This article will describe the various attributes of a Triangulated Group (TG). Some have noted that I use the term TG to describe both a Group of Matches as well as an ancestral segment. Well… yes, I do. Read on.

Once established, each TG has certain attributes which can be used to describe and/or define the TG:

A1. A TG is a group of shared segments from Matches. We often think about the Matches in a TG. They have a Common Ancestor. They can be contacted and encouraged to collaborate on finding the common ancestry. So in this sense a TG is a group of Matches. However, note that any of these Matches could, potentially, also share the same or a different ancestor with you on another segment (in a different TG)

A2. A TG occupies a specific physical space on a chromosome. It is, in effect, a segment in its own right – a segment from one of your ancestors. The TG is on one chromosome with a start location and an end location. These start and end locations are determined by the matching, overlapping, shared segments (from Matches) within the TG. Please review: Anatomy of a TG.

A3. As a segment, a TG has a specific string of SNPs on one chromosome. These would be the same SNPs in a segment on your chromosome, and on the segment each one of your Matches shares with you in the TG. All the SNPs would be the same. The SNPs have to be the same for IBD segments to match.

A4. A TG is the equivalent of phased data. The TG represents an ancestral segment on a chromosome. All of the SNP values (alleles) are on one chromosome, and are the same SNP values you got from your mother or father (depending on the chromosome). What you have in a TG (segment) is exactly what you would have with phased data.

1. We don’t see the actual ACGT values in a TG that we would get with true phasing (with a child-parents trio), but they are the same values in the TG. The TG segment represents part of one of your chromosomes – it must have the same ACGT values that your parent passed to you on that chromosome.
2. We can treat the TG as phased data, and any other shared IBD segment which Triangulates with the TG will have the same SNP values.
3. This is true, even if you have formed a TG (with matching, overlaying, shared segments from Matches) and do not have the genealogy to determine which side it is on. You can be confident that the TG exactly matches the DNA on one of your two chromosomes. In this case the TG is not entirely equivalent to a true phased segment. But, if you had the phased information, you’d already know which side the TG was on. And very often you can determine the side of a TG by imputation – by determining which side it’s not on; or by the admixture of the segment.

A5. Technically, each TG has a cM value. However, it usually takes a lookup table to determine the cM value for a segment on a given chromosome, between two points. This is what the testing companies and GEDmatch do for each shared segment they report. It’s a lot of work for genetic genealogists – and, in general, our TGs will morph over time as new shared segments are added, and the TG cMs will need to be adjusted. However, we can fairly easily make rough estimates of the TG cMs, which are plenty good enough for genealogy:

1. Subtract the TG start location from the end location to get the number of base pairs (bps), divide by 1,000,000 to get Mbp, which is roughly equal to the number of cMs.
2. Or, eyeball the cMs of the larger shared segments in a TG and extrapolate to the full TG (if you’re lucky, you may have a shared segment which nearly fills the TG)
3. Note that the cM is a fuzzy value anyway – it’s empirically derived (an average of many observations), and it’s an average of the female and male averages. So don’t go to too much trouble, and use round numbers. AND note that there is a wide range of possibilities when trying to use cMs to determine approximate cousinships. See Blaine Bettinger’s chart for the ranges of cMs vs cousinships.

A6. TGs have fuzzy ends. There is no “signpost” in our DNA to identify crossover points, or where a shared segment starts or ends. The company algorithms estimate shared segments by looking for areas of DNA that are identical, and it then continues until the DNA is not identical. This results in some, usually small, amount of overrun (a longer segment than is actually there from a Common Ancestor). So my convention is to use the start location of the first shared segment in a TG (the one with the lowest start in bp). This is the start location of the TG. The end location is determined several ways:

1. If there is no overlap with the next TG on that chromosome, then use the largest end location of all the shared segments in the TG – the shared segment which runs the farthest. This often is not the last shared segment in a sorted spreadsheet – you need to look at them all.
2. If there is a small, fuzzy overlap of 1-2Mbp with the next TG, I use the start location of the next TG, and accept the fact that there is a fuzzy overlap. We don’t need to be real precise for genealogy. Each TG represents a large block of DNA from an Ancestor – the fact that the edges of the block may be fuzzy should not obscure the big picture: the main TG segment came from an Ancestor!
3. If there is a large overlap with the next obvious TG (almost always from a large shared segment with a close cousin, which probably spans more than one TG), I start a new TG at the obvious point dictated by the next group of shared segments, and use the same point as the end location of the first TG. This involves judgment – there is no hard rule – and the data will usually indicate where to start a new TG. Just accept that close cousins may share large segment which span more than one TG.
4. If the shared segments in the TG all end a “few” Mbp before the next TG starts, I will just round up, and use the start location of the next TG as the end location. Again, use judgment.
5. If there appears to be a large enough gap between two known TGs, I create a “dummy” TG to fill the gap. And then I keep looking for some Matches with shared segments to fill that gap. At this date my dummy TGs are about 7% of my DNA.
6. Using these conventions will result in TGs that are adjacent to each other over all your chromosomes. Even with some “dummy“ TGs, this process will organize all of your IBD Match segments into TGs over all of your DNA. When done, this is a happy day! You can then focus on TGs that should link to specific ancestors. And all new Match segments will generally fit easily into existing TGs.

