We investigate the potential for coexistence of species that compete for a shared resource when the resource occurs in both a source area acting as a refuge and a sink area where it is used by the competing species. Our model shows that the mixing rate between the source and sink resource populations has a dramatic influence on the outcome of competition. When there is a strict sink–source dependence, so that resource renewal in the sink is entirely dependent on the source, only exploitation competition decides which species can survive at a very small mixing rate. Increasing the flow rate basically amounts to increasing the role played by interference competition. If interspecific interference is very small, compared with intraspecific interference, increasing the mixing rate allows coexistence of many species, indeed, unlimited coexistence if the species' resource exploitation efficiencies are similar enough. If interspecific interference is significant and there is a trade-off between the exploitation and interference competitive abilities of two species, it is possible to have one species replacing the other along a gradient of increasing mixing rate, with either coexistence or alternative single-species equilibria at intermediate values of the mixing rate. It is also possible to have one species always outcompeting the other, or alternative single-species stable equilibria at large mixing rates. When the strict sink–source dependence is relaxed by allowing the resource to have a partly independent renewal–loss dynamics in the sink area, the variety of possible outcomes along a gradient of mixing rate is further increased. These outcomes are often strongly sensitive to the parameters of resource dynamics and interspecific interference competition. The implications of these results for biological conservation can be profound; detailed knowledge of interspecific interactions appears to be necessary to determine the effect of any land management that alters dispersal opportunities.