LOL! That's funny! 140 years of trying to extirpate the song doggie and we got as many now as ever. In fact, we have them in states where they never existed before!
SDGF&P did a lot of research on 'yote population and the effects on hunting them. Increased hunting pressure caused the coyote populations to rise and litters of pups went from 2-3 per litter to up to 8 per litter. Also noted were the increases in livestock predation. What they learned was that stable populations with little or no hunting pressure led to lowered populations and larger hunting territories. This was because the 'yotes could hunt day or night for their normal prey base...small rodents, snakes, bugs, and the like. Hunting pressure reduced their "comfort" level with typical foraging and encouraged them to take larger prey at higher risk levels in order to obtain greater rewards for less exposure to shooting. The reduced territorial acreage meant more territories available, and an increase in numbers!
A new model of depredation control involves leaving them the heck alone unless a mated pair begins to take livestock. They will teach their pups those techniques, so by culling those problem doggies and leaving others alone tends to reinforce normal behavior of focusing on small prey.
I've enjoyed plenty of hours watching a Wiley mousing in a pasture or hay field. Several times it has been within a flock of sheep, taking advantage of the sheep disturbing the mice, I surmised. Love 'em or hate 'em, you gotta give them a lot of respect for their adaptability and cleverness.