From Texas Park and Wildlife, the role of genetics in antler development (of white-tailed deer).

There are 3 equally important factors that control antler development in white-tailed deer: nutrition, genetics, and age. Antler development is genetically based, environmentally influenced, and reaches its peak at maturity. The key to quality deer management is to remove those bucks which have the least desirable antler characteristics at an early age. Kerr WMA studies show that yearling antlers predict a buck’s antler quality at maturity. Kerr genetic studies indicate bucks with the best antlers will produce more progeny with exceptional antlers than will poorer bucks. The does influence antler production as well. Harvest of older does is important to insure younger does are products of better bucks. Habitat should be managed so that deer can achieve their greatest antler potential. There are no methods to “jump-start” a quality deer program.

Updated: Related article on nutrition (bottom line: want big antlers? feed ’em good, high protein). And on age.