Escape from the Overlap Zone

UPDATE: Additional simulations by Andrew Millard using different recombination rates for men and women indicate that half-siblings and aunts/uncles/nieces/nephews can sometimes be distinguished from one another if they are on one’s paternal side but not if they are on the maternal side. Please bear that in mind as you read this post.

With the exception of identical twins or parents and their children, a given relationship has a range of possible shared DNA. Grandparents and their grandchildren can share from about 1156 cM to 2311 cM, with an average of 1766 cM. (The values in this post were taken from user-reported values in the 2017 version of the Shared cM Project, by Blaine Bettinger; “cM” stands for centimorgan, the unit we use to quantify shared DNA in genetic genealogy.)

(A note for newbies: Words in bold in this post are defined in the glossary.)

Most family relationships have ranges that overlap with at least one other relationship, meaning that there’s no way to tell the possibilities apart using only the amount of shared DNA.  For example, the reported range for aunt/uncle and niece/nephew (an avuncular or nibling relationship) is 1349–2175 cM (average 1750 cM) and for half siblings it’s 1317–2312 cM (average 1783 cM). Compare to 1270–2365 cM (average 1766 cM) for grandparents. In an unknown parentage search or when faced with an unexpected match, we often want to know as much as possible before approaching the other person. Sometimes non-genetic factors can help to determine the relationship—if a DNA match is only 15 years older, they cannot be a grandparent—but often there is no way to tell.

Or, is there?

 

The Same Isn’t Always the Same

Although they have nearly identical averages and ranges of shared DNA, the grandparent–grandchild, avuncular, and half-sibling relationships differ fundamentally in how the DNA is inherited. Let’s take a look. Before we do, I’ll remind you that we each have two copies of each autosomal chromosome—one inherited from each parent—and each copy is a mixture of the two chromosomes of that parent’s parents (our grandparents). The mixtures occur when gametes (eggs and sperm) are formed, during a process called crossing over.

 

Grandparent Versus Grandchild

I am going to walk you through simplified examples for the three relationships, all using chromosome 1 with two crossovers per generation. Of course, in the real world, we have 22 autosomal chromosome pairs, any of which can cross over one or more times or not at all.

The first example compares a grandfather to his grandchild (his daughter’s child).

Grandpa’s two copies of chromosome 1 cross over where the black X-like marks are, and one recombined chromosome is inherited by his daughter.  She, in turn, has two copies of chromosome 1 (the other came from her mother) that recombine, and the child inherits one of them. (The grandmother’s chromosomes also recombine before being passed to the mother, but because they are not relevant to the grandfather–grandchild comparison, her chromosome 1 is shown in black for now.) A total of four crossovers have taken place, and the grandfather and grandchild match along a single, rather large segment of DNA (yellow bar). Note that a crossover took place within that segment, but with the tests we use for genetic genealogy, all we’ll see is a single large matching segment.

 

Half Sibling Comparison

Now consider half siblings who share a mother. After recombination, her first child receives a copy of chromosome 1 that looks like this:

And her second child receives a copy of chromosome 1 that looks like this:

Comparing the two half siblings to one another, we can see where they match one another (the yellow bars).

In both the grandparent–grandchild scenario and the half-sibling one, there are two generational steps (grandparent-to-mother, mother-to-child and mother-to-half-sib-A, mother-to-half-sib-B, respectively). What’s more, I used the exact same crossover points in the two examples. The grandpa’s two crossover points in the first example are exactly the same as the ones that produce Half-Sibling A in the second example, and the mom’s two crossover points in the first case are exactly the same as those leading to Half-Sibling B in the second.

But we end up with completely different patterns of sharing!  One large segment shared between grandpa and grandchild versus two smaller segments shared between half siblings.

That’s gotta make you wonder:  Can we possibly tell a grandparent from a half sibling using DNA alone if we consider not just how much DNA is shared but also how many segments are involved?

 

Avuncular Relationships

Before we answer that question, let’s look at the third case with an overlapping range, the avuncular relationship. This one is a bit more complicated to depict, for two reasons.  First, there’s an additional generational step involved, and second, it’s actually a double relationship.

What I mean by “double relationship” is that the child and uncle are related once through the child’s grandfather and again through the grandmother.

(If they were only related through one grandparent, the uncle would be a half uncle.)

In this example, I will use the grandfather–grandchild example from above, but instead of using a generic black chromosome for Grandma, we’re going to work her into the equation, too.

Let’s divvy up grandma’s chromosomes into her two children, the child’s mother and the uncle. Again, I’m using two crossovers per chromosome pair and placing them whimsically. The grandmother’s two chromosomes recombine into the uncle like this:

And into the mom like so:

Now, let’s take the mom’s paternal chromosome from the very first example above and replace the black stand-in chromosome with the maternal chromosome that we just created. The crossover points are the same as in that first example. Now, the recombination that produces the child looks like:

In this case, the child’s maternal chromosome 1 is comprised of segments that originally came from both grandparents.

Finally, let’s compare the child to the uncle to see where they share DNA segments (the yellow bars).

