There is plenty of room for those estimates to be off. A few cultures did exist on the Great Plains before 1700, but most did not move onto the Plains until after the arrival of horses. The Pawnee and Wichita did inhabit river valleys along the Platte and Arkansas rivers beginning around 1300 or so, but they were exceptions. The most common estimate for the number of Indians north of Mexico when Columbus arrived is 8 million. Truth is we can’t do much more than guess.
Well, they can certainly estimate how many people could live off a particular parcel of land - taking into consideration that they were migratory as well (following the seasons). I suspect the warmer climates accommodated larger populations (where gathering was much easier); while the Inuits/Eskimos would be at the other extreme.
One of the civilizations (possibly in Mexico - Olmec?) actually disappeared before any whites ever arrived; the myth of the Eden-esque paradise destroyed by whites is dying.
Also, interesting that you mention those rivers. While the US is huge on a map, remember that those early peoples were completely tied to those water sources (unlike later whites who irrigated massive sections of the country).
I have never been able to figure out why it is that the Basques and the Blackfoot are the two peoples with the highest rate of rh negative blood.
Don’t know if there is any way to make population estimates, but people found “lots” of arrow heads in blowouts - areas where the soil had been blown away - in the Dust Bowl country of the Oklahoma pan handle, Dalhart, Texas.