On Richard III's Y-DNA and the Need for Time-Asymmetric Mutation Rates

A skeleton excavated 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. 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 is attached to a mathematical framework within which it is possible that the traditional genealogy is correct. If this framework is the right framework for understanding genetic inheritance, then it has been wrongly assumed that Y-DNA mutation rates are line-like, constant and smooth - in reality they are wave-like and decrease erratically in the direction of the future, and the contrary impression is is an illusion created by an over-focus on the relatively constant and smooth nature of genetic change in the present and the near-present.