Journal of Mathematical Biology

, Volume 71, Issue 6–7, pp 1481–1504 | Cite as

Connecting deterministic and stochastic metapopulation models

  • A. D. Barbour
  • R. McVinish
  • P. K. Pollett


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.


Stochastic patch occupancy model (SPOM) Vapnik–Chervonenkis theory 

Mathematics Subject Classification

92D40 60J10 60J27 



We would like to thank the two referees for their helpful comments and suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Universität ZürichZurichSwitzerland
  2. 2.University of QueenslandBrisbaneAustralia

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