Richard Parker keeps Pi vigilant. Pi must always be on his toes, always working to fish, collect water, and maintain his life raft for his own survival and to keep Richard Parker happy. Pi keeps Richard Parker happy because if he doesn’t, he believes Richard will eat him, which means sustaining the supply of food and water. Remember the passages where Pi talks about different species learning to live together in the zoo. They do what they need to survive. I think he referred to this as zoomorphism; when one animal sees an animal of another species (even a human) as a member of its own species. Pi also appeases Richard Parker out of loneliness. A relationship is a relationship even if it is based on fear and uncertainty.
Earlier in the novel, Pi notes the danger of seeing an animal as human-like. In an ironic twist, Pi does the opposite with the cook. But he did so in order to maintain a zoomorphic relationship with him/Richard Parker. Treating his relationship with Richard Parker as two different species living together as if they were the same species allowed him to maintain a skeptical symbiotic relationship. This is what allowed Pi to survive.
Pi’s love of all religions is applicable here too. He saw the different religious narratives as equally valid and applicable in different circumstances. Likewise, Pi created his own narrative in order to survive. Real or not, Richard Parker was his religious allegory, which gave him the right perspective on his situation in order to survive. Richard Parker kept him company, kept him aware and forced him to structure his day meticulously, which ensured his survival and really kept him from losing his mind. As long as he was busy, he would not have time to dwell on the hopelessness of his situation.