On Richard III, The Livingstons of Callendar, and the Conflict Between Genealogy and Genetics

A skeleton excavated at the presumed site of the Grey Friars friary in Leicester in 2012 is almost certainly that of the English king, Richard III (1452 -1485), and mtDNA (which is passed from mother to child) extracted from the skeleton matches mtDNA taken from descendants of Richard's sister Anne of York. However Y-DNA (which is passed from father to son) extracted from the skeleton apparently doesn't match Y-DNA taken from descendants of Henry Somerset the 5th Duke Of Beaufort, who according to history descended from Richard's 2nd great grand father Edward III (1312 - 1377). The implication according to geneticists, and the media, is that there is a 'false paternity event' somewhere between Edward and the Somersets. Also, the false paternity events don't end there, for only 4 of these 5 Somerset descendants match each other. And it may be worse even than this: the patrilineal line of a Frenchman named Patrice de Warren apparently traces back to Richard III through the illegitimate son of Edward III's 4th great grandfather, Geoffrey Plantagenet, Count of Anjou (1113 - 1151). But de Warren's Y-DNA doesn't match that of either Richard III or any of the Somersets. In this note, a formula for calculating the time of the most recent common ancestor is introduced, and some of its consequences outlined. This formula arises from a mathematical framework within which it is possible that the traditional genealogy is correct, and that Geoffrey Plantaganet was the father of a male line incorporating Richard III, all 5 Somersets, and Patrice de Warren.