The interactions between livestock and wildlife are complex. In some cases, wildlife and livestock may compete for resources - forage, water, etc. In other cases, wildlife and livestock seem to be complimentary. In most cases, maintaining range livestock production (instead of residential, commercial or industrial development) favors wildlife.
We've been contacted by a concerned resident regarding the potential competition between the resident deer herd and our flock of sheep for limited forage resources. While it may seem obvious to me that the greater threat to the local deer is wildfire and urban land use patterns, this gentleman is genuinely concerned about the well-being of the deer. In my experience, deer and sheep have somewhat different dietary preferences - deer prefer browse (e.g., brush), while sheep prefer grasses and annual broadleaf plants. Given the limited forage available, however, there probably is some competition.
On the other hand, we notice increased raptor activity following the sheep. As the sheep remove (or trample) the vegetation, hawks (and I presume owls) have greater success in foraging for rodents. As we moved the sheep today, for example, I saw red-shouldered and sharp-shinned hawks cruising the previous paddock. I guess "forage" is the the eye of the beholder.
I know I'm fortunate to be out in the midst of wildlife habitat on a daily basis. We try to be as predator-friendly as possible - we use guardian animals (llamas and dogs) rather than lead to protect our sheep from coyotes and mountain lions (and domestic dogs - the far greater threat in our environment). As a livestock producer, I have more direct interaction with the "wild" than most folks. On the other hand, my livelihood (and the well-being of my animals) depends on my vigilance - both in terms of providing enough feed and in protecting them from harm. This balancing act is part of our larger struggle (as a species) to live within our environment (rather than "on top" of it).