Agreed. Any species may be very wild or not, depending upon the conditions that they are accustom to and their surroundings. Some of the least wild here in Texas are the huge "trophy" whitetail bucks that are hand fed. Some of these animals are sold to "hunters" at amazing prices, $25,000 and up, and are often rattled up with a feed bucket so that the "hunter" can shoot him.
My point is that on a sizeable place and with animals that have been there for generations, a hunt for exotics is not different from a hunt for the native species. As is true on any hunt, one usually sees more of things that you are not hunting than the ones that you are. When we hunt the Y O in September, whitetail season has not begun. We see gads of whitetail bucks every where. If we were hunting them, they would likely not be that easy.
Clearly, the easiest time to hunt any species is during their rut. The red deer and sika are kin to elk and rut in South Texas in early October. The fallow also rut about the same time. Thus, in late September these species are begining the rutting process and are less shy. That does not mean that they are standing under every tree just waiting to be shot. The bigger ones are plenty wary. They did not get big by being dumb.
It is very interesting to me that the auodad are very wild and shy at the Y O. Here in the Texas panhandle they re free ranging and have been established in the Palo Duro Canyon and along the caprock for many many years. I have seen auodad rams stand within 100-150 yds and watch us shoot metal targets on a shooting range that I used to have on the rim of the Palo Duro Canyon several years ago. However, these were not subjected to the hunting pressure that they have on the game ranches and we were not hunting them. I never considered them a particularly attractive trophy and have never shot at one. Others spend years hunting them and never get one.
Everyone has their own special animals that appeal to them. I like exotics. To me many of them are pretty and make excellent trophies. As with any hunt, if one sets his sights high enough on the quality of the animal that he seeks and the tool that he uses, he can make the hunt very challenging.
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It's more important where you hit 'em, than what you hit 'em with.