If you focus on regulated sport hunting in the 20th century, I'm sure you'll find a strong correlation between hunting interest in a species and the species population numbers. In other words, the more a species is hunted (under modern regulations) the more that species thrives. It's got to do with the money hunters pour in that gets applied to management programs, like 121553 said. The best cure for a species in trouble is to get a bloc of hunters interested in hunting it.

Examples: whitetail deer everywhere since the '20s, elk in the past 3 decades since the rise of the Rocky Mountain Elk Foundation, turkeys here in the west (ID and MT particularly).