The American indians were not the great hunters and trackers of the TV created myths. They did alright for themselves in most cases and it is interesting how they did develop the weapons and tool that they used. They were not far removed from the stone age in that regard as late as the 1800's.
If you're interested in learning more about the indians that inhabited the area west of the Mississippi you might want to read the Journals of Lewis and Clark ( Bernard DeVoto/Mariner Books). They have been reprinted in part, with thier spelling errors and all covering the greatest undertaking of their time in North America.
The greatest bowmen in history were most likely the English archers followed closely by the Asians. It had more to do with the equipment that they each were able to develop that provided them with the opportunity to advance their skills than did their cultures.