I have this theory that certain species of mammals have a "tribal" instinct. Like dogs, monkeys, and humans. Because an excessive amount of inbreeding is a bad idea, the markers for determining your tribe can't be based on anything genetic -- if the only people who are part of your tribe are related to you, you're going to end up with too many dead-end relatives.
So we needed different markers, self-selected markers, to identify tribe members. Why not? We have self-selected status markers -- in wolf packs, the less-dominant wolf will show its belly in case of a confrontation. The instinct is in the common language of the belly display, not in determining who displays the belly (wolves challenge each other regardless of their genes).
So here's my theory -- yawning is a marker of tribal inclusion. While yawning may serve other functions, it's also used to help identify members of your tribe. One creature yawns; it observes what other creatures yawn and takes that as a piece of evidence about their relative empathy. Not proof -- a piece of evidence.
Studies have shown that people with more empathy yawn more often. Monkeys yawn. And now we're sure dogs can catch yawns, too.
I wish I knew how to test this. Find out whether wolves yawn, for a start. Find out whether wolves yawn with packmates vs. non-packmates more. Dogs being domesticated, find out whether dogs yawn more often with their owners or with human strangers. Find out whether dogs yawn more or less often with human strangers if they've been trained as guard dogs. Find out whether wolves or dogs yawn more with human strangers. Find out whether opponents in contests yawn at each other more or less often than a control group. Find out whether the yawn of a pariah cause more contagion yawns than a member of the "in" crowd.
Anyway, with humans, I think the instinct goes further than just yawning, and covers some inane topics of conversation, like "So how about them Bears?" "Nice day, isn't it?" or "Whazzup?" Because the object of the conversation isn't information; it's finding out whether the other person reacts with empathy or hostility.
"Are you a part of my tribe?"
Yes: "It is a nice day."
No: No answer, a scowl, "Who cares?"
As for house cats, I suspect they're showing their teeth. Although I will have to conduct rigorous cat-yawning tests to make sure...