Can an animal commit copyright infringement?
Suppose Bob has a parrot who has learned a song from listening to the radio. If the parrot presses a button on Bob's computer to start a Livestream (or record a video) and records itself singing a copyrighted song, has the parrot committed copyright infringement?
No and no.
A non-human animal does not have legal capacity to sue or be sued, and is not capable of being guilty of a crime.* Since these are the only ways that copyright infringement can be enforced, a non-human animal cannot have liability, either criminal or civil, for copyright infringement.
For what it is worth, plants likewise cannot have liability, either criminal or civil, for copyright infringement.
This said, under some circumstances, one can imagine that a work "literally" done by an animal can be attributed to a human author. For example, if a human author samples animal sounds and edits them into a musical composition, even if there are no human created sounds in the final work, it would still be a work of human authorship.
On the other hand, there are documented examples of bird songs in a particular place being derived from human musical compositions that were played in the presence of the ancestors of the current birds. The birds can't be punished under copyright laws for copying the human songs that they copied, and derived their own songs from, in that case.
Likewise, a purely human musical composition derived from a bird song is not copyright infringing.
Under US law, the recording can't have a copyright since it doesn't have human authorship, but is the recording public domain, or is it a derivative work?
It would be in the public domain.
* This rule is basically universal in all modern legal systems that have copyright laws. But there have been a handful of outlier/flunk incidents in human history in which non-human animals have been made defendants in criminal trials, convicted, and sentenced in some way (usually executed) for crimes. These incidents almost always occurred at the dawn of modern legal thought, usually prior to the 19th century, and were exceeding rare even then. For example, "such trials are recorded as having taken place in Europe from the thirteenth century until the eighteenth." One of the last animal trials was of a donkey in 1750 (although there was one case where a bear was tried for and convicted of a crime in Kazakhstan in 2004). But, the time frame in which legal systems have had copyright laws, and the time frame in which there were isolated instances of criminal punishments of non-human animals, have little overlap. "The British Statute of Anne 1710, full title "An Act for the Encouragement of Learning, by vesting the Copies of Printed Books in the Authors or purchasers of such Copies, during the Times therein mentioned", was the first copyright statute."