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How likely is a lack of DNA match with a distant relative?

I have recently gotten interested in ancestry research and have had a DNA analysis performed by a prominent commercial provider.

I've been working on my family tree for a few months now and have gotten into contact with a lot of distant relatives of mine, which has generally been quite delightful. In one particular case, we discovered that we actually have a double-relationship about 5-7 generations back in time, depending on how you count (common links go back to about ~1790).

We found this quite interesting, and this distant relative had a DNA analysis performed on their own genome as well.

Much to our surprise, however, we didn't find any commonalities in our DNA, which seems odd given the double-relation, and the fact that we have what we believe to be original and authentic documents of all the relatives forming the link.

Of course, we began speculating about the possible reasons for this. Maybe a misattributed child somewhere in the family tree? However, this seems unlikely, given the double nature of the link - most likely, we would need two misattributed children to explain the lack of any commonalities.

The other explanation would of course be that the DNA analysis provided by these companies is less reliable than we think, and that just by random mutations and "unlucky" inheritance, any common DNA might have been lost or scrambled beyond recognition.

I would like to calculate the probabilities of this happening in order to judge whether it makes sense to dig further into the original documents to try and clear up this mystery, or whether a mismatch by chance alone is sufficiently likely to explain this oddity. Of course, I don't need super precise numbers, but a back-of-the-envelope estimation would be nice - are we talking a few percent, or one in a billion? Also, I would be curious anyway on how to calculate probabilities like this, given the publicly available data on these tests.

What are the relevant quantities for this calculation (number of SNPs, I suppose), and how would one define and calculate a probability like this?

About myself

I'm a physicist with a strong background in data analysis with some basic understanding of biology and genetics. Don't be afraid to hit me with those numbers and probabilities, but please explain any genetics jargon you're going to use!

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    $\begingroup$ Welcome! I think what renders this question difficult to answer is we don't know what test your commercial company employs. There are very, very many ways to compare DNA between individuals. It's complex: you can share a polymorphic gene variant with a great ape of another species that you wouldn't share with a grandparent, and parts of DNA are inherited paternally/maternally e.g. mitochondrial DNA is used to perform maternal ancestry tracing. To get an accurate picture, ideally one looks through the entire genome. If you provide the company/test name, it might help specify an approximation. $\endgroup$
    – S Pr
    Apr 12 at 10:04
  • $\begingroup$ I didn't know if providing a concrete company name was against the site policies, but I'm happy to provide it. I was using the DNA Test Kit from myheritage.com. $\endgroup$
    – carsten
    Apr 12 at 10:24
  • $\begingroup$ myheritage.com uses autosomal DNA testing for ethnicity estimate and DNA matching. I assume you went for the latter. I know that different testing companies use different matching algorithms, so some estimates and likenesses for an individual will vary between tests, quite more than one might expect. I think this question is unanswerable in the way that you want; we can't perform an informed calculation for specific regions or genes, but we have no idea which regions myheritage.com uses nor prioritizes, nor with which weight. I hope you can see now that it is probably an intractable question! $\endgroup$
    – S Pr
    Apr 12 at 11:40
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    $\begingroup$ I think the most help we could offer would be if you narrowed or refocused your question, perhaps after reading up a little about genealogical DNA testing. The wiki entry is more comprehensive than an answer you could expect here. $\endgroup$
    – S Pr
    Apr 12 at 11:41
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    $\begingroup$ Just so you know, "Genealogy & Family History Beta Stack Exchange" exists. - genealogy.stackexchange.com $\endgroup$
    – Malady
    Apr 13 at 2:29
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First, if you haven't read it already, I highly recommend Carl Zimmer's "She has her mother's laugh." for anyone interested in ancestry/genealogy.

In it, he presents the following figure showing the probability of sharing any autosomal DNA with a given ancestor as a function of the number of generations separating you from that ancestor. (notably, this analysis excludes the very real possibility of intermarriage within a family tree). Probability of shared DNA over generations

So, for example, if you were to look at one single ancestor from 10 generations before you, there's a little less than a 50% chance that you share any of that ancestor's DNA (remember that at 10 generations you have roughly 1,024 ancestors).

