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

Question

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!

Answer 1

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).

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.

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

Answer 2

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.

Answer 3

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".