With new advances in DNA tracing, anthropologists have made some surprising discoveries regarding past migrations. These include traces of apparently Polynesian DNA in a group of aboriginal (pre-contact) people in Brazil. How this particular group, which lived far to the east of the Andes, could have Polynesian ancestry is a mystery. The anthropologists have not been able to advance any theory that they themselves are satisfied with. Which leads me to wonder if maybe the science is flawed. I don't mean that the sampling was done in an unscientific way, but rather that the same mutation which arose among Polynesians, and is considered a marker of Polynesian heritage, might have happened independently in South America. In other words, it may be nothing more than coincidence.
Similar coincidences may explain other apparent genetic relationships which are hard to explain historically, between groups on different continents with no likely contact with each other. As more DNA sampling occurs, such coincidences are likely to appear with ever greater frequency.