The U.S. Supreme Court's general rule that a copyrightable work's âoeauthor is the party who actually creates the work, that is, the person who translates an idea into a fixed, tangible expression entitled to copyright protection."
... Broad and traditional notions of copyright authorship assumed the answer to that question was limited to human creators. But no definition of "author" appears in the copyright statute. Neither does the Constitution's reference to authors mandate that they be human.
From a theoretical perspective, the question often comes down to creativity - can animals be creative? Animal research tends to suggest that animals CAN be creative, to the same extent as humans. The issues are similar with computer generated "expression" - can a computer be creative? Should randomness be considered creativity?
However you come out on those questions, courts have decided, based on a policy choice favoring humans, to exclude animal authorship. Which makes some sense, since an elephant doesn't have capacity to enforce its rights (you could have a guardian do it, but we don't allow animal guardians to sue vets for malpractice, so it is hard to see why this would be different).
With elephant paintings, the copyright is typically in the name of the zoo, or whoever enabled the elephant to make the painting (e.g. selected colors, brush type, canvas type for the animal). In the case of a monkey who took a picture, probably the zoo or the camera owner.