"The burns kept trees from taking over."

No they didn't. I've addressed this misconception in a comment below.

You've outlined much of the reading that has lead me to sustainable farming. Anybody else who would like to start, or transition, to sustainable farming would be well-advised to check out some of this material. ATTRA (http://attra.org) is also a good source of information.

People might like to read up on slash-and-burn farming. People in the Amazon Basin have been practicing this method for thousands of years. It's a quick way to clear a field and returns nutrients from the plant matter faster than if left to rot naturally.

The problem? Nutrients in tropical soils are scarce. The input from burning doesn't last long and the farmer must clear another section of forest (every three years or so if I remember my class notes correctly). Since the forest takes longer to recover than three years, each farmer needs a significant amount of fallow land. The method still works well as long as population density is very low and the farmer is willing to sustain back-breaking amounts of labour.