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Updated: May 20, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
The limiting behaviour of a stochastic patch occupancy model
1School of Mathematics and Physics, University of Queensland, Brisbane, QLD, 4072, Australia. r.mcvinish@uq.edu.au
Abstract:
Metapopulation models have been used to better understand the conditions necessary for the persistence of the metapopulation. In this paper, we study a stochastic patch occupancy model that incorporates variation in quality and connectivity of the habitat patches. Two important assumptions are imposed in our analysis. Firstly, the distance between patches has a special form. This amounts to assuming that migrating individuals follow certain pathways. Secondly, the area of the habitat patches is assumed to scale with the number of patches in the metapopulation. Under these assumptions, a deterministic limit is obtained as the number of patches goes to infinity. Using the deterministic limiting process, a condition for persistence of the metapopulation is derived.
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