From Rob Holland:

Re: Why is yawning contagious? (March 5, 2005): I’ve long held thoughts that yawning, pre-sleep twitching and recently, sun-sneezing are all related to survival on a basic level; Many predators hunt at dawn and dusk and were probably near our most vulnerable moments when we’re just about to fall asleep (or just waking up) but also we’re still able to do somethings to protect ourselves.

These behaviors would all serve to startle and perhaps scare off predators who might be watching for the signs of prey falling off to sleep.

Yawning displays the teeth, twitching startles, and sun-sneezing could scare early morning hunters (one could imagine cave-mouth dwellers responding to sunlight this way. Also, sneezing could expel unwanted intruders first thing in the AM).

And why should yawing be contagious? I think the display of teeth and fangs would be a challenge in any setting so the response must likely be in kind and quite compelling.