I think you are missing the **true** pattern of that map. Note that it shows a higher percentage of natives in Canada than it does in the US, *and* shows the same lower percentage of natives in the USA as in a geographically contiguous area of South America (1% or less).

If anything, the real pattern there is that areas in the subtropics (but not subartic) have almost no natives left, whereas areas outside that zone tend to have more. For comparison, here's a map of the subtropical climate zones.


![enter image description here][1]

The correspondence between these areas and the "fertile crescent" is no coincidence. That's where almost all European crops were domesticated, and thus where they grow best. Other areas may be useful to rule, but to come settle and live, a European society needs a place its crops can grow. (Note the yellow bands in South Africa and Australia and New Zeeland. Its no coincidence those are the only areas of significant European habitation in Africa and SE Asia/Oceana respectively.

To take a more detailed look, below is a worldwide climate zone map. The European crop package can grow well anywhere you see tan ([semi-arid][2]), green ([temperate][3]), yellow ([Mediterranean][4]), or the lighter of the more greeny blues (warmer [Continental][5]). Those areas match up almost perfectly with your map above of where native populations were completely eclipsed. Which Europeans ended up colonizing an area doesn't seem to have had an appreciable affect.

![enter image description here][6]

So the answer here is that **natives were pushed(wiped?) out nearly everywhere their land was useful for European agriculture**.


  [1]: https://i.sstatic.net/Jrk36.png
  [2]: http://en.wikipedia.org/wiki/K%C3%B6ppen_climate_classification#GROUP_B:_Dry_.28arid_and_semiarid.29_climates
  [3]: http://en.wikipedia.org/wiki/K%C3%B6ppen_climate_classification#GROUP_C:_Temperate.2Fmesothermal_climates
  [4]: http://en.wikipedia.org/wiki/Mediterranean_climate
  [5]: http://en.wikipedia.org/wiki/K%C3%B6ppen_climate_classification#GROUP_D:_Continental.2Fmicrothermal_climates
  [6]: https://i.sstatic.net/xlbr6.jpg