Its a very confusing situation with them. They are no longer referred to as a "government hunter". They are formally educated "biologists" who work for the APHIS...Animal Plant and Health Inspection Service of the US Dept of Agriculture.
Here is the site for them: http://www.aphis.usda.gov/wildlife_damage/index.shtml
Here is the link to a job opening with them right now:
IIRC at some point, I think when APHIS became its own arm of USDA, they changed the "requirements"....and the guys I ran into years ago--your typical government trapper, sure did not have any "degree" in biology. They were pretty much retired cowboy/farmer/rancher/outdoors types people.
If you examine the site above, you'll find a "history" section. That is the part that is very confusing, as they interview many people who were just like I described, and they sure are not "biologists". I think the era of common sense/experience vs. formal education came upon them about a decade ago.
**I will say, I do know of a person that still works for them. COOL! is the only term to describe certain things he gets to use.
Hope that helps (at least for info).