The deer pictured are fallow deer, which I know to be a fact. They were once distributed throughout Europe, the middle east and Mediterranian. They have been introduced to New Zealand and parts of the United States and Canada in more recent times.
During the Holocene period there was a close relative that was endiginous to southeast and western Asia, which was the Persian Fallow deer. This deer was larger and carried a bigger set of antlers.
A perk of majoring in wildlife biology in college is the plethora of hunting knowledge that you collect throughout your course load. One of the most important factors in whether an area can hold large quantities of animals or produce large antlers is forage.
Most universities, state schools and even community colleges offer basic botany courses and plant ID courses. Although it might not be feasable for the average middle age hunter to pay tuition and go back to college to learn hunting...