I don't think European diseases caused a change of population in the Americans any more than visa versa. Native Americans were overcome by political astuteness, cross bows, battle hounds, horses, armor, gun powder, advanced agriculture and manufacturing and tactics.
TimV:
This book and others document that the vast majority of population decrease among native americans was due to diseases from exposure to Europeans.
Amazon.com: Mayflower: A Story of Courage, Community, and War (9780143111979): Nathaniel Philbrick: Books
In King Philip's War and other early wars, the flintlocks were terribly ineffective and the indians won several large battles and devastated many early english settlements. Had it not been for alliances with other indians, they might have fared much worse. the New England Indians taught the pilgrims how to farm. Later on, the pilgrims adopted indian war tactics due to their superiority over european-style linear tactics in rustic settings.
Disease, coupled with indian inter-tribal fighting and shifting alliances with the British, sealed the fate of the native americans.
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Up until this last century, Columbus is regarded as a visionary hero. The past 50 years or so, he has become a villain. I don't think either caricature is accurate.
In my grade school I was actually taught that Columbus taught that the earth was round whereas most europenas thought the earth was flat; what a crock of baloney. The medieval scholars knew from the ancient greeks that the earth was round. The matter at dispute was just how BIG the world was. And columbus thought it was only about 3,000 miles to Asia whereas the true route would have been about 11,000 miles and have killed his crew had he not bumped into that unknown continent in between.
So, Columbus was a mistaken visionary who still, many years later, never seemed to admit that it was not asia or india that he had landed on.