Dynamics of a meta-population model with two competing species

In this paper, a meta-population model proposed by Haski [I. Hanski, Coexistence of competitors in patchy environment, Ecology 64 (1983) 493–500] is studied. The model involves two competing species, and allows for a varying difference between local and regional time scales. Four parameters Ri,ℛi,i=1,2Ri,ℛi,i=1,2 are defined for species ii. Our results show that Ri,ℛiRi,ℛi are the thresholds which determine the invasion of species ii into the empty patches and the patches occupied by species j,j=1,2,j≠ij,j=1,2,j≠i, respectively. If ℛ1>1ℛ1>1 and ℛ2>1ℛ2>1 the coexistence of two competing species is proved by the theory of uniform persistence. For the pure migration competition case the results indicate that the limit set of the system is a closed orbit if it contains no equilibria.