I'm a retired wildlife biologist. I've examined many results of home range studies that involved radio-collared deer and elk. I've also studied research regarding home ranges (deer) and their reluctance to leave them, even if chased by hounds and how quickly they will return to their home range when the chase ends. The size, shape, and movement within home ranges is dictated by terrain, escape cover, food, and at times procreation. I've never heard of the concept of evolutionary movement patterns in deer.
From a rabbit hunter's perspective, when our dogs ran rabbits, foxes, or deer you could get a really good feel for how large a "circle" the animal they were chasing made. Invariably, the rabbit, fox, or deer would return to near the place where the track was cut.
Prey populations control predator populations both in numbers and movements. If you have a bumper crop of rodents, foxes, coyotes, and birds of prey flourish. When the bumper crop declines, the predators also decline. The wolf goes where the prey is going or has gone -- just like we do.
I've never heard of anyone bad-mouthing the flavor of elk. A cattle rancher friend in Wyoming hunts elk for the meat and he has access to alfalfa-fed beef all year long.