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Previous calculations could only estimate the expected value

I see a lot of articles and posts being shared about Charles II of Spain. He was the last of the Habsburg dynasty and that demise has been attributed to the extreme intermarriage in his recent family tree and his resulting health problems. Some people seem to be almost infatuated with his grotesque appearance and inability to function.

I’ve thought of a similar phenomenon by observing what type of television or movie characters are often popular. A bumbling, inferior character invokes some kind of good feeling in a lot of viewers. It seems to often be the case that people would rather have that feeling than to watch something they could learn from or be entertained by in a more wholesome way. I think Homer Simpson and the Ernest Worrell character from the ’90s are great examples of these lovable characters, whose main purpose I can only imagine is to make us feel superior. (I’m not knocking The Simpsons. Their jokes range from slapstick to some of the funniest and most intelligent ones I’ve ever heard.)

As far as Charles II, though, I just feel sorry for the guy. And that isn’t a feeling I typically have for monarchs.

But that isn’t why I’m here. Previous studies have determined that Charles II would have had about 20% identical DNA when comparing his two chromosome copies to each other, only counting long segments of identical-by-descent (IBD) DNA. When segments are identical on both copies, they’re called runs of homozygosity (ROH). This 20% figure is an estimation based on the coefficient of inbreeding.

But we don’t need a coefficient of inbreeding. There are several different models in use for autosomal DNA sharing, and I happened to have developed one of them. An advantage of mine is that its purpose is to most closely approximate standard deviations from peer-reviewed literature. Getting exact averages with a model like this is trivial, so I don’t need to “estimate if he had 20% ROH.” Rather, I can find the exact expected value of the ROH in a person who has the same family tree structure as Charles II. Training the model on standard deviations allows the model to produce expected ranges of shared DNA to very high accuracy.

See the relationship predictor or ranges of shared DNA that were developed from this model

So what are we dealing with in the Habsburg family tree?

Figure 1. The Habsburg family tree. Source:

Figure 1 shows the recent ancestors of Charles II and their relationships to each other. I created a simulated genome for every person in this tree, which is up to seven generations, sometimes fewer depending on the line. I ran this simulation 500,000 times, which is far more than what’s needed to get the exact expected values. (Probably 20,000 would have worked.) The larger number of trials allows for very accurate ranges of shared DNA, which are so variable that it usually takes a couple hundred thousand or even millions of trials to get fixed percentiles. The results of the 500,000 simulations are shown below.

Table 1. Runs of homozygosity (ROH) for Charles II of Spain. The mean value and the 99% confidence interval are included.

Charles II of Spain had a very high amount of ROH. Table 1 shows that the most likely value is 23.1%. This number, which is the correct value, is three percentage points higher than what was previously estimated. It is barely below the expected value for cases of first-order incest. If the parents of Charles had been brother and sister, mother and son, or father and daughter, he would be expected to have 25% ROH. Given only the relationship of his parents (uncle and niece), Charles II would be expected to have 12.5% ROH. The additional 10.6 percentage points that Charles II likely had must have come from the previous intermarriage within his family.

Another interesting aspect of the ROH in Table 1 is the narrowness of the 99% confidence interval. One thing that you learn pretty quickly when you study shared DNA between relatives is that a greater number of meiosis events results in a narrower range. That’s because meiosis events will tend to result in average values of shared DNA, by definition, and the resulting average values of shared DNA will moderate rare extreme values. This is why double 1st cousins, despite sharing 25% DNA, on average, have a narrow range than half-siblings.

The range in Table 1 is so narrow that the lower end of the 99% confidence interval is actually higher than the lower ends for two of the three possible cases of first-order incest, despite the latter having an average of 25% ROH rather than 23.1%.

It’s important to note that many people alive today have more ROH than Charles II had. Any criticism of someone based purely on ROH amount could be taken as insulting to anyone else with a high ROH amount, none of whom had any control over what their ancestors did. If you were to direct criticism, it should be towards the ancestors, although giving the person with high ROH would be a much better use of your time. Also, it isn’t solely ROH that determines whether or not a person will have health problems. Some people with much higher levels of ROH are healthy. Obviously, repeated and prolonged intermarriage such as that in Charles’ tree often has an effect on the descendants’ health. And it should go without saying that, like with ROH, a person should never be criticized for their health problems.

Moving on from ROH, let’s see how much DNA Charles II would have shared with his parents and grandparents.

Table 2. Percentage of DNA that Charles II of Spain would have shared with his parents and grandparents. The mean values and the 99% confidence intervals are included.

Charles II would have shared much more DNA with his parents and grandparents than most  people. Parents and children normally share exactly 50% of their DNA with no range in possible values. Grandparents and grandchildren normally share about 25% DNA, but it’s the relationship type that has by far the most variation as a proportion of the average. The expected value of DNA that Charles would have shared with his grandmothers is substantially higher than the maximum values that could be shared without intermarriage. And the percentage he likely would have shared with his grandfathers is very near to the maximum value that one would see out of 500,000 grandparent/grandchild pairs when no intermarriage is involved.

Recent intermarriage matters far more than distant intermarriage. Typically, the most recent few generations of a tree explain the vast majority of the effects seen in DNA. However, the case of Charles II is a bit different. It’s clear that ~12.5 percentage points of his ROH would have come from the uncle/niece relationship of his parents. If one were to re-calculate his ROH assuming that his four grandparents were not related to each other, the expected value is still 12.5%. Re-calculating his ROH assuming that his five (yes, only five rather than eight) great-grandparents weren’t related to each other only adds one more case of intermarriage two generations back—that of Maria Anna of Spain and Ferdinand III being 1st cousins. This only adds about three percentage points to his ROH. Five more percentage points of ROH must come from the drastic pedigree collapse that happens four generations back and further, which is a lot of ROH for that genetic distance.

It may be that the Habsburgs shared even more DNA that I report here. Judging by the intermarriage we can see in Figure 1, it’s hard to imagine that there aren’t additional relationships not shown. For example, there was likely some recent intermarriage in the tree of at least  one of the following: Isabella of Portugal, Anna of Bohemia and Hungary, Albert V, Christian II, or Francis I. And we didn’t need to create a tree of 3,000 Habsburgs—even with a much smaller tree we find that that study slightly underestimated the expected value of ROH for Charles II.

The averages and ranges shared between other relatives could easily be calculated, for example between Charles II and his half-brother, or between any other people in the tree compared to each other rather than to Charles II.

The important thing to note, though, is that we shouldn’t delight in the condition of Charles II. There are people alive today who have much more ROH in their DNA than Charles did. Reacting with exclamations of your distaste or with GIFs isn’t what they need. It actually deters some people from even trying to seek help, which they usually need in order to solve their family mysteries. There’s no need to join the conversation unless you’re ready to listen and help a person with what they need.

Feel free to ask me about modeling & simulation, genetic genealogy, or genealogical research. And make sure to check out these ranges of shared DNA percentages or shared centiMorgans, which are the only published values that match peer-reviewed standard deviations. That model was also used to make a very accurate relationship prediction tool. Or, try a calculator that lets you find the amount of an ancestor’s DNA you have when combining multiple kits. I also have some older articles that are only on Medium.