Very interesting, not to say astounding, that the first group went as far as Tierra Del Fuego and the Yucatan (Mayans) as well as northeast— Algonkians. BTW the Algonquians are not just Quebec but northern Ontario northern Saskatchewan and Maine. there is an Algonkian tribe and an algonkian language group which is much larger than the tribe.
I read elsewhere that the Tierra Del Fuegans are of another DNA group, far more robust. And the Mayans look absolutely nothing like the Algonkians. So this is confusing.
The Powhatan Indians of Virginia spoke an Algonquian language. At least three English words are based on words in their language (perhaps a bit garbled from the original form): tomahawk, moccasin, opossum.