Louis Kessler’s Behold Blog

#cangensummit2017 - On Thursday, I’ll be flying 2,600 km (1,600 miles), but still be in Canada, as I travel to Halifax, Nova Scotia for the Great Canadian Genealogy Summit being held from October 13 to 15.

I’ll be one of 12 speakers, all of us Canadian, giving 18 talks on various subjects of genealogical interest. With the conference taking place in the Maritimes, there are many talks on Acadians, Loyalists, immigration and Scotland. I’ll be giving 3 talks on DNA, 2 of which will be on DNA basics for genealogists and one a little more advanced on autosomal DNA analysis.

I’m anxiously looking forward to the conference, meeting the other 11 speakers, and spending time with the genealogists in attendance. This will not be a large conference, so there should be lots of opportunity to get to know most of the people. There will also be a small Expo Hall and a few mini presentations in the Hall.

This year’s Summit was organized by Kathryn Lake Hogan and Christine Woodcock. This is their 2nd Summit. Their first was successfully held last year in Brampton, Ontario. I had the pleasure of meeting Kathryn and Christine at RootsTech 2017 in February. I look forward to talking with them again.

I’ve never been to Halifax and am excited to go. It is said to be a beautiful city, and the Fall colours should dazzle. The genealogical highlight for me will be to go to and tour Pier 21, the home of the Canadian Museum of Immigration, and the place where many of my ancestors arrived to Canada in the early 1900’s. Yes, I’ve got my research list ready in case the opportunity arises. The keynote speaker on Friday night will be Jan Raska from Pier 21 and he will be talking about what the immigration experience was like for our immigrant ancestors.

Interestingly, the Lord Nelson Hotel in Halifax (a landmark unto itself!) where we will be staying and the conference will be held, does not have a computer available for the speakers, just projectors. I, being a developer, rely on my HP Envy i7 desktop computer and two big monitors to do my programming. On the road, I have always simply used my Windows phone for everything I need, and usually just take my presentations on my phone, on a USB, and have it in the cloud so that I can put it on whatever presentation computer I’m given.

So I looked around for the cheapest most portable full Windows 10 laptop that can run Office with at least 4 GB RAM (minimum for good performance on Windows 10), and I ran into a refurbished Lenovo x131e with a nice small 11.6” screen at Best Buy for $206. It’s even got a few features you normally don’t find at this price, like a 320 GB hard drive and two USB 3.0 ports. I like the Lenovo (IBM) brand, as I used that brand laptop at work for my last 8 years. I ordered it late Tuesday night last week and they said 2 business days for shipping, so I thought I was okay. Once ordered, UPS said it would arrive “by end of day” on Wednesday … and I leave on Thursday, so I’ve got my fingers crossed.

Followup:  My laptop arrived on Wednesday at 2 p.m. A nice little thing, just the perfect size for taking to conferences. I like feel of the keyboard and the touchpad works so nicely that I don’t think I’ll need a mouse. Cortana helped me through the Windows 10 setup it and I was impressed that it understood my answers without requiring voice training. It then went through some Windows updates that I expected via wifi would have taken hours. It finished in a couple of minutes and then rebooted.

After I activated the copy of Windows 10 from the product key that was listed on the computer, it asked me to sync my OneDrive files and then activate Microsoft Office which I have an Office 365 license for. Just 30 minutes after the laptop was delivered, I was able to open my Powerpoint presentations I created for the Conference this weekend that were up on OneDrive and were to my surprise already listed conveniently as recent files in the File Open menu.

I am very impressed with how smooth this procedure was and how short a time it took. Now to install a few programs I regularly use and I’m good to go.

In the DMT documentation on the Interpreting Results page, I have a section called Deep Ancestors. It says:

If the Triangulated Group is from a common ancestor, then there may be smaller identifiable groups within it that are either from a later crossover down one descendant line (in which case all the people having that crossover are in that line) or are from an ancestor of the common ancestor. In the latter case. everyone with the segment to the left or the segment to the right can be placed into a deeper ancestor Triangulation Group. Some research will be needed on how exactly to determine and do this and it may be possible one day for DMT to identify these for you.

