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.

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.

My understanding is that this is not the case. A dozen years ago, I made a similar statement in an ecology class and the professor thought that the issue was important enough to ignore his planned material and spent half-an-hour raking me over the coals. The natives did burns, but their population was too small to have much of an impact. Lightning was by far the bigger contributer, but even so, burns aren't a long-term advantage. You would have seen a similar impact after grazing by sheep or goats as you did after the prescribed burn. In the long-term grazing is the better option.

Infact, ruminants and climate are what made the natural prairies. Lack of water favours grasses over trees. It's only in artificial prairies claimed from forest (ie. my farm) where one has to make an effort to keep the trees from taking the land back. But this effort is better made with livestock or a "brush-hog" than with fire. Rather than recycling nutrients into the soil, burning gassifies most of the nitrogen and potassium that would otherwise be incorporated into the soil. Enlightened farmers don't burn anything that they don't have to.

Here's the first link that "burning organic matter fertility" yielded on Google:

http://www.new-agri.co.uk/00-1/pov.html

Basically, rather than burning, they are advocating charring crop residues which leaves much (well, half) of the carbon. My gut tells me (warning: WAG ahead) that it would probably be more effective, and safer (less risk of starting an uncontrolled fire), to just leave the residue in place or let livestock clean it up. Letting a ruminant get much of it's diet from crop residue seems most attractive to me, but letting residue remain as a moisture conserving mulch makes a lot of sense too.

It would be interesting to see the approach in the article compared to the alternatives. Rather than just holding up an orange and saying, "Lood at this nice orange," we could compare it to the other oranges and apples.