RECONCILING THEORETICAL APPROACHES TO STOCHASTIC PATCH-OCCUPANCY METAPOPULATION MODELS

There appear to be two different kinds of theoretical results about st ochastic patch-occupancy metapopulation models: those recently propose d by Gyllenberg and Silvestrov about metapopulations including a very stable patch, and those by Darroch and Seneta about more general metap opulations. Based on the spectral theory of linear operators, it is sh own that the results by Gyllenberg and Silvestrov are a limiting case of those by Darroch and Seneta. Taking the examples proposed by Gyllen berg and Silvestrov as a case study, the application and relevance of these results are discussed, with a particular stress to their bearing on real metapopulations. (C) 1998 Society for Mathematical Biology.