We analyze a two species discrete competition model with dispersion between two patches. In this model, the two species, species 1 and species 2, compete in patch A with species 1 being the sedentary species. Patch B is a safe refuge from competition for species 2. We obtain exclusion principles as mathematical theorems. We demonstrate that providing a safe refuge does not always make a species a superior competitor. In addition, we show that a species persists whenever its carrying capacity is sufficiently large. These results are used in a study of a three-trophic-level food chain of an ecological community.