Simple conditions to evaluate the persistence of populations living in fragmented habitats are of primary importance in ecology. We address this need here using a spatially implicit approach that accounts for discrete individuals in a metapopulation. Demographic stochasticity is incorporated into a Markovian model in a natural way, as local extinction is characterized by the death or the dispersal of the last individual inhabiting a patch. The variables of the model are the probabilities p(i) (i=0, 1, 2...) that a patch be occupied by a finite, integer number i of individuals at a given time. We compare the stationary distributions predicted by the model with field data and discuss the role of dispersal in determining different distributions of local abundances. The analysis of the model leads to a persistence criterion which is equivalent to a condition formerly proved by Chesson (Z. Wahrscheinlichkeitstheor. 66, 97-107, 1984) namely that E(0)>1, where E(0) is the expected number of successful dispersers from a patch begun with one individual and to which immigration is excluded. We provide an analytic way of computing E(0) as a function of the main biological characteristics of the species (natality, mortality and dispersal rates, and colonizing ability). We can thus obtain persistence-extinction boundaries in the space of model parameters.