Supplemental Post for DNA & A Question of Paternity: Part 6

In the blog post “DNA & A Question of Paternity: Part 6 – Statistically testing hypothetical relationships,” I described how I tested the statistical likelihood of many different relationship scenarios in an attempt to clarify the uncertain paternity of “Bob.” All tests I performed are described here (only a subset of these were spelled out in the original post).

Question 1: Did Bob descend from a sibling of Helen Black? Possible relationships were tested as shown in Figure S1 (the same as Figure 2 in the original post). Results from these tests are shown in Figure S2 (the same as Figure 3 in the original post).

Figure S1. The family tree shown illustrates possibilities for Bob’s placement in relation to Helen Black’s descendants (genetic matches A-E). Hypothetical placements for Bob in the family are shown with the yellow boxes.
Figure S2. Probabilities were calculated for each of the placements for Bob in the context of the family structure shown in Figure S1. Each scenario tested here, colored gray, was given a score of 0, “not statistically possible.” 

Conclusion 1: Bob likely did not descend from a half or full sibling of Helen Black.


Question 2: Did Bob descend from a child of Helen Black other than Patty McGonagall or Zoe Bell? Possible relationships descending from Helen and her first husband Trevor Bell, from Helen and her second husband Gene McGonagall, or from Helen and an unknown man were tested, as shown in Figure S3. Results from these tests are shown in Figure S4.

Figure S3. (click to see larger) The family tree shown illustrates possibilities for Bob’s placement in relation to Helen Black’s descendants (genetic matches A-E). Hypothetical placements for Bob in the family are shown with the yellow boxes. Note, fewer possible relationships were tested in the descent from Helen and Trevor because Trevor died young and could not have had a son late enough to have been Bob’s father. An arrow with a red “X” indicates that descent from that line was already tested (see above), and that all possibilities were given a score of 0, “not statistically possible.”
Figure S4. (click to see larger) Probabilities were calculated for each of the possible placements for Bob in the context of the family structure shown in Figure S3. Placement of Bob as a grandson of Gene and Helen (Black) McGonagall is statistically possible, with a score of 1 (in green). The rest, colored gray, were each given a score of 0, “not statistically possible.”

Conclusion 2: Bob could have descended from Helen Black and Gene McGonagall, where his father would have been their son, a full brother to Patty McGonagall.


Question 3: Did Bob descend from a child of Zoe Bell? Possible relationships descending from Zoe and her husband Mr. Evans (other than through their son Charles), from Zoe and an unknown man, or from Charles Evans were tested, as shown in Figure S5. Results from these tests are shown in Figure S6

Figure S5. (click to see larger) The family tree shown illustrates possibilities for Bob’s placement in relation to Helen Black’s descendants (genetic matches A-E). Hypothetical placements for Bob in the family are shown with the yellow boxes. Note, age-wise, Bob’s father could have been Charles Evans, but Bob’s mother was not Charles’s wife, so Bob, Match D, and E. Evans could not be full brothers. An arrow with a red “X” indicates that descent from that line was already tested (see above), and that all possibilities were given a score of 0, “not statistically possible.”
Figure S6. (click to see larger) Probabilities were calculated for each of the possible placements for Bob in the context of the family structure shown in Figure S5. Each scenario tested here, colored gray, was given a score of 0, “not statistically possible.”

Conclusion 3: Bob likely did not descend from Zoe Bell.


Question 4: Did Bob descend from a child of Patty McGonagall? Possible relationships descending from Patty and her husband Mr. Lovegood, from Patty and an unknown man, or from Vera Lovegood were tested, as shown in Figure S7. Results from these tests are shown in Figure S8 (the same as Figure 4 in the original post).

Figure S7. (click to see larger) The family tree shown illustrates possibilities for Bob’s placement in relation to Helen Black’s descendants (genetic matches A-E). Hypothetical placements for Bob in the family are shown with the yellow boxes. Note, Yuri Potter could have been the right age to have been Bob’s father, but the shared amount of DNA between Bob and Match A are incompatible with a half sibling relationship. Yuri was not born early enough to have been Bob’s grandfather. An arrow with a red “X” indicates that descent from that line was already tested, and that all possibilities were given a score of 0, “not statistically possible.”
Figure S8. (click to see larger) Probabilities were calculated for each of the possible placements for Bob in the context of the family structure shown in Figure S7. Only a few possibilities tested were statistically possible; those shown with a score greater than 0 (and colored yellow or green). Higher scores (and darker green coloring) are shown for the most likely possibilities; the most likely possibility (with a score=858) is 858 times more likely to be true than that with a score=1. Note: the possibility with Bob as a son of the child of Gene and Helen (Black) McGonagall now has a score of 80, whereas before its score was 1. With the addition of new hypotheses, this scenario was given a higher score as less likely, though possible, scenarios were added; the most likely hypothesis is ten times more probable than this one, however (with a score=858).

Conclusion 4: The most likely placements for Bob in this family suggest that Bob’s father was either a son or a grandson of Patty (McGonagall) Lovegood.

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