# Shared DNA when MRCAs are Cousins

On average, 2nd cousins are expected to share about 1/16 of their DNA. If parent-child share 3600 cM, then the 2nd cousins would share on average 1/16 of that or 225 cM.

The 2nd cousins share a set of great-grandparents, and they would on average share 112 cM through their great-grandfather and 112 cM through their great-grandmother. The great-grandparents are their Most Recent Common Ancestor (MRCA).

Now I know that these values can vary a lot, but for simplicity, lets just deal with theoretical averages.

My question is if those great-grandparents were known to be 1st cousins, i.e. the great-grandfather shared about 900 cM with the great-grandmother, then how would I calculate and how much would be the sharing of the 2nd cousins, who are the great-grandchildren of these two?

What I want to know is how much would their theoretical sharing of 225 cM be increased?

• Talking averages, the great-grandparents would share abt. 25% as 1st cousins. So, their children (the 2nd cousins' grandparents) would each show abt. 12,5% fully identical (on average), yes? I suspect from that point you need to calculate separately for the half-identical and fully identical DNA, but it gets complicated pretty quickly (I couldn't figure out the next generation offhand). Good question, though - a definitive answer would be enormously useful. Feb 9 at 21:27

If generation 1 share (average) 900 cM, then their children will, on average, inherit half of that (450 cM) from each parent. That could be anywhere from the exact same segments from each parent (450 cM fully identical) to completely complementary segments (0 cM fully identical), with the average being 225 cM. So members of generation 2 will have (average) 225 cM twice (fully identical), plus 225 cM twice (once from each parent, total 450 cM half identical), so would therefore match 675 cM (75%) of their parents' shared 900 cM.

Each member of generation 3 will inherit all of their parents' 225 cM fully identical segments, plus half of the 450 cM half-identical, for a total of 450 cM of their grandparents' shared DNA, with the remaining 3150 cM from their grandparents' unshared DNA. Each grandchild therefore has (average) 25% of their grandparents' collective unshared DNA and 50% of their shared DNA.

First cousins match about 900 cM, or 25% of the grandparent-inherited DNA, assuming that the grandparents shared none. The inherited shared DNA is proportionately more likely to match, so:

(3150 cM x .25) + (450 cM x .50) = 1012.5 cM (900 cM + 112.5, or 12.5% more)

This bump will naturally get diluted in further generations, but since everything is half-identical at this point, the usual generalizations should apply. So, 2nd cousins would match at 225 cM + 12.5%, or about 253 cM average.

• I like the logic you are using. But over the 900 cM where the parents share, I wonder if you got the fully and half identical sections of the children's matches correct. e.g. If their parents are 1st cousins because their father's father (FF) is a sibling of their mother's mother (MM), then they will match fully identical whenever they both get their FF or FM, and MF or MM which is 25% as you say. But also whenever one gets FF and the other gets MM. They only wont match when one gets FF and MM and the other gets FM and MF. And I don't think half-identical match is possible. Feb 13 at 14:54
• I don't understand the circumstances under which a half-identical match isn't possible - aren't the vast majority of vendor matches half-identical? I think only FTDNA and GEDmatch are even capable of detecting fully-identical matches. Feb 14 at 0:06
• I'm talking just about this case, on the 900 cM where the parents share. And I'm talking about the children who normally match 25% fully-identical, 50% half-identical and 25% no match. Those percentages change when the childrens FF and MM segments are identical. There will be more fully-identical matching, less non-matching and likely less or maybe even no half-identical matching. Feb 14 at 3:44
• It's a bit weird. Because if one child got FF and MM segments, and the other got FF and MF segments, then the first child will appear to be fully-identical to the second because the FF and MM are the same, but the second child will only appear to be half-identical to the first because the first doesn't have the MF segment. That's a big problem in analyzing this top down. I think it may have to be analyzed bottom up. Feb 14 at 3:56
• If the children of the first cousins were submitting samples to vendors, then yes, depending on the vendor, the match results might look a bit odd. However, by the next (and every subsequent) generation, everything is half-identical and looks just like any other matches, albeit with slightly elevated % due to the ancestral shared DNA. I don't see a problem here. I think this is actually much more quantifiable than if multiple sets of common ancestors were involved. Feb 15 at 4:22

This is how I think it works. We've got this situation:

The great grandparents are first cousins, meaning they share a set of grandparents. They are expected to share about 900 cM with each other, and each of the segments that make up that 900 cM come to both of them from one of their grandparents:

So the great grandparents each get one full chromosome of 3600 cM from the unrelated parents, and they were passed 2700 cM from their related parent that the other didn't get, and they get 900 cM from their related parent that are the same segments that the other was passed.

They pass 1/2 of their DNA to their children, 1/4 to their grandchildren, and 1/8 to their great grandchildren who are the 2nd cousins.

So there is a 1/8 chance that each 2nd cousin gets one particular segment, meaning there is a 1/8 x 1/8 = 1/64 chance that each 2nd cousin gets the same segment.

From the diagram above, you can see that the great grandparents have in total 3600 x 4 = 14,400 cM. If they did not share any segment, then the 2nd cousins would be expected on average to get 14,400 x 1/64 = 225 cM.

But they do share DNA. They share 900 cM. What that means is that if one 2nd cousin got a piece of that shared DNA from either grandparent, and the other got the same piece from either grandparents, then the 2nd cousins would share that segment. The Most Recent Common Ancestor (MRCA) in this case would not be one of the great grandparents, but it would be one of the great-great-great grandparents.

Since the 2nd cousins can get that piece from either great grandparent, there are therefore 4 possible ways the two of them could get the segment. Both from GGP1, Both from GGP2, One from GGP1 and the other from GGP2, One from GGP2 and the other from GGP1.

This means there is 4 times the chance of the 2nd cousins both getting DNA from the 900 cM shared between their great grandparents than there is from anywhere else.

So the 2nd cousins are therefore expected to share in the unshared great-grandparent region:

(3,600 + 2700 + 2700 + 3600) x 1/64 = 196.875 cM

And they'd share in the shared great-grandparent region:

900 x 1/64 x 4 times the chance = 56.25 cM

The total expected shared is 196.875 + 56.25 = 253.125 cM

This is 28.125 cM or 12.5% more than the expected amount of 225 cM.

• I didn't completely understand the logic in @cleaverkin 's answer, so I worked this out a different way. I did come out to exactly the same as cleaverkin did. So I'm giving cleaverkin the accepted answer, and leaving this here as another way to answer the question. Mar 23 at 2:42
• OK, yes, this is better with the graphic Mar 23 at 20:19