Sorry, I will clarify.
They traced it back to it's appearance in an individual after the plague. They traced it back beyond that, to the parents and other lines descended from those parents where it did not appear. Thus they proved the mutation in the gene was caused by the Black Plague. Further, there was not one Black Plague outbreak and they did the same research on survivors descendants for those also.

They stated their luck was in because the stories and breadth of the DNA links were documentable and easily verifiable, the family/village populations were documented, stable and settled until and past the 20th century.

The definition that I found is that evolution is "the adaptation of mutations".

http://info.bio.cmu.edu/Courses/034...vo/mutation.htm
Mutations are naturally occurring events in any genome. They are one of many mechanisms that bring change into genome of a species. When the characteristic brought about by the mutation, allow the organism to better fit the changing environment, the organism survives and passes down the trait through reproduction. Thus, species as a whole evolve.