That's an interesting question that deviates from the normal connections that people make to these animals. Normally, people connect these animals to real people that Pi shares in an alternate story that he relates at the end of the book. So, to relate each of these animals to Pi himself is an interesting exercise. I'll give it a go.
The hyena represents Pi's brutal, animalistic side that was willing to do whatever it took to survive. If it meant being unkind, and doing questionable things, he would do it. It can represent that deep, instinctual side of all of us, the one that tempts us to do unacceptable things, to be cruel and violent, that prompts us with inappropriate urges that we have to fight, strongly, to control in order to function as civil human beings in society. Every person has that side, and battles it throughout life. So, that is the side of Pi that the hyena--the ugly, awful animal that it is--represents. The Zebra represents the helpless victim, the one that just wants to lie down and die any time something difficult happens to him. Pi was in an awful situation, and it would have been just easier to lie there and let fate dictate his circumstances. It is the side of Pi that felt sorry for himself and his situation, the one that cried and whined about life and how unfair it was. We too, all have that side of ourselves, and have to struggle not to give in to it, because after all, it's not very productive.
The orangutan represents the compassionate, loving, protective side of Pi, and his longing for his family and mother. It reminded him of his mother, and made him feel homesick for her. It also gave him comfort and security during a difficult time. The monkey was Pi's personality trying to find strength in memories of home and family. It was the side of his personality that longed for better times, and clung to them with all of his heart--however, it didn't help him to survive, in the end. It was too soft, too inefficient, to impractical.
Richard Parker was the perfect blend of all of his different sides of his personality, the meld of them all that was the most efficient and logical choice to let come out in survival. Richard Parker represented a strong, alpha character that could dominate any situation, but not with the senseless barbarity that the hyena represented. Richard Parker, though suffering, did not whine about the situation, as the zebra did, or muck about in the past, as the monkey did. He sat there and patiently took it, and gave Pi the determination and reason to survive. It represents the survival part of Pi, the side of his personality that wanted to live, would do things he had never done before in order to survive, but did it all with dignity and grace, just like a tiger.
I hope that those thoughts help a bit; good luck!