I hate to sound like I disagree with everyone on this issue because I’m sure hawks and coyotes do kill a few pheasants, but what I’ve heard in the past and it makes since to me is that hawks and coyotes help the quail population, I would be willing to assume that it would be close to the same with pheasant. I don’t live around an area with pheasant populations so I could be completely wrong about the similarities between quail and pheasants, but what I’ve been told makes sense to me.
A hawk’s main diet is field mice, and snakes. The field mice and snakes actively search for and will devastate a quail nest and kill several soon to be gamebirds in one go around, instead of a single bird at a time.
Coyotes displace foxes, a coyote’s main diet is rabbits, they don’t pay much attention quail, and I’m not saying if given the opportunity they won’t kill and eat a quail, but they don’t actively hunt them. Foxes play a much larger roll in killing quail. Again also coyotes eat a lot of field mice that do search for the nests of quail.
So with low numbers of these two animals the rodent population will boom, and with a large population of rodents, quail and pheasant eggs will have a hard time making it through, therefore taking a large toll on these birds that we take so much enjoyment in.