What the article, after a QUICK reading, is suggesting is this: the hunter-gatherer indigenous population(s) of 'europe,' when the last major ice sheets retreated north, were mostly replaced by agrarian settlers from the 'middle east.' It suggested that this was similar to the experience of many first nations in the western hemisphere upon their 'meeting' major colonizing efforts of the Europeans.
The article, also suggests that the methodologies used by many scientists who use statistical analysis of mitichondrial DNA to 'track' population patterns in the past is less accurate than previously thought. Mitiochodria have their own ring of DNA totally separate from the parent cell. If fact, mitrochondria have lots more in common (structurally) with bacteria than they do with the more advanced animal cells that house them. They dipulace on their own schedule, etc, as well. Now, the assumption: since sperm cells have very few mitochondra, while egg cells have many - the offspring of a mating will have many, many more mitochondra from 'momma', than from 'pappa.' Hence, it is supposed, there is more accuracy in some measures using mitochondrial DNA as opposed to the DNA in body cells when trying to track past population patterns. Based on this new evidence, their modeling of past population patterns seems to be less accurate than previously thought.
Bottom line, what the Europeans did to the pre-colombian nations in the western hemisphere, their ancestors had done before to many of the earlier residents of 'europe.'
BTW, I am neither a geneticist, nor an advanced mathematician... just someone who likes to learn.