Many spatio-temporal patterns have been observed from numerical simulations of two-dimensional Gray-Scott model, including spot-replication, spot-annihilation, spatio-temporal chaos, etc. We explore the mechanism of multiple spot patterns by analyzing their existence and stability in two distinct regimes of feed rate parameter A. In the low feed rate regime, there is a saddle-node bifurcation structure in A, so an existence condition A > A_k should be satisfied for k-spot pattern. A nonlocal eigenvalue problem is derived and analyzed to predict the onset of competition instability in some specific parameter regime, which explains the spot-annihilation pattern. In the high feed rate regime, we derive a core problem for the equilibrium state, and the critical values of A for splitting can be obtained by stability analysis. In the end, we try to develop a qualitative theory for the replication-annihilation loop.