David Boyles on the DNA Tools Facebook group asked me to explain this more fully and I thought that was a good idea.

The example diagram used in the documentation may not have been the best one to explain this concept because it didn’t have easily identifiable crossovers in it. So here’s a new example of DMT output taken from the DMT sample files.
(Click on the image to expand it)

In the graphic area in green, you’ll find one triangulation group outlined by the box. This group is made up of all 87 of the people who triangulate with both Harry B (Person A) and Joel S (person B). The match between the two of them is shown by green X’s on the yellow line between base addresses 72,881,715 and 79,080,783 on chromosome 2.

For the other 87 people, e.g. on the first line, Sara m is person C, the green X’s shows the double match where Person A matches Person C and where Person B matches Person C. Since this double match segment overlaps with the match between Person A and Person B, we have all three sides of the triangle and we have a triangulation.

The red a’s are where Person A matches Person C but Person B doesn’t. The blue b’s are where Person B matches Person C but Person A doesn’t. 

You’ll notice the lower and upper bounds of the triangulation group contains all the X’s and all the a’s but not all the b’s. That’s because we are looking from Person A’s point of view. A single match of Person A with someone in the triangulation group is likely to have also come from the same common ancestor. This is likely also true for Person B’s. But Person A doesn’t share that match. Person A has a crossover that Person B didn’t get, thus the triangulation group for Person A ends while Person B’s doesn’t. If you want Person B’s triangulation groups, then run Person B as Person A. You’ll find the groups will be different because every person’s chromosomes map to their own ancestors.

Deep Ancestors

Now for the fun part. Look at the green X’s in the diagram. They are all in the Triangulation Group. That means there should be a Most Recent Common Ancestor (MRCA) for all of people in the group (if not by chance or different parental chromosomes). You’ll see the green X’s shift from the left to the right of the segment. Only about 10 of the matches in the middle of the diagram overlap with the majority of the Person A match with Person B. All the people are descended from a MRCA.

What about the shorter segments. Generally, a shorter segment means a more distant common ancestor and a larger segment means a closer common ancestor. Of course a crossover can happen anywhere, so there can be exceptions both ways with a small segment from a close common ancestor and a large segment from a distant one. But we are talking here about the matches within a triangulation group. They all have an MRCA and that forms the basis of the longest triangulating segments in the group.

So let’s consider our MRCA. Say she’s our gggg grandmother and she passed down that segment from 68,184,338 to 79,767,734 to Person A and the segment from 72,881,715 to 79,080,783 to Person B.  What can we say about her? 

So lets say her father gave her that entire segment. Going back farther, her father’s segment is a combination of his parents, her paternal grandparents’ segments. They may or may not have crossed over right in the middle of this segment. Whether or not they crossed over, any of their ancestors that the segment came from may have crossed over somewhere on this segment. Here’s a 3 generation example:

The segment from the MRCA is in green. She got her entire segment from her father, but that came in pieces from her grandparents, which are subdivided further from her great grandparents. That subdivision can of course continue on to deeper and deeper ancestors.

Each generational level may subdivide the triangulated people. There will be people who are descendants of the MRCA and her father whose triangulating segment could span the entire triangulation group (or could be truncated by a crossover on their side from the MRCA).

And then there will be people who will be descendants of the g6 grandfather or g6 grandmother. Their segment will not overlap with each other but will fill a smaller portion – their own area of the triangulation group. And (very important) they will not be related to each other (unless they are related some other way).

Same goes for the g7 generation and further back. We are identifying the descendants of deep ancestors, deeper than our MRCA.

So then, how do we identify these people? What you have to do is look for the deep crossovers. Generally you can find them by identifying a common triangulation endpoint of a number of people that is just before a common triangulation startpoint of a number of people. The people to the left of the common endpoint could be from one deep ancestor. The people to the right could be from that deep ancestor’s partner, i.e. the other parent of the descendants they share.

