Everything needs food and water to survive. Bucks use their nutritional intake for their bodies first and then their antlers. When they have the proper amount of good food to sustain their bodies, the rest goes into antler development. Better and more ample food -- and age -- and they will have bigger antlers if their genetics are good.
A buck could have the best genes in the world but if it's eating chitty food, the antlers won't show it. If it has chitty food and dies young, the antlers won't show it.
Age, food and genes all work in concert to get to the max outcome. Those B'ham bucks aren't big just because of genes. They clearly have good food sources and are older (probably due to lack of pressure, mostly), too.
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