Well, you didn't miss much excitement, Bryce. Research on insect ocelli, mostly in the mantids' cousins, the grasshoppers, was being done back in the thirties. Almosy every article or abstract that I have read, though ends up by stating what new has been discovered. !Even Christian has admitted to being stumped as to their function!
Modern sources suggest that they might serve at least two functions: as a means of distinguishing a change in photoperid and as a means of recognizing the horizon during flight. Neither of these is more than a hypothesis, so far as I know, but both may have very important consequences for mantises (or mantids or mantes!
![Big grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
).
1) The ability to detect photoperiod may be redundant. In a discussion of diapause, Gullan and Cranston confidently state that photoperiod is detected directly by brain photoreceptors and not by the compound eyes and ocelli (p.158), but this relies on an unsupported assumption that all diapausing insects use the same sensors
2) I have wondered why, if the ocelli are used as a device for horizon detection, they are present in mantis (and dragonfly) nymphs and in essentially flightless females. Although the Prete book doesn't adress this issue specifically, it does show (though this is not a new discovery), that the adult's ocelli are better developed than those of nymphs and that the males have larger ones than the females, which is consistent with the horizon finding hypothesis.
I don't know whether this helps or adds to the confusion!