol 81, 1916–1942 (2019). https://doi.org/10.1007/s11538-019-00593-1

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  • DOI: https://doi.org/10.1007/s11538-019-00593-1

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