There aren't any actual animals in Wyatt's poem, but the speaker sure tries to make us think there are. In the first stanza in particular, he implies that he's talking about birds. Elsewhere in the poem, he drops some hunting metaphors and even some clever punning. Those animals never really disappear.
Line 1: The speaker says something is "fleeing" from him. This is a <strong>metaphor</strong>: the women are his prey, and they flee from him, the hunter.
Line 2: The word "stalking" can refer to the woman's movements. It makes us think of "stalks," an old Renaissance word for a part of a bird's leg.
Lines 3-4: Our guy continues to compare women to animals by saying that they were once "gentle tame and meek," but now are "wild." Now that we think of it, none of this is exactly flattering.
Lines 5-6: The women used to take bread from the speaker's hands. The speaker compares women to birds (that's a metaphor) and also compares sexual activities to the bread that feeds these animals (yet another metaphor).
Line 12: Now the speaker is "caught" by the woman. "Caught" is a metaphor in which the speaker is compared to some type of animal and the woman compared to a hunter. See how things have changed from the first stanza?
Line 14: The word "heart" may be a bit of a <strong>pun</strong>. Given all the hunting and animal words in the poem, we think of "hart" as well, which is an old-school word for a deer.