The story of the confirmation of the discovery of Richard III‘s remains under a parking lot in England is all over the news today and is a great story. Reading the details it shows that they did their research the right way. The mitochondrial DNA testing used to confirm the identity of the remains got a lot of press and it is a valuable, but not conclusive piece of evidence in an exhaustive study that included other details like radio-carbon dating and skeletal analysis. All these different types of evidence were used to make the proof case.
For the DNA portion of the research, they went generation-by-generation to confirm the female-line descendancies of two living men whose DNA could be tested. Their mothers were in a direct line of female descendants from Richard’s sister Anne of York. Because mtDNA does not change much from one generation to the next, and because it is passed from a mother to her children but not from a father, the mtDNA for all female-line descendants of Anne of York should be the same. Any sons of those women will also have the characteristic mtDNA but will not pass it on to their children.
Scientists did mtDNA tests on the two living descendants as well as on the skeleton. The mtDNA of the two descendants matched that of the skeleton.
This in itself does not prove the relationship. Because mtDNA does not change much over time, it is possible that the Richard III and the person found under the parking lot share a common female ancestor. If the mtDNA of the descendants had not matched what was drawn from the skeleton then it would have proven that it was not Richard III, but the match does not prove that it was him.
One thing that I have heard a number of times in learning more about genealogy is making a case is not about finding one record or fact that says what you want. You always want independent confirmation from different directions to make a stronger case. In this investigation the researchers did their work well, presenting varied evidence to prove their point.