A7. As you work this process of forming TGs and assigning them to sides using genealogy, you are creating a chromosome map. As new Matches are posted, their shared segments may adjust the start and/or end locations of the TGs. When you get lucky, you’ll find a new shared segment that fills a “dummy” TG.

A8. Naming TGs. I label each TG (and all the shared segments in it) with a short code – like 07C25. The 07 means Chr 7; C means the TG starts within the third group of 10Mbp – in this case between 20-30Mbp; 25 means this TG ion on my father’s (2), mother’s (5) side – using Ahnentafel numbers. If I were starting over I’d use 07.027PM to indicate Chr 7; start 27Mbp; on Paternal, and his Maternal ancestry. Note: before you do any assigning, the label might be 07.027, then add P or M when determined. I usually add this code in the subject line of emails and messages – it just helps me keep organized.

A9. Also note that each TG also has within it, many genes. Each of your 22,000 or so genes will have a specific location on your DNA. If you become curious about any particular gene, you can look up where it is located (chromosome and location). You will have two of each gene, one on your maternal chromosome and one on your paternal chromosome. You can then look at your chromosome map of TGs and see which maternal TG and which paternal TG it’s in. If you’ve determined a Common Ancestor for those TGs, you’ll know which ancestor passed that gene down to you. You can also add a gene to your spreadsheet, so that it sorts with all the segments and TGs. Examples: Short Sleepers gene BHLHE41 would be 12.026M and 12.026P (very close to LRRK2 (Parkinson’s) at 12.031. Also my Neanderthal segment is 10.130 (I don’t know which side)

Have fun with your TGs!

15B Segment-ology: The Attributes of a TG by Jim Bartlett 210919

Each Triangulated Group represents a segment of DNA that come from a specific ancestor in your ancestry. It comes from that ancestor, down one specific path, to you. Even if you have the same ancestor in your ancestry more than once, a specific TG segment comes from only one instance of that ancestor, down one specific path to you.

Review Ancestral Segments

Let’s review ancestral segments. Please also refer to the posts and figures for Segments: Bottom-Up and Segments: Top-Down. At each generation of ancestors, each one passes down specific segments to you. In other words, your entire DNA is made up of segments from your ancestors of each generation. All 4 of your grandparents passed down various specific segments to you that make up all of the DNA on all of your chromosomes – all of your DNA came, in various segments, from those 4 ancestors. The same statement can be made of all 8 of your Great grandparents – you have different segments from each of your 8 G grandparents, which, in total, provide all of your DNA on every chromosome. Some Great grandparents may not contribute to each and every chromosome, but all of your chromosomes will be a patch-work-looking quilt of segments from your Great grandparents. The same is true for every generation: your DNA is made up from segments from your ancestors in that generation. As you go back 6 or 7 or 8 generations, some of the ancestors of that generation will drop out. That is you don’t get DNA from every one of them. They are still your ancestors, you just didn’t inherit DNA from them. Review The Porcupine Chart.

Another way to put it is that segments from distant ancestors are combined to make larger segments in closer ancestors. The smaller segments are still there, it’s just that the closer ancestor passed down larger segments which are made up of the smaller segments from their ancestors. Your parent passes complete chromosomes (very large segments) to you, which are made up of smaller segments from his/her ancestors. See the graphics in Top-Down.

Mapping with Triangulated Groups

Now the hard part of chromosome mapping with Triangulated Groups (TGs) is that the TG segments don’t generally create a map for any specific generation. The TG segments could come from ancestors of different generations. It all depends on how your TGs are laid out, and on the shared segments you get with Matches. You will only “see” TG segments that are made up of shared segments from Matches. So some TG segments may be from closer generations than others. But, in general, your TG segments will be adjacent to each other from the start to the end of each chromosome.

Cousinships with Matches in a TG

A TG is made up of Matches with shared segments. Review: The Anatomy of a TG. The shared segments (with Matches) in a TG will generally fall into 3 categories:

