We've got something of a similar situation up here on Manitoulin Island - the coyote population's pretty high, and the deer are really low. People are trying to blame the coyotes, and while I don't doubt they kill a lot of deer, the amount of deer taken in the gun season here is huge, and the last few seasons before the deer decline the MNR was issuing extra doe tags.
Perfect storm after that,really. Lots of does killed meant fewer fawns, followed by a hard winter that made coyote predation easy. Mostly our fault, I figure. The local game clubs are now calling for fewer tags issued - courageous of them, and about time.
Now I've never hunted elk, but I know the coyotes up here are really wary coming to anything but a electronic call...and now they won't even do that necessarily. Animals adapt to heavily-used tactics.
And that's my rant for the day. Hope I didn't ruffle anyone's feathers.