I'm just trying to point out that if you kill less gobblers you have more gobblers to hunt.
It sounds like you guys manage you properties very well for the birds. Yet people complain that there no birds.
Here is my point.
You have 2 identical clubs with the same amount of birds. 1000 acres each. 5 hunters each. 1 club harvests 25 birds. 1 club harvests 10 birds. Which club would you want to hunt next year. Remember, both clubs had the same amount of birds starting out.
For sure the one that killed 25. They've obviously got far better habitat than the other club, and when you have the habitat you will have the turkeys. Your example is impossible; there is no way to ever know that both had the same number at the beginning of the season.
We do a lot more down here than scout for turkeys and then kill them. Many of us spend the rest of the year managing the land for turkeys. We don't see that as the government's job; its our job to do stuff like this:

And this:

And this:

When you spend much of the year giving back to the land, then you can do some of this and still have plenty the next season:
