During the period from 1519-1620, what happened to the Native American population?
For the most part, nothing.
I am going to assume that this question was asked about the Native American populations in the Northeastern North America. The unsatisfying answer is: we are unsure.
What we do know is that the Native Americans of what is now New England and Eastern Canada underwent a dramatic fall in population. It has been speculated that either Norse or English fishermen who frequented the coastal areas brought with them some disease for which the natives had no inherent protection. It could have been something as simple as influenza or worse, one of the plagues which Europe suffered through.