The Population of the Americas in 1492 is Disputed

After an email exchange, I have learned that some prominent people want to believe that the population of the Americas in 1492 is known closely. Here is why I say it is debated within a factor of 20.
Colin McEvedy and Richard Jones have the following to say in their 1978 Atlas of World Population History:1
The estimate of 1m Amerindians north of the Rio Grande- which breaks down into 0.2m in Canada, 0.05m in Alaska, and 0.75m in the rest of the Continental USA- goes back at least as far as J. Mooney (Smithsonian Miscellaneous Collections 80.7 (1928)); it seems to be generally accepted, though the California school of revisionists has issued a trial balloon in favour of 20m (sic). The present population of 0.6m represents a recovery from the all-time low of 0.5m reached in 1925. … The size of the population of Mexico in 1492 has lately become the subject of much academic argument. … The point at issue is this: was the population of Mexico in 1492 no more than 5m (Rosenblat) or was it more than 30m (Cook and Borah)? Comparisons with other parts of the world at comparable levels of culture leads us to throw in our lot with Rosenblat.
So McEvedy and Jones acknowledge disputes about the pre-Columbian population of the USA and Canada within a factor of 20, and disputes about the population of Mexico within a factor of 6. Their arguments for one end of the range are no more sophisticated than “it seems to be generally accepted” and that if the population of Mexico had been as high as 30 million, then the rate of decline which this implies would be an “improbability.” Most of their numbers for the period 1 to 1500 CE were copied by Angus Maddison whose numbers are very widely used today. But 1978 is a long time ago, so if you prefer you can check a more recent survey.
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