Introducing the first relationship predictions to come from a peer-reviewed data source

Two new relationship predictors are now available, one with population weights and one without weights. The data came from Ped-sim. This is the future of relationship prediction. These innovative tools are collectively named “Orogen,” which derives from a geologic term meaning “mountain building.”

Update, 3 Feb. 2023: You can now get relationship predictions from number of segments and total cMs. This tool often tells you the exact relationship for close family members, including which side the match is on (paternal or maternal).

For the vast majority of our needs, the population weighted predictor is the one to use. Population weights are necessary because we have vastly more distant cousins than close cousins. In the uncommon case that you had a known relative take a DNA test so that you could compare your results, you can use the relationship predictor with no population weights to see if you share a normal amount of DNA for the known relationship type.

Building relationship predictors takes a lot of work, but the process is fairly simple. To get the probabilities of each relationship type relative to other relationship types, one simply creates “bins” for the frequencies of each relationship type. Orogen predictors use 1 centiMorgan (cM) bins. After that, the probabilities for each relationship type can be calculated by dividing the counts of each relationship type in a bin by the total count of all relationship types in that bin. There’s a little more to it, which I’ll describe below, and the work is arduous, but the result of the analysis is a figure like the one below.

Figure 1. Probabilities for several relationship types as reported in centiMorgans (cM) at AncestryDNA. These probabilities should be understood to be relative to the other relationship types listed. The curves show what the probability is at a particular cM value, which is what you see when you enter a value into one of the new relationship prediction tools. In the two new tools, relationships go all the way to 8th cousins once removed (8C1R).

Figure 1 above and Figure 2 below look remarkably similar to the probability curves I published in April of 2021. However, there will be some differences in the tools when zoomed in on the probabilities. And one great benefit to the new tools is that the data source has been through the process of peer-review.

AncestryDNA uses the half-identical region (HIR) metric of reporting cMs, which will show full-siblings sharing 37.5% of the total cMs, on average, even though we know the true average is 50%. (Confusingly, they report percentages by the total identical-by-descent (IBD) metric, and as a range.) Below is a figure for 23andMe probabilities. In Figure 2, you can see clearly what a benefit it is to use the IBD metric rather than HIR. When all of the fully-identical regions (FIRs) are included, the full-sibling curve is shifted to the right. This provides more room for the grandparent/grandchild relationship relationship to stand out from the other close family relationships.

Figure 2. Probabilities for several relationship types as reported in centiMorgans (cM) at 23andMe. These probabilities should be understood to be relative to the other relationship types listed. The curves show what the probability is at a particular cM value, which is what you see when you enter a value into one of the new relationship prediction tools. In the two new tools, relationships go all the way to 8th cousins once removed (8C1R).

There is a great site called DNA Painter that’s full of useful tools. One of those tools is very popular and has been skillfully built by Jonny Perl. The data source for the probabilities came from a plot from simulations done at AncestryDNA. This was groundbreaking when it came out in 2016. The methodology doesn’t discuss much about how the probabilities were generated. The relationship predictor at DNA Painter uses data points that were obtained from the graph using an online plot digitizer. (It probably shouldn’t have to be mentioned that it would’ve been ideal to obtain the original data that made the curves.) Moving forward six years, we now we have relationship predictors from Ped-sim, which has been peer-reviewed in a science journal. This makes the predictors at DNA-Sci much more trustworthy than the data from Ancestry simulations. Additionally, at least 18 million data points went into the new relationship predictors versus a mere few dozen that are visible in Figure 3, resulting in much smoother curves for Figures 1 and 2.

Figure 3. Probability curves from the 2016 AncestryDNA matching white paper.

Methodology

Update: 29 Sept. 2022: the methodology for Orogen is now published in a science journal.

The data used for the Orogen predictions came from Ped-sim. In this case, the refined genetic map of Bhérer et al. (2017) was used as well as the crossover interference parameters of Campbell et al. (2015). I compiled 500,000 data points for each relationship type.

