Revisiting Speed and Balding - Sun, 5 Nov 2017

Louis,

On an intuitive level, your analysis and conclusions have a ring of truth that I have found lacking in Speed and Baldwin. You present a much more encouraging picture for genetic genealogists!

Louis, Thank you for this analysis and post - a tremendous service to the genetic genealogy community! We need someone like you with the math skills to help us understand and properly use the Speed and Balding paper. I had reluctantly accepted the way others had interpreted their widely seen Chart. But it just didn’t seem right to me. I have tried, in vain, to develop two different sets of curves. One I took a stab at in my segmentology blog - a distribution curve of IBD shared segments for each cousinship. It seems to me they would be centered around the calculated average value with longer and longer tails, which are needed to get cousins beyond 4th cousin to show up above 7cM. We have so many such distant cousins (as you pointed out in this blog), that some will be in the matching range. My second desired curve is a percent at each cousinship for our Matches - say 1% are 1C, 3% are 2C, 6% are 3C, 9% 4C, 12% 5C; 14% 6C; 16% 7C; 10% 8C; 5%9C; 4% 10C 2% for each of 11C-20C. Somewhere, the diminishing size of very distant cousin shared segment has to overtake the impact of the growing number of cousin. My gut estimate is that most of our Matches are in the 6-8 cousin range. Clearly this curve increases from very small number of very close cousins out to 4th cousin, but at some point a distribution curve has to peak and then fall - keeping the total under the curve at 100%. Two weeks ago, AncestryDNA had me at 50,000 Matches (probably over half are false), and 2,000 4C Matches (some probably 5C or 6C) - that would result in a flatter curve than my percents above..

Thanks again for your expertise and level headed reasoning about this topic. Jim

Hi Louis, as my username probably gives away, I’m the first author of Speed and Balding (not to be confused with that terrible work from Speed and Baldwin infodoc rightly dismisses ;) ). I don’t follow the ISOOG blog, but a colleague alerted me to your blog post

Firstly, I’m incredibly flattered if it’s true that people have been using the figure we made. My research is mainly in common diseases, and particularly how we can use subtle similarities between very distantly related pairs of individuals to find genetic variants which increase / decrease risk of developing different conditions. Because I use very distantly related individuals, the similarity estimates are very small - between one pair it may be 0.001, between another -0.001. The tie in with the NRG paper you comment on, is that if I instead were to use more closely related individuals, the similarity values would increase, to the point they become recognisable as estimates of relatedness (ie 0.5 for full-siblings, 1 for twins). This poses an interesting problem, because when we examine distantly related individuals, there are 100s of different ways to measure similarity, each of which corresponds to a different assumption regarding how we believe causal variants affect risk for a particular trait (e.g., we might use one measure of similarity if studying type 2 diabetes, another for rheumatoid arthritis). Therefore, when people measure similarity between more closely related individuals, why do they tend to only use one or a few methods? Also, does our work on distantly related individuals provide an insight into which is the best method to use on more closely related individuals?

Hope some of that made a bit of sense. As for your article, it was very interesting to read your thoughts. Sorry that all the details are not clear in the paper - we thought there was a lot of important material to cover, but journal space is always at a premium, so I think we did very well to get as much as 10 pages. I really liked how you tied together the table and figure 2B, however, from my point of view, they were completely separate, except that I used the same mutation rates. Basically, for Figure 2b, I wrote a code (in the programming language C) which started with 10,000 individuals (5000 male, 5000 female). At each iteration, the code produced 10,000 children, each with a mum and a dad (while it’s standard convention to pick pairs at random, we modified this to reflect this is not how it works in the real world ;) ) Because it was a simulation, I could keep track of exactly what happened in each mating, i.e., which pieces of DNA a child got from their dad’s maternal DNA, and which from their dad’s paternal DNA, etc. I ended up with a long list of identity by descent (IBD) segments of varying length, allowing me to ask the question, if I observe a segment of length 10-20mb, what is the most likely G. One limitation is that the simulation is stochastic (lots of chance events) so I repeated it to check the results looked almost identical (i.e., the results were stable). A second is that we considered a finite number of generations (50) but I think I repeated with different numbers, again to check results were stable.

So it seems to me, your key point is that our figure exaggerates G for small chunks - for example, your results suggest that if we find two individuals share a segment 1-2MB long, they are more likely than not to have G<10, whereas our results suggeet the chance G<10 is about 20%. I am confident my simulations were reasonable and I think our estimates tied in with other results in the paper (but it’s been a few years so it’s not fresh in my mind). In response to one of your points, I am fairly confident my simulation kept track of the first most recent common ancestor (this was fairly easy to do, simply by recording each basepair of each of the 10,000 individuals as a number between 1 and 20,000 which indicates from which of the parental haplotypes it came, then it is straightforward to compute fraction IBD <=G generations (ie what fraction of the genome two individuals have inherited from a common ancestor no more than G generations ago), and in turn the fraction IBD exactly G generations (by subtracting the fraction <=G-1 from the fraction <=G). Therefore, I think the differences come from us asking slightly different questions rather than an error in either mine or your calculations (and yours may well be a more relevant question to ask). Hope this explanation helps in working out what this difference is!

Cheers, Doug

Louis

It makes no difference whether one is studying diseases or detecting DNA relatives. It’s still necessary to identify related people in the database.

The reason the testing companies filter small segments under 6 cMs or 7 cMs is not to exclude small segments from distant generations but for the very practical reason that these small segments cannot be accurately measured with genotype data and with the current IBD detection methods. An additional problem is that all the companies, with the exception of AncestryDNA, are giving us unphased matches. Without phasing there is a high false positive rate when reporting segments under 15 cMs. Even with phasing there are many false positives for small segments. See the 2014 article by Durand et al:

https://www.ncbi.nlm.nih.gov/pubmed/24784137

With computer simulations, as Doug has stated above, it’s possible to trace all segments, however small, because that can be controlled within the simulation.

