Are centimorgan contributions additive?

Question

I share a 50 centimorgan 6 segment match to person "J".

My maternal side aunt shares 54 centimorgan 5 segment match to that same person "J"

I see two possible blood-line connections between my aunt and myself and this person "J", (there is a third possible blood-line - but for the moment I'm considering that unlikely)

Of the two possible blood connections, one is my 10th Greatgrandmother, the other is a 7th Greatgrandfather (but on a different branch). Considering that I get DNA contributions from each, is it possible that if both blood connections are valid, and the result (my DNA and my Aunts) appear to be of a common ancestor to "J" that is closer than 7th Greatgrandparent.

That is to say, are DNA contributions from differing branches additive?

These DNA results are from Ancestry.

Additional information: below is a table that lists several (15) persons that I have been DNA matched with. The second column of this table lists classification of the corresponding common ancestors by documentary evidence.

Now, considering that I have an (as yet not fully documented) 50 cm DNA match with the person "J", it occurs to me that the common ancestor is more likely to be closer to me than 3rd GGP. However, documentation thus far suggests multiple common ancestors at the 9th or 10th GGP level. Hence the question, can DNA contributions from separate branches add.

I'm open to other suggestions

Answer 1

I'm afraid you're over assuming on just about everything, especially when you're talking about going back to 10th GGPs.

First of all, there is no guarantee that just because you find a 5th GGP as a common ancestor through genealogical research between yourself and a DNA match, that the 8.6 cM to 24.9 cM of matches that you share are from that particular 5th GGP. The 5th GGP is 7 generations back. You have 128 ancestors 7 generations back and your DNA match also has 128 ancestors 7 generations back. (Maybe less due to pedigree collapse, but we can ignore that for this discussion).

You've found one of your 128 ancestors is the same person as one of your DNA match's 128 ancestors at that level. That is great! That's why we do DNA analysis so that we can find people who we are related to and potentially link our trees together and help take one of our lines further back.

But those segments that the two of you match on could very easily have been from a different one of your 128 ancestors, or it could have come from an ancestor 3 generations further back and have been from one of your 1024 8th GGPs.

The bottom line is you can't just assume that because you have found a connection and one common ancestor with a DNA match, that it is the only one and that it is the one that passed down all the DNA to both of you. Maybe that ancestor did pass down all the segments, but maybe they only passed one or two of the five segments you share, or maybe they didn't pass any of them and other common ancestors who you haven't identified passed down those segments.

With respect to whether centimorgan contributions are additive, well yes they are. If one common ancestor passed two of you 2 segments totaling 22 cM and a second common ancestor passed the two of you 3 segments totaling 32 cM, then both of you would have received in common 5 segments totaling 54 cM from the two ancestors.

But an ancestor 7 generations back only passes down on average 3400 / (2**7) = 26.5 cM to you and 26.5 cM to your DNA match. Yes, both of you may get more, e.g. 54 cM, but the likelihood of all of that matching between the two of you from 7 generations back is extremely small. More likely you are only sharing 1 or maybe 2 segments totaling 10 or 20 cM, and the rest is from some other common ancestor(s) you have yet to identify.