I'm not above taking the occasional coyote when the opportunity arises, but when the vermin population booms, I leave the 'yotes alone.
I despise the rat, mouse and rabbit explosions.
I set a game feeder in my chicken pen to scatter scratch grains early in the morning. The feeder went off and about 30 rats came out to feast on the grain!

I just don't shoot bobcats. They be's bootiful!