Exactly, we are the apex predator, even if deer are the most deadly animal in the US (from car crashes). I can't quickly find any details on the total annual harvest, but it looks like there are about 10 million of us hunting deer every year. And in general we control the populations of various animals in all sorts of ways (sometimes unfortunate ones, e.g. changes in farming practices have virtually eliminated quail hunting in my part of SW Missouri).