So, at 5-7 generations there's still a high probability that you both have at least some genetic material from the same common ancestor(s). But, it's much less likely that you both share the same pieces of that genetic material (probably in the 10-14 range on this graph).

Plus, very few (probably none) of the commercial DNA ancestry sites do full genome sequencing for ancestry comparisons. They look at a limited number of specific regions that can help identify familial relations. So, even if you do share common ancestral DNA, it's less likely that it would be detected without whole genome comparison.

Image Credit: https://gcbias.org/2013/11/11/how-does-your-number-of-genetic-ancestors-grow-back-over-time/

Edit I just wanted to edit and reference that the above analysis was calculated by Graham Coop and colleagues. I did a little more digging and he's got a blog post (How many genomic blocks do you share with a cousin?) with a more relevant analysis for you're specific question, showing the probability of two "cousins" having zero shared DNA blocks as a function of how many generations back the two shared common ancestors. Probability of zero genetic overlap for cousins

Reference: https://gcbias.org/2013/12/02/how-many-genomic-blocks-do-you-share-with-a-cousin/

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    $\begingroup$ Nice answer. Another factor that might be significant is that there might be parallel relationships that I'm not sure have a specific term in English. That is, siblings who each couple with other siblings. For example, two brothers who marry two sisters. The children of these couplings then are cousins on both sides. This situation is probably was probably rather common in times when families were large, communities were mostly small and transportation was limited. $\endgroup$
    – JimmyJames
    Apr 12 at 21:51
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    $\begingroup$ you have roughly 1,024 ancestors well, you definitely don't have more; you might have less. $\endgroup$
    – Strawberry
    Apr 13 at 10:38
  • $\begingroup$ It seems to me that this answer is presented in a way that inappropriately suggests that there is something universal about these graphs. If I'm understanding correctly, then the results shown on these graphs depend entirely on which regions of the genome are used. $\endgroup$ Apr 13 at 13:28
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    $\begingroup$ @BenCrowell - According to the Coop Lab website, these calculations do seem to apply universally (at least with respect to autosomal inheritance), and are not limited to region-specific analyses. I've updated the references to link to the source page for both figures in the answer. Dr. Coop does a pretty good job of walking through these calculations and providing primary references to backup any claims. He has a number of other posts on the topic of genetic genealogy as well. $\endgroup$
    – MikeyC
    Apr 13 at 15:10
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    $\begingroup$ @MikeyC: Perhaps I'm misinterpreting the first graph? It seems to show the probability of sharing some DNA with an ancestor 6 generations back as close to 1.0. $\endgroup$
    – jamesqf
    Apr 14 at 3:40
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5-7 generations is a long time

Mother and child or brother and sister each share 50% of their DNA. If you find a link between two people that is five generations back, that means you take 50% of 50% of 50% ... for five generations. For both you and the other. Then there is a brother-sister link. That means that 2^11 = 1 in 2048 pieces of DNA are held in common between the two of you.

If your ancestor had some unique form (allele) of a gene, the relationship could still be proved! However, at least a quick glance at myheritage.com doesn't make me think they are doing a full genome sequence from scratch. If they are focusing on known variations in the genome, (maybe SNPs, single nucleotide polymorphisms) then by definition those variations should not be unique. There will be a certain percentage of identical forms between the results for any two people and the effect of changing that by 0.05% will be minimal.

Oh, hold on a minute...

