I doubt if anyone could claim a pure-blooded succession as the whole history of the human race has been founded upon migration and conquest and subsequent colonisation and America is just one of the most recent examples of that (along with Australia and Africa). Scotland itself has experienced similar events with the Picts being usurped by the Scots (from Ireland) at the same time as the Norsemen (Vikings) followed by the Normans (yet more Vikings). Recent migrations have been less intrusive, perhaps because the climate is inimical to people from the Caribbean, Asia and Africa but anyone claiming to be a pure-blooded Scot is probably deluding themselves. Scots over the past few hundred years have settled and inter-married in all parts of the world and brought their own particular values and ideas with them. It was Scots who valued and fostered education for all above all else, who decried the class system so beloved of the English ("The man's a man for a that") and these are sentiments ingrained into the Scottish psyche. If you too espouse these values then who is to say you don't have Scottish blood somewhere in your veins.