Macbeth and The Crucible both deal with how superstition drives decision making, and to a degree Life of Pi involves how a belief system interplays with reality. The main character, Pi, having grown up around zoo animals, recognizes something in the tiger's behavior and has a set of beliefs about how to survive. Pi is a bridge between the natural and human world.
The tiger in Life of Pi is the otherworldly creature, symbolic and dangerous, that is similar to the Witches (and overall atmosphere of threat) in Macbeth and the suffocating religious philosophy in The Crucible. All three texts deal with threats that are powerful and non-human, and yet require respect.
At the same time, these existential threats are unclear. Their course and behavior is difficult to discern. The tiger is right before Pi, and a threat, but also a companion. So the story shifts back and forth while Pi attempts to dominate the tiger, but never forgets its true nature.
The theme that underlines all three stories is Man vs. the Supernatural. It's a bit of a stretch, but ultimately Pi is dealing with supernatural forces in this tiger. Since the tiger is a zoo animal, he has already been removed from his habitat. Since they are companions, the tiger is also ever-present. It is not a natural tiger, but neither is it another person.
Macbeth has a foe in his own nature, represented by his tendency to believe witchcraft (especially when it serves him) but is constantly at odds with the witches because they are unclear by nature and because they don't really want what's best for him. He also has to deal with the supernatural in Banquo's ghost and Lady Macbeth's madness.
In The Crucible, the supernatural force is the supposed witchcraft that turns the girls into untrustworthy individuals. The whole town has to face the repercussions of supernatural forces, and their human nature is threatened by their fears. They don't know what's real, to some extent, yet continue to negotiate with the shifting supernatural forces.