I've looked at a few notes and it's a rigorous topic, actually.
Key words to note are NEPHESH, RUACH, SARX, NESHAMAH, PSUCHIKOS, PNEUMA,
Four views on the origin of the human soul.
1) Pre-existence of all human souls (Origen and the Mormons)
2) Metempsychosis or reincarnation.
3) Traducianism,...soul transmitted through biological life. Body and soul are propagated by human generation or that God creates mediately, rather than immediately, hence body and soul originate from parents. (Tertullian, Greek Orthodox, Eastern Orthodox)
4) Creationism,..view of Pelagius, Jerome, most RCC, Charles Hodge, Berkoff, many reformed theologians, ..Creationsm regards the soul as being immediately created by God and joined to the body either at conception or at birth.
Above are just a few notes as a starting point. Once one firms up doctrinal positions on the origin of life, then identifying the animal life and its components seems to drive the appropriate conclusions.
A few added ticklers include: Spirits are able to indwell animals,...the demons cast out of the demoniac and then entered the swine that ran into peril. Also Balam was able to converse with the donkey/jackass. Just from the top of my head,...I don't know the proper answer, but these topics do come to mind.