This isn’t so cleanly divided between North and South America: if we consider those areas which have a higher proportion of indigenous people, we see Peru and Bolivia as one major hotspot, Mexico and Guatemala as another, with the region in between still quite high. Paraguay provides another. Argentina, Brazil, the Caribbean and the U.S. have a much lower proportion at up to 1-2%, and Chile and Canada are also quite low, with a few %.

It is very common to assume that this derives mainly from different policies between the English and Spanish, like more intermarriage by the Spanish based on fewer female immigrants (the gender ratios of settlers were male-skewed but similar between the English and Spanish), or the ‘one drop rule’ (which mainly related to white-black relations). There furthermore was a great deal of mixing in the US, and there were wars and massacres in Latin America, to varying degrees which don’t always have a clear impact on the relative demographics today. Some speculation claims that English colonists and their Americans offshoots were much more genocidal than the Spanish, and I might expand on the evidence for/against and discussion here if I have time. There are nuances, but taking this as a simple explanation does not quite square with the cases of Belize (British from 1783) having a high indigenous percentage, while Argentina and Cuba have a very low indigenous percentage.

Yet other speculation focuses on smallpox immunity, but there is no clear evidence that the indigenous peoples of today’s U.S. were somehow less immune than those of, say, the Aztec Empire, which was also devastated.

But there is another angle:

1. The chief driver is the fact that the population of indigenous Americans in the countries where it is larger today was, in most cases, already much larger to begin with. Why was that? Well, the hotspots for indigenous population density are Meso-America (southern Mexico and Guatemala) and the northern Andes (especially Peru and Bolivia). These are also the centres of advanced civilisation in the Americas, the two New World ‘cradles of civilisation’: they built large cities and developed advanced agricultural techniques and other material culture, and thus sustained far larger pre-Columbian populations than the rest. The region in between also had many groups with a material culture more developed than those of Argentina or most of the U.S., eg the Muisca Confederation of what is now Colombia. This is not to dismiss the likes of the Mississippian culture, with its large settlements like Cahokia, but this was the exception, and not at the level of, say, Tenochtitlán, which was one of the largest cities of the world. However, pre-Colombian population estimates vary enormously, even by an order of magnitude: however, it is generally accepted that Meso-America, despite its much smaller area, had a much smaller population than what are now the US and Canada, some estimates being close to twice as much (both usually estimated in the eight digits).

2. That is with regards to absolute population, but you seem to be talking about relative population too, and there’s another clear issue there. The U.S., Canada, Brazil and Argentina received a far higher level of European immigration relative to their indigenous population than Peru, much of Central America, etc. That is, if we are only looking at the proportion of the population that is indigenous, the sheer number of Europeans is a factor as well, and the U.S. especially was a much more popular destination for Europeans from the late 18th century than Mexico. Bolivia, in addition to having a high population and much of it forming part the Inca Empire and Andean civilisation more generally, was relatively remote for European settlers who preferred to stick to the coast, where the major cities are.

3. Canada actually has a rather larger indigenous proportion of its population than some Latin American countries like Argentina and those of the Caribbean (where the Taino and Island Carib peoples are effectively extinct as ethnic groups, though many can trace mixed ancestry to them). There are a few reasons at play here, not least later concerted European settlement of the interior than in the United States - the inner prairie provinces only seeing massive European immigration at the late 19th c., some decades after what are now the U.S. states south of them. But another factor when it comes to proportion is that indigenous Americans were often consigned to the less hospitable regions, where Europeans often did not want to go, and Canada just has more of this across its area than the U.S.: we see this pattern with the higher indigenous proportion in Alaska, as well as the Canadian far north, and in the very dry states like New Mexico, as well as more arid regions of northern Mexico, and the Amazon rainforest - despite an actually quite low indigenous percentage in Brazil, ‘the Guianas’, etc., since these less hospitable areas have a lower total population per area than the rest of their countries.

4. Paraguay is a rather unusual case. It was relatively remote for European settlement, and today it has just under 2% of its population identifying as indigenous. However, the majority do identify as mestizo, and unusually in the Americas, the main indigenous language, Guarani, has a not only de jure official but even de facto prominent role in public life, with a majority claiming to speak it - though it is still second to Spanish. How Guarani maintained this status is a question all on its own, with Jesuit policy Long being credited but this explanation being drastically re-examined.