I just re-read Adam's posts in this topic. Food Savannah is a great term. I haven't heard it before. It makes sense, though. Savannah is nothing but a great big natural pasture.
I live in a dry pine forest as he mentioned. We found that the chickens can feed themselves, even in winter, but they have to range a lot farther. This means that a big flock is going to have a bigger impact in a small area. No surprise there. The problem with bigger paddocks, etc is that extra land costs. It makes profitability an issue.
Having said that, the chickens have had a positive impact. The ground within their range has green plants under the snow. It's not scientific but the only difference between that area and the rest of my land is the chickens. I'm assuming that their "grazing" kept the plants from lignifying. It could be the chickens' waste, but there wasn't really that much. It's pretty neat to scuff the snow away and see yarrow that's still green.