Interesting! We used the same number of crossovers per generation, and we’re looking at three relationships that would be indistinguishable based solely on total amount of shared DNA, but we see different patterns when we look at the number of segments.

How can we apply this to genetic genealogy?

 

Simulations by Dr. Andrew Millard

It turns out that the idea that there might be differences among these relationships isn’t new. Scientists from 23andMe published a scientific paper entitled “Cryptic distant relatives are common in both isolated and cosmopolitan genetic samples” back in 2012. They include a figure that indicates almost no overlap between grandparent–grandchild (the orange “cloud” of dots) and avuncular (the yellow cloud) relationships when both total shared centimorgans and the number of segments are considered. However, this paper didn’t include half siblings.

 

In 2013, William Hill and Ian White of the University of Edinburgh, UK, did a study that included half siblings, but they counted segments far smaller than we use in genetic genealogy (down to 1 cM) and reported their results in awkward tables.

To counter these limitations, Dr Andrew Millard of the Durham University, UK, designed a computer simulation that mimics crossovers, segment inheritance, and the matching parameters used by GEDmatch. He then simulated thousands of avuncular (UN in the chart below; the black cloud), half sibling (HS; the red cloud), and grandparent–grandchild (GP; the blue cloud) relationships and plotted each simulated result by the total amount of shared DNA and the number of segments.

 

 

Here’s another view, with the red and black colors reversed to give you a different perspective on the overlap area.

Yes!  We can often tell these relationships apart! The grandparent–grandchild relationship is almost always distinct from the other two, and while there is a fair amount of overlap between the avuncular and the half-sibling clouds, there are also regions where one or the other is the only possibility or is significantly more likely.

 

Try It!

To use this chart, do a one-to-one comparison of two kits at GEDmatch. At the bottom of the resulting table, find the Total of segments > 7 cM and the number of matching segments, like shown.

Then find the place on the plot that corresponds to the total shared cM (the left–right axis) and the number of shared segments (the up–down axis) and observe which “cloud” is densest.  Let’s do a few examples.

 

 

Example 1: Two people at GEDmatch share 1530 cM across 26 segments. The yellow ❶ on the example plot shows where that match falls. That’s firmly in the blue (grandparent/grandchild) cloud with neither of the other two relationships having that few segments, so they are grandparent and grandchild to one another.

Example 2: Two people at GEDmatch share 1756 cM across 51 segments. The yellow ❷ on the example plot is in a dense part of the black (avuncular) cloud and in a very sparse part of the red (half sibling) cloud, so there’re almost certainly an aunt/uncle/niece/nephew, with a very slim chance that they’re half siblings.

Example 3: Two people at GEDmatch share 1803 cM across 42 segments (the yellow ❸). This one’s a bit more iffy. It’s in a dense part of the red (half sibling) cloud but still well within the black (avuncular) cloud. If this were an unknown parentage case, I would acknowledge to the match that both are possibilities, but that we should explore a half-sibling connection first.

In the three examples, I emphasized that the matches were compared at GEDmatch, because Dr Millard’s simulations were based on the parameters used there. That means that if your data came directly from one of the DNA companies, you should use the chart with caution.

Some considerations:

• AncestryDNA’s phasing algorithm both reduces the total amount of shared DNA and often artificially breaks up continuous blocks of DNA. For example, comparing my two children to their three grandparents who have tested at AncestryDNA, GEDmatch reports an average of 58 more centimorgans and 9.1 fewer segments (about 26% fewer).
• Family Tree DNA includes segments down to 1 cM, while GEDmatch’s threshold is 7 cM. Data from Family Tree DNA must be manually tabulated to include only segments that are 7 cM and larger before using the chart.
• 23andMe includes segments down to 5 cM, so their values should also be adjusted by manually excluding the segments less than 7 cM.
• If you come from an endogamous population, you may share more segments with your relatives than expected, because you are actually related to them more than one way. The additional connections may be numerous and too distant to trace. In this case, the “extra” segments will generally be quite small (under 10 cM). Hopefully, in the future, segment size can be incorporated into our relationship predictions along with total shared DNA and number of segments.

 

In a forthcoming post, I will describe how simulations by Dr. Millard helped solve a 50-year-old mystery.

 

UPDATES

Kitty Cooper has just posted a set of empirical (observed, as opposed to simulated) data from self-reported comparisons that addresses the overlap zone.  The distinction among groups isn’t as clean-cut with the real-life results. You can read her post here. The difference between Kitty’s data and Andrew’s simulations seem to be attributable to whether the connection is on the maternal or the paternal side. Paternal half-siblings and aunts/uncles/nieces/nephews can sometimes be distinguished from one another, whereas those on the maternal side cannot.

 

29 Aug 2017 — This post was updated to demonstrate how to get the total cM and number of segments from GEDmatch and to better credit the figures that came from other sources.

1 Sep 2017 — This post was updated to add the second “colors reversed” version of the simulations graph and to add a link to Kitty Cooper’s blog.

8 Oct 2017 — This post was updated with a notice that the distinction between half-sibling and avuncular relationships only holds for paternal relatives. Additional simulations by Andrew Millard indicate that maternal half-siblings and niblings are indistinguishable based on total cM and the number of segments.

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