This study estimates that 50% of all British men with a variant of the surname Stewart are related to the Royal House of Stewart. They were able to isolate a genetic mutation that originated with Sir John Stewart of Bonkyll who died in 1298. If I have it figured right, James Stewart, the brother of Sir John, was the grandfather of Robert II.
The results are not extrapolated to men with this surname outside of Britain, so the ancestral fate of the Scotch Settlement Stewarts is uncertain.
You can read about the story from The Telegraph here. Read more about experience of a study participant here. You can follow ScotlandsDNA on Facebook here.
FWIW: I am an affiliate of ScotlandsDNA, but I would have written about this story anyway.