When we first moved up to the desert foothills north of Scottsdale, AZ some 15 years ago, almost every day we had several coyotes wander past the house. Often they’d spend some time browsing for rabbits or other prey just outside.
A few years later, we had an infestation of bobcats. 
Every few days, up to the present, one will come wandering across our back patio, peer in the windows, walk around the side and look in at us again, and finally wander off.
I posted some pics of the astonishing interaction between a juvinile bobcat and our Bengal cat Mehta here some time ago, which you may find intersting.
However, since the bobcats began their frequent treks past our hourse, we saw fewer coyotes, and in the past couple of years, haven’t seen a single one.
I asked others in the area if the coyote population seemed to have diminished, and they all said they saw as many as ever.
So, finally, the question: as both bobcats and coyotes hunt similar prey, has the presences of the former caused the latter to give up the hunt here? Seems unlikely, yet what else could have caused old Wile Coyote give up visiting us (very few roadrunners do we see)?
And, do bobcats and coyotes ever fight over territory?