For example, in the example diagram at the top, we can find 4 people whose triangulating segments end at 77,509,668 and 3 people whose triangulating segments start at 77,511,553. Putting these people together, we get:

Base addresses less than a few thousand apart are generally next to each other in the raw data file. We can check and see that in fact, 77,509,668 is followed in the raw data file by 77,511,553. The base pairs in-between are not included in the raw data.

There are about 3 billion base pairs (aka SNPs), but only 700,000 of them are determined in a DNA test and those are what are included in the raw data file. Therefore, each base pair included is only about 1 in 4000, and that is why the base address jumps from a few hundred to a few thousand between lines in the raw data file.

Those 4 people ending at 77,509,668 are therefore all likely descended from an ancestor of our MRCA. And the 3 people starting at 77,551,553 are all likely descended from the partner (other parent) of that ancestor of our MRCA. Note they are still all descendants of our MRCA. But the fact that their segments end and then start at a crossover gives us more information. Once the MRCA is determined, we might be able to piece together the family trees of the 7 people, to help us go back a few more generations from the MRCA.  Doing this will help find deeper ancestors than the MRCA.

The above example actually has 6 other sets of people with some stopping at some base address and the rest starting at the address of the next base pair.

There are a whole number of caveats with this process. Again, some triangulations may be by chance. Some segments may be extended with a random bit that prevents the end or start point from aligning properly. Some of the people may have a crossover that occurred down from the MRCA that happens to fall in the right place. But the toughest problem is that the genealogical evidence often will not go back far enough to determine who the deeper ancestors are.

None the less, this is how earlier ancestor’s crossovers manifest themselves in the match data. You should be aware of how this works as it will give you a way to subdivide triangulation groups into smaller components that will represent more distant ancestors.

And hopefully I can figure out a way to program all this into Double Match Triangulator for you.

When I was first learning about autosomal DNA analysis, just over a year ago, I was under the misconception that if three people triangulate on a segment, then that segment is IBD (Identical by Descent).

A segment that is IBD is one that is passed down from a common ancestor. These are the segments you are looking for. By identifying people who received the same IBD segment, you can use traditional genealogical research to trace back and figure out who was the common ancestor. This is way autosomal DNA analysis and genealogical research can work together to extend your family.

Triangulation means that Person A matches Person C on the segment, Person B matches Person C on the segment AND Person A matches Person B on the segment. If other people also triangulate with them over the same segment, then all people must match all the other people on the segment. Under this condition, all the matching people are said to be in the same triangulation group for this segment. If the segment is IBD, then they all share a common ancestor who has passed them that segment or some portion of that segment.

In a Chromosome Browser, if you are Person A, what you see is:

So you as Person A match Person C, and you as Person A also match Person B over the same segment. Don’t make the mistake of thinking that this means you triangulate with Persons B and C. You still have one more check to make. You must verify that Person B matches with Person C on that segment before you can say that the three of you triangulate. Unfortunately, your own Chromosome Browser will not tell you that.

Simply using what’s called ICW (In Common With) is not good enough. That means Person B and Person C are considered a match with each other. They definitely match on some segments, but those matches might not be the one specific segment you are looking at.

If you are at GEDmatch, you can do a one-to-one check of Person B against Person C and see if they match on the segment. At Family Tree DNA, you must ask either Person B or Person C to check in their Chromosome Browser to see if they match each other on the segment. At 23andMe, the “Y” indicator will tell you if you and a second person triangulate on at least one segment with a third person and then you can set one of them as the primary person in their Chromosome Browser and see if they match each other on the segment.

A Chromosome Browser does what I call “Single Matching”. It compares one person to all that person’s matches. By comparison, “Double Matching” uses the matches of two people and combines them and doing so can find all the triangulations that those two people have between them. It’s like having two Chromosome Browsers side-by-side:

Using double matching, you can tell that Person A matches Person C (orange) and that Person B matches Person C (green) and that Person A matches Person B (blue) all on the same segment. This is what Double Match Triangulator does for you.