The step you are proposing is therefore completely unnecessary which is why your figures differ so much from Speed and Balding’s. If you wish to translate the chart into data supplied by the companies all you have to do is ignore the data for the smaller segments that aren’t reported by the companies.

The point that both you and Jim seem to be missing is the fact that segments can date back a very long way. The distribution curve doesn’t end 10 generations ago. As Speed and Balding have shown, segments can trace back for 50 generations, and sometimes this includes very large segments. The number of our ancestors and the number of our cousins doubles every generation so we have many millions more cousins who share ancestors with us between 10 and 50 generations ago than we do cousins from the last 10 generations. Even though we are unlikely to match one specific cousin that long ago the fact that there are so many means that these are the cousins that dominate our match lists.

Speed and Balding’s simulations are backed up the informal research published by the geneticist Steve Mount in his blog post on “Genetic genealogy and the single segment”:

http://ongenetics.blogspot.co.uk/2011/02/genetic-genealogy-and-single-segment.html

It is also backed up by empirical data from the Ralph and Coop paper on “The geography of recent ancestry across Europe”:

http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001555

See in particular this quote from the discussion:

“A related but far more intractable problem is to make a good guess of how long ago a certain shared genetic common ancestor lived, as personal genome services would like to do, for instance: if you and I share a 10 cM block of genome IBD, when did our most recent common ancestor likely live? Since the mean length of an IBD block inherited from five generations ago is 10 cM, we might expect the average age of the ancestor of a 10 cM block to be from around five generations. However, a direct calculation from our results says that the typical age of a 10 cM block shared by two individuals from the United Kingdom is between 32 and 52 generations (depending on the inferred distribution used). This discrepancy results from the fact that you are a priori much more likely to share a common genetic ancestor further in the past, and this acts to skew our answers away from the naive expectation—even though it is unlikely that a 10 cM block is inherited from a particular shared ancestor from 40 generations ago, there are a great number of such older shared ancestors.”

Ralph and Coop also have some very useful FAQs that explain some of these difficult concepts:

https://gcbias.org/european-genealogy-faq/

Can I also suggest that people have a read of the comments in the ISOGG group on Facebook in the discussion about this blog post.

https://www.facebook.com/groups/isogg/permalink/10156092253692922/

In particular I recommend reading the comments from Dr Andrew Millard from the University of Durham. He has a background in mathematics and Bayesian analysis and has a good understanding of the issues.

If you have a stable population over 50 generations then you do get extreme pedigree collapse. This is pretty much what has happened throughout human history with the exception of the last 300 years: https://en.wikipedia.org/wiki/World_population_estimates All humans are highly endogamous. It’s just a question of degree. After 50 generations each one of the 10,000 people in the simulation in the most recent generation would have a quadrillion genealogical ancestors which is clearly impossible because we know that the founding population was only 10,000 people. What happens is that people always marry someone to whom they are already related multiple times over. There are also simulations on this website that you might find of interest: http://burtleburtle.net/bob/future/ancestors.html The author provides a useful table showing the predicted number of genealogical and genetic ancestors at each generation. Like Speed and Balding he finds that it’s still possible to have genetic ancestors tracing back much further than people intuitively realise.

I don’t believe it makes sense to apply the Speed and Balding equation as far back as 32 generations. From what I understand this type of calculation assumes that our ancestors double with each generation when in reality the population just collapses upon itself and everyone is related. That is also why Ralph and Coop are seeing 10 cM segments going back such a long way. All Europeans are related to each other in multiple ways within the last 1000 years.

You have been dancing around the phrase “conditional probability”, which is the big distinction between looking at data before and after the filter is applied. There is another conditional probability issue that arises because peoples match lists are sorted — regression to the mean, i.e., the regression effect.

When you look at list of matches, each has some DNA in common with you and each has some distance to a MRCA. The goal is to guess the latter based on the former. When correlation between two variables is strong the regression effect is minimal and the guesses should be pretty accurate. But lets ignore the matches with MRCA of, say, 4 or fewer generations back. The rest of the data is usually a huge list of weak matches, and the correlation between amount of DNA shared and generations to MRCA should be much weaker. Now when you sort this list of matches by shared DNA (still ignoring the strong matches) and just scroll through the beginning of that list, as most people probably do in practice, you are singling out among all of your weak matches those who have more shared DNA than most. And typically, the explanation for why these people would share more DNA than most of your weak matches is “luck”, rather than having a very close MRCA. What you should observe then is that the MRCAs with a lot of these “closer weak matches” is farther back than would be predicted by the regression model. I have found this anecdotally myself: for the handful of weak matches for whom we have traced a MRCA, the generational difference has usually been larger than had been predicted by the model. I am interested to know if other people have the same experience, since its impossible to tell here if the assumptions are in place for regression to the mean, or if so, how strong the effect should be.

The lack of information is possible, but I think unlikely. I have complete information back 5 generations, except for three ancestors who are all in Switzerland, and none of the three matches I am thinking of have anyone near Switzerland. At least two of my matches have similar completeness of records. So our predicted MRCAs of 4.2 and 4.8 generations back are definitely wrong.

There’s no way to rule out endogamy, as you say. But the point of my post is, attributing these issues to anything other than statistics is known as the “regression fallacy”. Yes, other factors may be contributing to regression toward the mean, but this effect will happen regardless. Everywhere I see discussion of endogamy, incomplete information, etc, but regression to the mean could play as big a role as these other factors and I never see it discussed.