Barbour AD McVinish R Pollett PK 2018 We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously. application/pdf https://sonar.ch/global/documents/47651 eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00285-018-1231-0 info:eu-repo/semantics/altIdentifier/pmid/29671043 info:eu-repo/semantics/openAccess Journal of mathematical biology. - 2018 Equilibrium Fixed point Incidence function model Metapopulation Spatially realistic Levins model Animals Linear Models Mathematical Concepts Models, Biological Population Dynamics Probability Spatio-Temporal Analysis Local approximation of a metapopulation's equilibrium. http://purl.org/coar/resource_type/c_6501