Number of source patches required for population persistence in a source-sink metapopulation with explicit movement

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Date
2019
Authors
Arino, J.
Bajeux, N.
Kirkland, S.
Journal Title
Journal ISSN
Volume Title
Publisher
Bulletin of Mathematical Biology 81, pp. 1916–1942.
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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Keywords
Metapopulations, Source-sink dynamics, Population persistence, Applied linear algebra
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