Q. Our family has been discussing the brains of creatures and how they may be similar to or differ from the brains of humans. Do creatures have triune brains with three functional layers as do humans? I couldn’t find anything written about this.
A. What type of “creatures” are you discussing? That makes a difference. My understanding is that many (and perhaps all) mammals have parts of all three brain layers. The section they may lack is the prefrontal cortex.
Many birds are very bright, as well. Parrots, for example. And recent studies of crows have shown that they "think" and “can make tools to use as tools" and so on, which suggests cerebral function of a fairly high order.
The first functional layer in the human brain is often referred to as the reptilian layer to reflect the sense that reptiles and lizards likely have (or at least function from) primarily the first layer.
My brain’s opinion is that animals and birds may possess a sensory preference, as well. Many people have pets that "talk" to them using sounds; other pets want to be touched or not touched; and some are more visual than others, as well. My little French poodle was very clear about how good she looked after a trip to the groomer and would hold up a front foot so you could notice her toenail polish. Friends told me their hated bows and polish and would chew it off as soon as possible. Hmmm.
Individual animals and birds may also fall along the Extraversion-Ambiversion-Introversion continuum. There are pets that run and hide when strangers come to visit (Introverted), versus those that love to greet strangers before they are even through the door (Extraverts). Most are likely Ambiverts; they may not run and hide or rush up and greet everyone immediately, but they tend to observe a bit and then warm up to the guests or decide they do not want to warm up to them for some reason or other.