You are referring to the “animal imagery” found in Shakespeare’s works. In Macbeth, for example, the birds act unnaturally, which suggests that something is amiss. Shakespeare acted as an augur when using bird imagery to foreshadow upcoming events. The augur was a priest and official in ancient Rome. His main role was to interpret the will of the gods by studying the flight of birds: whether they are flying in groups or seen alone, what noises they make as they fly, the direction of flight, and what kind of birds they were. This evaluation was known as "taking the auspices.”
Consider these lines from Hamlet:
HAMLET: Do you see yonder cloud that's almost in shape of a camel?
POLONIUS: By the mass, and 'tis like a camel, indeed.
HAMLET: Methinks it is like a weasel.
POLONIUS: It is backed like a weasel.
HAMLET: Or like a whale?
POLONIUS: Very like a whale
It is at this point in the play (3.2.355-64), where the "play-within-the-play" ("the mouse-trap") has convinced Hamlet of his Uncle's guilt. In addition, Hamlet has also identified his friends from university, Rosencrantz and Guildenstern as agents of King Claudius. Hamlet declares that they cannot "play upon me" (3.2.351) but proceeds to "play" with Polonius. Polonius, ever the meddling politician, agrees with everything Hamlet says. The animal symbolism is rich.
A camel is a beast of burden and a pack animal. It is a creature that goes for long lengths of time without water. Camels can also be slaughtered for meat or water in times of crisis. Hamlet might have to be the camel that carries a tremendous burden of revenge.
A weasel is traditionally associated with a cunning and sly person. "Weasel words" tend to mislead and confuse. A weasel is a stool pigeon or an informer. Polonius, Rozencrantz and Guildenstern are all trying to "weasel" Hamlet's intentions out of him.
A whale, of course is amongst the largest mammals of the sea. Hamlet may be referring to hunting a great sea beast (Claudius) or he might be alluding to the informal use of the term "whale" which means something big or great. His act of revenge might be seen as a "whale" of a task.
Essentially, Hamlet manipulates those who would manipulate him, expending his anger through verbal mockery rather than physical aggression.
Another example of animal imagery in Hamlet is seen in Act 4, Scene 5 when Laertes tells Claudius about his father’s friends: “To his good friends thus wide I'll open my arms/ And, like the kind life-rend'ring pelican,/ Repast them with my blood.” The symbolism of the mother pelican feeding her baby pelicans is rooted in an ancient legend that preceded Christianity. The legend was that in time of famine, the mother pelican wounded herself, striking her breast with the beak to feed her young with her blood to prevent starvation. Another version of the legend was that the mother fed her dying young with her blood to revive them from death, but in turn lost her own life. Laertes is telling Claudius that he will do anything for his father’s friends (versus what he would do to his father’s enemies including those who killed him.)
Always look to the animals in Shakespeare’s plays for clues.