1. Shared segments with Matches who are cousins on the Common Ancestor who created your TG segment. For a TG segment created by a 6G grandparent, this would be 7th cousins. Note: it would be very unlikely for you to have more than three exact 7th cousins (each one from a different child) from a 6G grandparent on one segment (i.e. in a TG). More on this later.
2. Shared segments with Matches who are closer cousins – they share a Common Ancestor with you who is closer than the 6G grandparent who created your TG segment. Note: it would be very unlikely for you to have more than three exact 4th or 5th or 6th cousins (each one from a different child) from the same xG grandparent on one segment (i.e. in a TG). More on this later. These closer cousins would share a Most Recent Common Ancestor (MRCA) who is in the direct path of descent from the 6G grandparent (who created the TG segment) down to you. Because of this they also share the 6G grandparent ancestor with you. But, in this case, you will both descend from the same child of the 6G grandparent, and that does not count against the “limit” of three 7th cousins from a specific ancestor.
3. Shared segments with Matches who are more distant cousins – they share a Common Ancestor with you who is ancestral to your 6G grandparent who created your TG segment. This frequently happens when the shared segment is less the full TG segment from the 6G grandparent (for example). So these Matches could be 8th or 9th or 10th cousins or even more distant. They descend from a smaller “sticky” segment which is passed down to them (along a specific path) and down through your 6G grandparent to you, along the same path as categories 1 and 2 above. So you might be 9th cousins on an 8G grandparent, who is a grandparent of your 6G grandparent. In fact, when your shared segment (in a TG) is in the 7 to 10cM range, the odds are roughly 80% that the Common Ancestor will be more than 10 generations (9th cousins) back. That’s the bad news – most of these smaller shared segments will be at the far reaches, or beyond, our genealogies. The good news is that roughly 20% of the Matches (sharing 7 to 10cM segments) will be closer – spread among 1st to 8th cousins. For shared segments in the 10 to 20cM range, the odds are roughly 60% that the Common Ancestor will be more than 10 generations back – which means 40% of those Matches will be closer cousins. In fact, with 100 shared segments in a TG in the 10-20cM range, you’d probably have two or three 3rd cousins, two or three 4th cousins, two or three 5th cousins, two or three 6th cousins, etc. You can see a graph of these probabilities in this article at ISOGG.

100 Matches on a TG!

So the next issue is: can we have 100 Matching cousins in a TG? The answer is absolutely!  The odds are almost nil that more than 4 children will pass down the same matching segment to cousin descendants. Hence the caution that we almost certainly cannot have more than 4 cousins, from different children of a specific ancestor, passing down matching shared segments to cousins in one TG (i.e. on one segment). Each child inherits a different mix of DNA from the parents – rarely will more than four of them get the same DNA, and much more rarely would their descendants wind up sharing that DNA on the same segment (i.e. in a TG).

However – 100 Matches can easily descend from an ancestor 10 generations back without violating that concept. You and a sibling could share the same segment with two siblings who are 1st cousins from a grandparent. Similarly 4 Matches could be 2nd cousins with no more than two children from each ancestor. And 8 more Matches at 3rd cousin level – up to 512 Matches at 9th cousin level (10 generations back). And you could double that number by adding a once-removed cousin at each level. All without using more than two children at each generation. And this is all within a genealogical timeframe of 10 generations. If you consider that 80% of the Matches sharing 7-10cM will be well beyond the 10 generation level, the potential number of Matches in a TG becomes quite large. Of course this means the Matches are not all exactly at the same cousinship level – they are very likely to be spread over a range.

Large numbers of Mathes in a TG is not a pile-up!

So clearly a large number of Matches in a TG should not sound an alarm. Or arbitrarily define the TG as a pileup area, or require that all the Matches should be discarded. Nonsense! Large TGs, with Matches matching each other on overlapping shared segments, just indicates that many of the Matches will be more distant cousins. Some Matches will be beyond the genealogies of some – it depends on each genealogist and how far back their Tree goes, and the same for their Matches. But, statistically, there will be some closer cousins in the mix of Matches in the TG. We won’t know which are the closer cousins until we share with them.

The ancestor who “created” your TG segment

In the above discussion I note the ancestor who “created” the TG shared segment. This means the most distant ancestor who had that full segment. His or her ancestors did not have that full segment. His or her parent created (at least) that full segment from their parents. And the segment you inherited from that ancestor is all or, probably more likely, a subset of the segment that ancestor passed down, and eventually got to you. We are talking about the unique segment you inherited from that ancestor, and that segment did not exist in any ancestor further back. The TG segment is unique to you and your ancestor.

Your TG/Segment is unique to you

The ancestor who created your TG segment, probably passed down various overlapping segments to your Matches. These segments may be larger or smaller than the segment you got. What you “see” in a shared segment, is the part your Match got that overlaps the segment you got. So from a Match’s perspective, there is almost certainly a different segment from the Common Ancestor than you got – the Match would have a different TG than you from this same ancestor. Or some of your Matches may get segments from a more distant ancestor. These segments would be smaller and, when combined with other DNA, would result in the DNA segment that your ancestor passed down to you. Thus, those other Matches would be more distant cousins, on a smaller segment than what you got. There are many scenarios that would result in a Match (sharing a segment with you) being a more distant cousin – refer back to alternative 3 above.

The name of the atDNA game is sharing and collaboration

This accounts for some Match cousinships which can be pretty distant.  I have to emphasize that, although some of the TG Matches will be fairly distant (and often beyond your genealogy), some Matches in each TG are probably within a genealogical timeframe. This brings up two important points when using TGs:

1. Contact every Match you can – you never know which ones may have a Common Ancestor you can identify.
2. Encourage Matches within a TG to share Trees among the group. Some Matches in a TG may be closer cousins to each other than they are to you, and they may in fact have a Common Ancestor who is ancestral to the ancestor of your TG. Sharing and collaboration are the name of this game.

15A Segment-ology: Understanding and using TGs by Jim Bartlett 20160917