There are many references that Pi makes to Richard Parker, either directly or indirectly, saving his life over the seven months that he is adrift at sea. First, on page 136, Pi says that if it weren't for the fact that Richard Parker was under the tarpaulin, the hyena would have eaten him. He explains that the hyena wouldn't want to eat the stronger predator's food, so Pi was reserved by the hyena for the tiger. The only problem after that is the fact that there are two predators on board that could kill Pi, not just one.
Next, in chapter 57, Pi says that Richard Parker calms him down, which is ironic, because he also incites the greatest fear in him as well. Pi explains as follows:
"If I still had the will to live, it was thanks to Richard Parker. He kept me from thinking too much about my family and my tragic circumstances. He pushed me to go on living. . . without Richard Parker, I wouldn't be alive today to tell you my story" (164).
Then, Pi comes up with a plan to tame Richard Parker, thereby claiming his position as the alpha male of the territory. Pi explains that predators don't usually attack each other; so, if Pi can establish himself as a predator, rather than prey, this will help to tame the tiger and save his life. Fortunately, something else about the tiger's motivation saves Pi's life as follows:
"If I survived my apprenticeship as the high seas animal trainer, it was because Richard Parker did not really want to attack me" (206).
Pi proceeds to explain that Richard Parker gives him four warnings before he attacks. These warnings are life-savers because once Pi learns this, boundaries are more clearly defined for survival of both of them.
One way that Richard Parker directly saves Pi's life is with the human they encounter in chapter 90--another castaway. When the man tries to kill Pi, it is Richard Parker who kills him instead.
"He gave me a life, my own, but at the expense of taking one. He ripped the flesh off the man's frame and cracked his bones. . . Something in me died then that has never come back to life" (255).
Many of the times that Pi says Richard Parker saved his life is psychological in nature. The only time that Richard Parker physically steps in and saves Pi's life directly is as shown above in chapter 90. When the reader discovers that the whole story has an alternate, real-life application, it is possible to infer that Richard Parker actually represents Pi's alter ego--the life-saving/survival one. If this is actually the case, then it is Pi's sense of survival that saved his life, not an imaginary tiger.