Connecting deterministic and stochastic metapopulation models.
In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.
Universität Zürich, Zurich, Switzerland. a.d.barbour@math.uzh.ch.
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Barbour
University of Queensland, Brisbane, Australia. r.mcvinish@uq.edu.au.
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McVinish
University of Queensland, Brisbane, Australia. pkp@maths.uq.edu.au.
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Pollett
D000818:Animals; D017753:Ecosystem; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics / Q000706:statistics & numerical data; D013269:Stochastic Processes; D013997:Time Factors
Stochastic patch occupancy model (SPOM); Vapnik–Chervonenkis theory