You may have meant "population", although WRT whitetail deer "pollution" makes a certain amount of ironic sense. I'd rather the excess deer be killed with a Winchester than with a Ford ... the former method does less damage to human life and property.
Unfortunately it is true that birth control methods have yet proved effective in controlling populations of wild, free-ranging deer. But that is the best case long term scenario. And experimental efforts are still in a very early research stage.