Modal Roger1 chart: All the nitty gritty, for those interested

Obviously, we can ignore all those markers which have the same value for every testee. For those markers there have been no mutations at all since Roger1’s time, in any of the lines tested so far. So we can size our explanation table to include just those markers where mutations have occurred. Also, we’ll eliminate WDTerrill since his 12-marker results are the same as CWTerrill’s and JRTerrill’s (others in the Thomas2 line), and so don’t affect the analysis at all. Note that we’ve highlighted the “different” values (the mutations) in our table to make them easier to spot.

ID	Line	389-2	447	448	GATAH4	456	607	576	CDYa	CDYb	534
RRTyrrel	John2	29	22	18	12	15	15	18	38	40	15
RTerrill	Samuel2	29	22	19	12	16	15	19	38	40	15
CWTerrill	Thomas2	29	22	19	11	16	16	18	38	39	15
JRTerrill	Thomas2	29	22	19	12	16	15	18	38	39
ASTurrill	Daniel2	30	22	19	12	16	15	18	39	40	16
TMRoberts	Daniel2	29	23	19	12	16	15	18	38	40	15
Modal John2		29	22	18	12	15	15	18	38	40	15
Modal Samuel2		29	22	19	12	16	15	19	38	40	15
Modal Thomas2		29	22	19	11/12?	16	15/16?	18	38	39	15
Modal Daniel2		29/30?	22/23?	19	12	16	15	18	38/39?	40	15/16?
Modal Roger1		29	22	19	12	16	15	18	38	40	15
Modal John2		29	22	18?	12	15?	15	18	38	40	15
Modal Samuel2		29	22	19	12	16	15	19?	38	40	15
Modal Thomas2		29	22	19	12	16	15	18	38	39	15
Modal Daniel2		29	22	19	12	16	15	18	38	40	15

There are five blocks in the table, which we’ll call “header,” testees,” “modal-son-1,” “Modal Roger1” and “modal-son-2.” First, you can see in the testees block how very few mutations have occurred. For every marker where a mutation has occurred (except CDYb), it has occurred in only one testee’s line, in one of the ten or so generations since Roger1. In the modal-son-1 block we have computed for each line and for each marker the modes of the appropriate values from the testee block. For the John2 and Samuel2 lines we have only one testee for each, so there’s only one input value per marker, and the mode is simply the same value. So we’ve just copied those two testee rows into Modal John2 and Modal Samuel2. For the Thomas2 and Daniel2 lines we have two testees per line, and thus two input values per marker. Since the mode is the most frequent value, it’s undefined when the two input values differ, and we’ve represented the result by “29/30?”, for instance—meaning that it could be either 29 or 30. Modal Roger1 is of course the mode, marker by marker, of the four input values from the modal-son-1 block. You can see that the undefined values do not matter—they could be anything and the modes would still be the same. So Modal Roger1 can be determined for all 67 markers.

Knowing Modal Roger1 we can now re-examine the modal-son-1 block, and produce the better-determined modal-son-2 block. In the cases where the mode for a marker could be one of two values, and the marker value for Modal Roger1 is one of the two, the simplest explanation by far is that the value for Roger’s son was the same as Roger’s, and that the mutation occurred in one testee’s line in a generation beyond that son of Roger. This eliminates all of the questionable values in Modal Thomas2 and Modal Daniel2. We think there’s nothing questionable about the value 39 for marker CDYb, for Thomas2. Since that mutation is common to both CWTerrill and JRTerrill, and because CWTerrill is descended from Thomas2’s son Josiah3 and JRTerrill is descended from Thomas2’s son Ephraim3, the most likely explanation is that the mutation occurred in Thomas2’s yDNA. It seems much less likely that the mutation occurred at some other generation in each of the two lines. This gives us a mutation indicator for the Thomas2 line. The situation is different in the cases of the questionable values in Modal John2 and Modal Samuel2, because each is based on a single input value. So we cannot yet determine these marker values. Most likely, they are the same as Roger1’s—but we can actually compute the probability that one can serve as an indicator: In the case of Modal John2, RRTyrrel is nine generations removed from his ancestor John2, and each of the two mutations could have occurred at any generation in the line, including John2 and RRTyrrel. So the chances of each having occurred at the John2 generation are 1-in-10 (and the chances of it having occurred at any other generation in the line are exactly the same, of course). The chances of at least one of the two having occurred at the John2 generation are nearly double (19.0%, actually).^‡ So it’s possible that one of the two mutations could serve as a John2 line indicator, but the probability is only 19%. Likewise, in the case of Modal Samuel2, RTerrill (2) is eight generations removed from his ancestor Samuel2, so the chances of the single mutation in his line serving as a Samuel2 line indicator are 1-in-9 (11.1% probability). In both cases, to know for sure whether or not a particular mutation serves as a line indicator we need another testee who is descended from a different grandson of Roger1. RRTyrrel is descended from Josiah3 (John2), and RTerrill (2) is descended from Adam3 (Samuel2).

‡ For the general case of 2 mutations which have occurred in g generations, the probability of at least one mutation having occurred in the beginning generation is 100% x { ( [ 2 x g ] – 1 ) / ( g x g ) }. In the RRTyrrell-to-John2 line case, g = 10.