We present the general lattice model for a multi-component atomic Bose-Einstein system in the optical lattice. Using the model, we analytically study the quantum phase transition between Mott insulator and superfluid. A mean-field theory is developed from the Mott insulator ground state. When the inter-species interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak inter-species interactions, the multi species system is miscible. Finally, the

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... diagram is discussed with the emphasis on the role of inter-species interactions. The tips of the Mott insulator lobes do not depend on the inter-species interactions, but they indeed modify the range of lobes.