After I received an unwarranted number of upvotes, the other response raised a great point: there will be potentially recognizable regions that have not been recombined in 11 generations. A previous StackExchange question cited that about 53 meiotic crossovers per meiosis were observed in careful measurements of 8 human cells. A genealogist addressing the question cites figures of 42 for females and 22 for males during gametogenesis. Taking a figure of 3.3E9 basepairs / (32 crossovers x 11 first-degree steps + 23 chromosomal ends), that means the segments of non-recombined DNA should still be about 9 million basepairs long! With one SNP every 1000 basepairs or so, that gives 9000 SNPs in a row! That's true, of course, only if you do inherit such a piece - the overall odds should be low, since that's 1/352 of the genome and only 1/2048 is inherited on average. But ... that's still a 17% chance that a large block of syntenic SNPs might be found - one so large that it should jump out of the statistics if the myheritage data set contains a large number of SNPs. That probability would be larger if your common ancestor was mostly via the maternal lineage. It seems surprising to study linkage disequilibrium between two individuals, but with the preexisting SNP data set that isn't really the case.

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  • $\begingroup$ +1. Ancestry sites do use SNP arrays (source), so you're correct, and most determinations of relatedness are statistical $\endgroup$ Apr 12 at 16:44
  • $\begingroup$ Your statement about a brother and sister is wrong. It's possible for a full brother and sister to share no non-mitochondrial DNA (e.g. each received the opposite contribution from each parent). However, sharing no such DNA is extremely unlikely, just as much so as non-twin brother and sister sharing 98% of their DNA. On average, it will be about a 48% share, but any amount between 0% and 98% is possible (can't be 100% and opposite sex). OTOH, two brothers or two sisters must share at least one chromosome from their father (i.e. either the X or Y chromosome from their father). $\endgroup$
    – Makyen
    Apr 13 at 17:00
  • $\begingroup$ @Makyen: I don't think I said anything to disagree with what you said (aside from my ignoring mitochondrial DNA, that is - you remind me that if the genetic relationship happens to be entirely maternal, they should see a very clear confirmation by that means!). $\endgroup$ Apr 14 at 0:28
  • $\begingroup$ @MikeSerfas Your first sentence in this answer says "... brother and sister each share 50% of their DNA." That's what I was saying is inaccurate. $\endgroup$
    – Makyen
    Apr 14 at 0:33
  • $\begingroup$ When used to predict a simple numerical expected value for the overall amount of shared DNA, we can use the average figure. Besides, the binomial distribution gives a >98% probability of inheriting more than 6 and fewer than 17 chromosomes in common even without crossing over - adding say 64 more fragments (they overlap, so I can't really use binomial distribution accurately in that case) would give 38% to 62% shared genes. $\endgroup$ Apr 14 at 1:29
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It's not all that surprising for no actual segments of the genome to be shared between distant relatives.

The back of the envelope figure I've heard is that there's about one crossover per chromosome arm per generation. So, when you're composing the chromosomes for your child, you pick a point along each arm of each chromosome, and splice your two chromosomes together at that point to make the chromosome to pass along.

This means that there's a fairly limited number of chances to share DNA: if you overlay all the crossover points that happened between you and your relative, they don't define that many distinct segments. Each segment has a chance to be shared or not shared via descent from the common ancestor in question, but can't really be fractionally shared.

23 chromosomes * 5 generations * 2 lines of descent * ~2 crossovers per chromosome * 1 segment created per crossover = ~460 segments

If each segment has a 1 in 2048 chance of being shared, as @Mike Serfas suggests, then it has a 2047/2048 chance of not being shared, and if you AND together not being shared across all the segments you get:

(2047/2048) ^ 460 ~= 0.799

So there's about an 80% chance of seeing what you observed, by my back of the envelope math. If you fudge the numbers up and down a bit, the probability still stays in the realm of "could go either way".

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  • $\begingroup$ This calculation doesn't seem to have enough connection to the way the tests are actually done to tell us anything useful. These companies pick certain specific parts of the genome to look at, and those are parts that may be identical in people who are unrelated. The calculation suggests that I would have zero DNA in common with a human if our last common ancestor was many generations back, whereas in fact I have quite a bit of DNA in common with all humans, and even with my dog. $\endgroup$ Apr 13 at 13:37
  • $\begingroup$ +1. I handwaved this issue out of mind, but as you showed here, it is quite relevant. $\endgroup$ Apr 13 at 16:51

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