We consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly. Strong spatial heterogeneity is considered, represented by a position dependent reproduction rate. The geometry of the problem is that of two patches where the reproductive rate is positive, surrounded by unfavorable patches where it is negative. We focus on the particular case where the population would not persist in the single patches (sinks). We find by means of an analytical derivation, supplemented by a numerical calculation, the conditions for the persistence of the population in the compound system of weakly connected patches. We show that persistence is possible even if each individual patch is a sink where the population would go extinct. The results are of particular relevance for ecological management at the landscape level, showing that small patches may harbor populations as long as the connectivity with adjacent patches is maintained. Microcosmos experiences with bacteria could be performed for experimental verification of the predictions.