That’s how you can find if people triangulate on a segment. Now what can you say if you have a triangulating segment?

My misconception a year ago was thinking that segments that triangulate are all Identical by Descent and thus the People who triangulate must share the common ancestor who passed the segment down. Debbie Kennett took a fair bit of her personal time back then through a number of emails and explained to me that this was not necessarily true. Thank you, Debbie, for your time and patience. My misconception has been corrected.

Here are the correct rules and what you need to know:

All IBD (Identical by Descent) segments will triangulate.
    but
Some segments that Triangulate are not IBD

This is very important, especially the 2nd statement. Never assume that a triangulation is IBD. Here are a couple of reason why they may not be:

1. One of the People Match by Chance

A matching segment in a Chromosome Browser means that we half-match. Each line the Chromosome Browser shows actually represents a pair of chromosomes, one from your father and one from your mother. To be IBD, one of your parental chromosomes must match just one of Person B’s parental chromosomes and just one of Person C’s parental chromosomes. What can happen instead is that they match by “zigzagging back and forth” between the parental chromosomes. Check out the section “False Positive or Identical by Chance Match” in the article Concepts – Segment Size, Legitimate and False Matches by Roberta Estes who explains this very well.

You could theoretically have 3 people who all match each other zigzagging back and forth between their parental chromosomes. But this is quite unlikely, since instead of just one chance match, for this you need three chance matches. I haven’t seen any studies of this but my reckoning would be that it would be a rare event.

Still, there’s a much more likely way for a triangulation to happen with a chance match. Let’s say a segment of Person A matches Person B the correct way: over just one of their parental chromosomes. Then that segment of DNA is effectively the same for both of them (only differing because of a few no-calls, misreads and/or mutations). Person C may triangulate with them on this segment by zigzagging between its parental chromosomes to match at each location. If Person C matches by chance to Person A on this segment, then Person C will also match by chance to Person B.  This appears to be a triangulation but is a match by chance and is therefore not IBD.

This match by chance in a triangulation is bad because it is difficult to discern the people who are by chance matching into a triangulation group. The by chance match will match everyone else in the triangulation group. The only way to tell the difference would be to look and compare the raw data – not a simple task, and something you can’t do at GEDmatch because they don’t give you access to the raw data.

One thing triangulation does do for you is reduce the likelihood of a by chance match. In Single Matching, any match between two people that is less than about 15 cM may be a match by chance. As the segment gets smaller, the likelihood of a match by chance increases. But in triangulation, we do have one leg matching two of the people on one of their parent’s chromosome. The by chance match can zigzag on its own pair of chromosomes, but cannot zigzag on the other connection.

That forced connection reduces the worry of matches by chance but do not eliminate it. Jim Bartlett has concluded that all triangulations of 7 cM or more cannot be chance matches. He suspects that threshold might even be as low as 5 cM.

So triangulations could still include a match by chance. Be wary of triangulations under 7 cM.

2. Matching Segments are on Different Parental Chromosomes

This one really caught me off guard. I think it was in January during a discussion about triangulation on Facebook in a DNA discussion group, Blaine Bettinger posed the question to me:  What if the three matches of the triangulation are on different parental chromosomes?

That threw me for a loop. I had never thought of that before. Blaine was right. It could happen. Let’s say person A matches person C on one specific segment on his father’s chromosome, but matches person B on the same segment on his mother’s chromosome. Person B and C would likewise have to match the same way, on the opposite parental chromosome than they do with Person A.

In the above diagram, all three people match each other on the same segment.  This is a Triangulation. Person A matches Person B on the same segment (albeit different parental chromosome) as Person A’s match with Person C and person B’s match with Person C.

When Blaine first brought this up, I had a bit of a panic attack. My entry of Double Match Triangulator in the Innovator Showdown at RootsTech was coming up. This was at the time a new technology based on triangulation … and if we’ve just discovered that triangulation didn’t work, then what?

