DNA Doesn’t Lie, but It Sometimes Speaks in Riddles

“Danielle” was a participant in my recent lecture to the Eastside and South King County (Washington State) genealogical societies, and she has an interesting family situation.¹ 

Danielle shares only 944 cM with her granddaughter Lisa, well below what we expect for that relationship.  Of the more than 1,100 data points in Blaine Bettinger’s Shared cM Project, the lowest reported value for grandparents is 984 cM.  In fact, at first glance, the match between Danielle and Lisa appears to be a first cousin, half-niece, great-niece, or great-granddaughter, rather than a grandparent and grandchild. 

Danielle was so perplexed that she tested Lisa a second time.  She got the same results.

There is no doubt that Lisa is Danielle’s granddaughter.  Danielle has tested her son Martin, who is Lisa’s father.  Danielle and Martin share 3,436 cM, and Martin and Lisa share 3,481 cM.  Both amounts are perfectly in range for parent–child relationships.

What’s more, Lisa shares 2,632 cM and 2,430 cM, respectively, with her two siblings, Owen and Farrah, who share ≈3,485 cM each with their father and 1,854 cM and 1,753 cM with Danielle.  That is, these matches all look normal except for the match between Danielle and Lisa.

My first thought when Danielle told me she only shares 944 cM with her granddaughter is that the connection had to be through her son rather than a daughter.  Why did I think this?  Because we’re more likely to get outlier matches through our male relatives than our female ones.

To understand why, we need some background information.

Crossing Over Affects DNA Inheritance

Parents and children share half their autosomal DNA with one another.  We have two complete copies of each autosomal chromosome, with one copy from each parent.  That amounts to about 3,500 cM in a parent–child match, with minor differences among matching databases. 

On average, a grandparent and grandchild will share half that, ≈1,750 cM, but with quite a bit more variation.  That “extra” variation happens because we don’t evenly divvy up the DNA we got from our parents before passing it on.  Instead, our bodies mix-and-match our chromosome copies in a process called crossing over.  

Crossing over happens at random positions along a chromosome pair, and that affects how the DNA is apportioned.  Consider the images below.  Both show a single crossing over event between a paternal (blue) and a maternal (red) chromosome to create a new mix that is passed on to the child.

Crossing over can happen almost anywhere along a chromosome.  On the left, it happened near the middle of the chromosome, so the child inherited nearly equal amounts of DNA from grandma and grandpa.  On the right, the crossing over event happened near the end of the chromosome, and the child inherited far more of grandpa’s DNA than grandma’s.

With more crossing over events, the proportions of “grandma” and “grandpa” should be more equal.  This example shows three crossover points per chromosome.

And this one shows five.

Notice that the only difference in the left and right sketches is the position of the first crossover event, the one that yielded such imbalanced inheritance and an extreme outcome.  Otherwise, the crossover points are the same.  The take-home message is that the more crossover events there are, the closer a grandparent–grandchild match should be to the average of ≈1750 cM, even if any individual crossover event is biased toward one grandparent..

Crossover Rates Differ Between the Sexes

Now we have enough background knowledge to understand why outliers are more common with a father than a mother.  It turns out that egg production has a higher crossover rate than sperm production.  Don’t ask me why!  I don’t think anyone knows. 

With a higher crossover rate, you’re more likely to get middle-of-the-road match amounts than extreme ones.  Mathematically, we say that the distribution is narrower and has fewer outliers.  

A good analogy is flipping coins.  If I were to flip two coins over and over, I’d get all-heads 25% of the time, all-tails 25% of the time, and a mix 50% of the time.  If I flipped it 100 coins repeatedly, there’s almost no chance I would get all-heads or all-tails; most of my flips would be somewhere in the middle. 

In this analogy, eggs have more coin flips (more crossover events) than sperm.  The difference isn’t nearly as stark as between two flips and 100—it’s more like the difference between 10 and 16 flips—but it’s enough to have an effect on our closer matches, like grandparents and grandchildren.

The histogram below shows what I mean.  It’s the result of 10,000 computer simulations each of a maternal grandparent (red) and a paternal grandparent (blue).²

The two sets of data have the same average (≈1,772 cM), but paternal grandparents have a somewhat broader range, 912–2,592 cM versus 1,070–2,534 cM for maternal grandparents.

Another conclusion we can draw from this histogram is that a known grandparent match near the middle of the range, say ≈1,600–1,950 cM, is slightly more likely to be maternal, and one at the edges of the range, below 1,500 cM or above 2,000 cM, is slightly more likely to be paternal.  I wouldn’t base a whole tree on this inference, of course; it’s just interesting to think about.

In 2019, Blaine Bettinger blogged about an even more extreme example, a confirmed granddaughter who shared only 658 cM with her grandmother.  That was also a paternal grandparent.  Blaine did a very careful analysis of that case to establish that I encourage you to read.  If Lisa is a one-in-ten-thousand case, the 658-cM example is probably more like one-in-a-million.

Back to Lisa

There’s one more thing we can learn from Lisa.  Hopefully you’ve figured it out already!  If Lisa shares an extreme low amount with Danielle, she should share an extreme high amount with her paternal grandfather.

Unfortunately, Danielle’s husband Alex passed away long before DNA testing was available, so Danielle did the next best thing:  she tested Alex’s brother.  And, indeed, Lisa shares more than average with her great-uncle Walter (1202 cM versus an average of ≈850).  Similarly, we’d expect Lisa to share much less than average with Danielle’s brother Colin, and that’s exactly what we see (493 cM versus 850 cM).

The diagram below summarizes Lisa’s DNA matches in a family tree format.  This tree was created in the forthcoming BanyanDNA tool, which will be able to test family scenarios like Lisa’s to highlight potential problems.

BanyanDNA will launch at RootsTech 2024.  You can sign up for our mailing list here to get insider information before then.

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¹ All pseudonyms in this post were brought to you by the 2028 tropical cyclone season.
² Simulations were done in Ped-sim assuming crossover interference, a sex-specific crossover rate, and a genetic map of ≈3500 cM modified from Bherer et al. 2017.