After obtaining all of the data, I applied low cM cutoff values for each of the two DNA sites. For 23andMe, a match with all segments less than 7 cM was discarded. If a match does have segments of 7 cM or more, then only segments below 5 cM were discarded. For AncestryDNA a simple cutoff of 8 cM was used, so any segments less than that were discarded.

I also had to do a conversion. I used the lengths of the genetic map lengths from this article to convert all segments proportionally to the centiMorgan length of the Bhérer et al. map. The low-cM cutoff values for 23andMe and AncestryDNA also took this into account.

The parent/child relationship was the only one for which I wasn’t able to obtain variable data for from Ped-sim. For relationship prediction, including parent/child and full-sibling relationships isn’t entirely necessary, as it’s very easy to tell the difference in other ways and the DNA sites will assign the appropriate relationship label for you based on those methods. However, I wanted to include those two relationship types just in case, for example, two people aren’t on the same site, but have both uploaded to GEDmatch. For parent/child relationships, I generated a normal distribution of data that approximates the data found in the figure below.

Figure 4. Graph from AncestryDNA in 2020 that shows the range of DNA possible for parent/child matches after genotyping errors.

Once the counts for each relationship type were placed into 1 cM bins, I had to smooth the data curves. It’s an arduous process and I was meticulous in my work to ensure that each final curve was smooth without being altered on the whole. For each relationship type, I generated individual plots showing the original, fuzzy data, and checked to see that the smooth curve was contained within the original data points. The figure below shows what the curves would look like if the smoothing hadn’t been performed.

Figure 5. Unsmoothed probabilities for several relationship types based on the AncestryDNA genetic map. This figure can be compared to Figure 1 to see how smoothing is necessary.

After smoothing the curves, I simply had to calculate the probabilities. This is done for each 1 cM bin by dividing the count for each relationship type by the total count of all relationship types. Then I saved a file of probabilities, which can then be looked up by a web-based tool like Orogen. This is how I generated the probabilities for the tool with no population weights. But I also had to create a relationship predictor with population weights.

The way that I added population weights was very simple. Since each person’s family tree is different, we will never know the exact number of cousins for each person. But what’s really important is that everyone has vastly more distant cousins than close cousins. And this isn’t very hard to approximate on average. I’ve used a typical rate, similar to a birth rate, that others have also used for population weights: 2.5 surviving children per family. This results in five times as many cousins with each generation of ancestors, for example there would be five times as many 2nd cousins as 1st cousins.

Since April of 2021, I’ve been using the formulas found in this article to determine the number of cousins at a given generational distance. These formulas have the same effect as those used in Henn et al. (2012), as I can see that the values in Table 2 are identical to those from my formulas with two exceptions: they round to the nearest tens or hundreds place in most cases and they seem to not include “removed” cousins in their table.

Please note that a “population growth model” doesn’t require a population to grow. We have many more 5th cousins than 1st cousins regardless of whether or not the population is growing. Even if the rate of surviving children per family were only 1.9, we would have population decline, or negative growth, and we would still have way more 5th cousins than 1st cousins. To avoid confusion I call the above process the applying of “population weights.”

When I had the idea to do all of this work, even when I had already done it for several other relationship predictors, I knew that going with Ped-sim was the smartest thing to do. This is the future of genetic genealogy. I plan to continually improve the process for generating and displaying the probability curves shown here and would happily work with other scientists to do so.

All of the most advanced relationship predictors use the same peer-reviewed data source. Here are the tools of note:

• Relationship predictions with number of segments
• A double cousin relationship predictor
• Relationship predictions for X-DNA matches

DNA-Sci — advancing the science of relationship predictions. You can also find mobile apps. for relationship predictions in the Apple Store and on Google Play. Feel free to ask a question or leave a comment. And make sure to check out these ranges of shared X-DNA, shared atDNA percentages, and shared atDNA centiMorgans. Or, try a tool that lets you find the amount of an ancestor’s DNA you cover when combining multiple kits. I also have some older articles that are only on Medium.