# Using shared cM to determine likelihood of misattributed paternity?

My ancestor Harriet Smith was born in the mid-1850s in England. Her birth certificate shows both of her parents (John Smith and Sarah Johnson). For the purposes of the birth registration, John and Sarah were recorded as if a married couple.

John and Sarah were married the month after Harriet's birth.

However, Sarah was baptised a year later and the baptism registration records her as Harriet, illegitimate daughter of Sarah Johnson. This baptism record also notes the date of birth, and given this was in a small rural parish I am certain that this is the same Harriet.

John and Sarah went on to have 8 more children.

Harriet does not appear on any census with her parents (she is with her maternal uncle in 1861, and in service by 1871).

Harriet's marriage certificate shows her father as John Smith.

The question remains whether John was actually the father of Harriet, particularly given he is omitted from her baptism record over a year after her birth and marriage to her mother.

I have been trying to use DNA to solve this problem. Fortunately I have been able to test the DNA of Harriet's granddaughter.

Harriet's granddaughter (E) matches with several descendants of Harriet's sister (or half-sister?) Eliza. Eliza was certainly a daughter of both Sarah and John. E matches with the following people:

• W (presumed 2nd cousin twice removed): 61 cM, 5 segments
• G (presumed 2C2R): 54 cM, 3 segments
• S (presumed 2C3R): 17 cM, 2 segments
• M (presumed 2C3R): 11 cM, 1 segment

These matches shown as a tree:

These matching segments seem smaller than I would expect for a full second cousin twice removed, although only marginally so. According to the most recent data of the Shared cM Project:

• 2C2R: average 74 cM, range 0 – 261 cM
• 2C3R: average 57 cM, range 0 – 139 cM
• Half 2C2R: average 61 cM, range 0 – 363 cM
• Half 2C3R: insufficient data

Note there is a small sample size for each of these relationships, particularly the half-relationships.

Clearly the shared cM for E and the cousins are within the range for both the full and the half-2C2R and 2C3R relationships, so it would seem to me that this DNA data is not particularly conclusive as to whether John was Harriet's father.

The questions:

• Does this DNA data provide any evidence at all as to whether John was Harriet's father?
• If not, are there any further methods (either DNA or otherwise) that may be used to elucidate this relationship?

If there are siblings of John Smith with descendants, they could possibly be compared to E. Testing for DNA matches between E and relatives of John Smith may not be conclusive - a negative result could be by chance, while a positive match may support a relationship with John Smith yet not necessarily prove paternity - but it could shed some light.

• This is a good thought, unfortunately I have yet to identify any possible candidates to test for this purpose. John had multiple siblings, 4 of whom died without issue, 1 sister who did have a few children but I've yet to locate any descendants, and 1 sister I have not been able to trace due to the common name. – Harry Vervet Jun 4 '18 at 1:15

In addition to trying to test descendants of John Smith's siblings, I would suggest trying to test descendants of Harriett and Eliza's other siblings.

A really good set of articles on using DNA to determine relationships based on probabilities is The DNA Geek's "Science the Heck Out of Your DNA" series (currently six parts). In particular, I think that Part 5, and the probability tool mentioned, is quite relevant to your question. Part 6 also appears to be relevant to the case you're looking at.

• Cheers, those articles contain some great resources – Harry Vervet Jun 7 '18 at 15:23

Using the advice contained in the answers of @Erin and @Leah, I have made some good progress on this.

I have identified a number of other DNA matches who I believe are related via the Smiths:

For clarity I have removed many details from this diagram, and simply denoted the new matches as letters from A to P. Match distances are as related to E (Harriet's granddaughter). Dashed lines refer to relationships which I believe are correct but need additional evidence to confirm.

I did manage to trace some additional descendants of Harriet's siblings:

• E matches with A at 187 cM. If Harriet was John's daughter, then A is a second cousin once removed. Otherwise, a half-2C1R. Going off the probabilities, this is more likely to be full 2C1R (50% probability) than half 2C1R (7% probability). So this would support the hypothesis that John was Harriet's father.

• E matches with B at 6 cM (2 segments). B is a descendant of one of Harriet and Eliza's other siblings. I do not have segment data for this match yet. B is a 2C2R. This is not a strong match for a relatively close relationship, but whether it is full 2C2R (7% probability) or half 2C2R (15% probability) is not easy to ascertain. This match not particularly helpful in terms of probabilities.

• E matches with C at 21 cM (2 segments). C is also a descendant of another one of Harriet and Eliza's siblings, and is also a 2C2R. Again in terms of probabilities it is a toss-up whether full 2C2R (8%) or half 2C2R (16%).

I had no luck tracing any descendants of John's siblings (his sisters Mary and Fanny did have children). However, I was able to trace a number of matches who I believe are descended from Harriet's great aunt Edith. These range from 4C to 4C3R, and are all 20 something cM matches. If the genealogy is correct (which I believe it is), and the common ancestry is via the Smiths, then Harriet must be the daughter of John.

I also identified an additional match (P) who is also descended from Smiths in the same small parish – I believe he is descended from one of Harriet's paternal great great uncles. This would make him a 5C1R to E.

I do not have segment data for all these matches, but interestingly the 16 cM match of P and E triangulates with I (a descendant of Edith). This seems to tie the three main branches together. Frustratingly, P, I, and the other descendants of Edith for whom I have segment data do not match with any of the descendants of Harriet's other siblings; if this were the case then I would be absolutely sure that Harriet was John's daughter.

Based on these DNA matches I am now confident that Harriet was John's daughter. I will be on the lookout for additional matches that may make things clearer.

• That is very impressive. You're down in the weeds of match strength, but the sheer number of matches leaves few other options. (And eighteen DNA tests! O_o) Does it rule out, e.g. John's brother being Harriet's father? I have a similar paternity mystery a few generations back, which seemed intractable, but I am feeling inspired to go back to it. – AndyW Aug 23 '18 at 8:26
• @Andy I hadn't thought of John's brother! He did have one brother who never married and (I assumed) had no children. Since posting this I have found an additional match on Edith's line, and I'm guessing there are more to find. Edith's son moved to Utah, so there are many American descendants which explains why so many on that line have tested. – Harry Vervet Aug 23 '18 at 14:43
• Yes, impressive the number of matches you've been able to add. As @Leah mentioned, the DNA Geek's posts are great - and there's a new tool based on these ideas, What Are the Odds? (dnapainter.com/tools/probability) that can help quantify how likely one hypothesis is compared to alternatives. – Erin Hill-Burns Sep 1 '18 at 18:17