Fortunately, this turned out not to be a concern. This was just another case like the match by chance situation, where a triangulation occurs but the segment is not Identical by Descent. It does not invalidate triangulation as a tool, and triangulation is still required (but is not sufficient) for a segment to be Identical by Descent.

Don’t think these opposite parent triangulations are a rare thing. They likely are not. I’ve found a number of examples in some of the work I’ve done. And here’s the bad thing about them. It could happen with segments of any length. There is no protection by using only large segments, say 15 cM or more.

So then I thought of how to eliminate this possibility of elimination of opposite parent triangulations. Redrawing the Person A, B and C matches as a diagram, we have this:

To prevent this, all we need is a 4th person who is part of the triangulation group. When you add that 4th person, and try to connect them to each of the other three, as below:

you’ll see there is no possible way that you can make that last connection (the dashed red line) without forcing each line to be an identical segment. For example, in the above diagram, we can logic that:

A Pat = C Pat
A Mat = B Mat
B Pat = C Mat
    and
D Mat = A Pat = C Pat = D Pat
    so D’s parental segments would match each other,
    and
C Pat = D Pat = B Pat = C Mat
    so C’s parental segments would match each other,
    and
C Pat = C Mat = D Pat = D Mat = A Pat = B Pat
    so all people match on an identical segment

IOW, to force the triangulating segments to match, we need 4 people in the triangulation group. This could be done with an extension to Double Match Triangulation that could awkwardly be called: Triple Match Quadrangulation, which would use the segment matches of 3 people (Person A, B and C) to find all the people D who match A, B and C where A, B and C also match each other.

An alternative that would be simpler is to do two sets of Double Match Triangulations (A with B, and  A with C) and combine the results. Doing so would avoid the need to ever have to use the word “quadrangulation”.

One caveat with regards to this. If any of the four people are siblings or other forms of double relatives that fully match on the segment on both chromosomes with one of the other people, then you can still include them in the triangulation group, but you can’t count them as one of the four and you’ll have to add another person who triangulates to bring the total up to four or more.

Double Match Triangulator already allows two or more sets of Double Matches to be combined in a “By Chromosome” run, but it does not yet merge the triangulation groups together. I’ll attempt to do so in a future version of DMT using this new knowledge that a 4th person in the group can guarantee that its the same segment that’s being triangulated.

Remember: Triangulation is still Very Useful

Even though triangulations may match by chance, or may triangulate on opposite parental chromosomes, that only means that triangulations are not necessarily Identical by Descent.

Despite this, what triangulating does for you is remove from your consideration a very large number of single matches that cannot be IBD. The matches that remain that triangulate are the only ones from which IBD segments will be found.

Said another way:  Identical by Descent segments must triangulate, so by triangulating you are greatly reducing the matches you have to look through to find the common ancestors of your DNA relatives.

Just be wary. Don’t assume all your triangulations are IBD.

 
 
—-

Update Sept 25:  Ann Turner informed me on the ISOGG Facebook group that 23andMe allows you to put anyone as the primary person in the Chromosome Browser, so you can determine by yourself if Person B matches Person C without having to contact them. I’ve now corrected that in my article.

Additional notes in my reply to Ann:

From a mathematical analysis, I am pretty sure you would only need 3 people’s matches, A, B & C to triangulate an unlimited number of people: D, E, F, G, …. into the same triangulation group (which is what I horribly named: Triple Match Quadrangulation). Using only two people, A & B, will determine all the triangulations, but those might include some triangulations with matching segments on different paternal chromosomes.

So no, you wouldn’t need to compare D & E. If you add F, you wouldn’t need to compare D & E, D & F or E & F.  Etc.

What you will find, however, is that some people may not have enough total cM to make a match criteria. They may match just on a few small segments including the one of interest. But you can’t tell because they are not an overall match for you. You will then need to match them on the segment with a third person from the triangulation group to prove that they belong.