One thing that never gets brought up in these sweepingly generalized discussions is family planning. Pre-reservation Native Americans experienced few periods of famine compared to Europe due to numerous factors. One is that birth control and abortion, though not universally sanctioned by all tribes at all times (certainly not today), were commonly practiced and accepted. Women enjoyed more rights in historical Native American societies than in pre-20th century European societies and were not forced to have children against their will—and especially not more than they were capable of feeding.

Population control is a major, if not the most important, factor in humans' relationship to their environment.

Check out this show. It is called America Before Columbus and is quite interesting

Contrary to popular belief, the Native Americans controlled and altered the environment they lived in and did not live with zero impact.

This is an interesting Wikipedia article on the use of fire by Native Americans to control the environment they lived in.

I read a book a few years ago called 1491:New Revelations of the Americas Before Columbus that explored the pre-Columbian Native American societies all throughout the Americas, and I think that a good answer to your question can be found there. Additionally, the book explores other popular conceptions, such as the sophistication of the Native American society and population levels before Europeans arrived.

Here is an excerpt from the book: http://www.charlesmann.org/articles/1491-Atlantic.pdf

Sorry that this isn't a direct answer, I'm not an expert in the area.

William Cronon in Changes in the land contends that Native Americans were just as damaging to the environment as the new colonists were. However, because natives in New England tended to be migratory the ecosystem could repopulate itself. In sedentary native groups and the english colonists the damage to the ecosystem was consistent.

If I am remembering correctly.

Edit: As a side note Cronon would not use the word "damages" to describe changes wrought by natives and colonists, rather he would describe it as a change in the land (hence the name of the book).