Conundrum: The Math of Khan
When I first started this blog, one of my very first posts suggested that almost all of the current natives of Mongolia and China were probably descendants of Genghis Khan. I literally had no readers at the time – I hadn’t yet told anyone about the blog – and so there was nobody to challenge my sweeping statement. I didn’t even make an argument. I’d like to give my argument now, and reopen the question as a Conundrum.
The idea was based on a National Geographic article about the biological legacy of Genghis Khan:
An international group of geneticists studying Y-chromosome data have found that nearly 8 percent of the men living in the region of the former Mongol empire carry y-chromosomes that are nearly identical. That translates to 0.5 percent of the male population in the world, or roughly 16 million descendants living today.
I went on to note:
16 million descendants. And that’s only men descended from Khan directly through the male line, father to son, for the past 800 years. The total number of Khan’s descendants living today is truly incalculable.
If you figure an average of four generations per century, that’s 32 generations between Genghis and his living descendants. Each person living today should have around 2 to the power of 32, or roughly 4.3 billion, living ancestors that are contemporary with Khan. Obviously, many individuals will have to be counted more than once, so let’s take a different tack.
Let’s pick a year somewhere between 1200 and 2000, say 1500. The total population of mainland Asia in 1500 was 268,400,000. Each living person today would have approximately 2 to the power of 20, or about a million, ancestors who were around in 1500 (and that’s if we don’t count anyone with a living parent).
So how many of the 268,400,000 around in 1500 were Khan’s descendants? Well, there are 16 million men living today that share the Y chomosome. If Khan and his direct male heirs had an average of 1.68 sons over 32 generations, that would give us our 16 million. That would only account for 505 men carrying that Y chromosome in 1500. But that calcuation leaves out two factors.
First, by 1500, Khan’s seed had been pretty well spread. The factors that account for his prevalence today came mostly into play during Khan’s life and the few generations following (see the article for details). So the distribution was a lot more top-heavy than the calculation above would suggest.
Second, we’re only counting direct male-line heirs. Passing a Y chromosome down from father to son over 32 generations is only one of 4.3 billion different permutations of inheritance. Each of those 16 million Y chromosome carriers alive today probably has an average of at least one sister or daughter. That doubles the known descendants right there. Extend that back over 32 generations, then consider all of their descendants, and you get the idea. If we change “average of 1.68 sons over 32 generations” (which we know is true) to “average of 2 children of either sex over 32 generations” (which doesn’t seem like too great of a leap from there), then 16 million becomes 4.3 billion, greater than the population of mainland Asia today.
It seems to me that today’s ethnic Mongolians and Chinese would almost all have to be descended from Khan, some many times over.
Now I am no math expert. I’m a Shakespeare Teacher. It’s very possible I could be wrong about this. I’d be interested to hear what other people think, particularly people with more professional experience with statistical analysis.
And I should also point out that I pin no political, moral, or judgmental significance to being a descendant of Genghis Khan. This is simply a math, history, and logistical Conundrum. I truly hope no offense is taken (though if you read my original post and the Economist article it is based on, it actually seems to be a point of pride for both Mongolia and China to be the descendants of Khan). And my family comes from Belarus, so this would mean I’m probably a descendant of Khan as well. So don’t screw with me.
Now, with all that in mind, for this week’s Conundrum, I hereby submit my original conclusion up for public scrutiny:
So, China and Mongolia should probably stop arguing over which of their people are the true heirs of Genghis Khan. My guess is, almost all of them are.
May 18th, 2009 at 5:43 pm
Did you take into account that the Mongol Empire and G.K.’s family took residence across Eurasia, including most of the Middle East and a large part of Eastern Europe? You mentioned Belarus, but did your posted calculations go beyond modern-day China and Mongolia? Many or most of the descendants are outside those areas…
-Signed, a 100% non-Genghis-Khan descendant
May 18th, 2009 at 6:04 pm
My calculations do not go beyond the geographical region of the Mongol Empire because I have no such data. The numbers are based only on the 16 million people in Asia that were part of the study. So my conclusions center on Asia as well.
But you make a good point. World-wide there are probably more people descended from Khan, maybe even some who are 100% sure they are not.
May 27th, 2009 at 11:40 am
Ha, ha–sorry to continue to dredge up your old post with a tangent, but I just note that my family has been quite boring in their centuries of homogeneity and insularity. However, my generation has broken out and married central Europeans (Catholics! Oh my!) and some of us escaped the area in PA where most of our ancestors have lived for 200+ years (add 200 more before that in MA for many). Interestingly, my husband’s father’s Slovak family has an oral tradition explaining why some of his older aunts have Asian-looking eyes: they say that many years ago, a group of Asians traveled to and settled in eastern Europe, and some of their ancestors were these Asians. They didn’t know the history of Genghis Khan, but how cool is that link and continued story 800 years later?
May 28th, 2009 at 6:59 am
Actually, I like it when people revive old posts with fresh ideas.
My point is this: Every human being has two biological parents, who had four parents between them, and they had eight, and so on. If you take that back to 1200, I estimate that each of us has roughly 4.3 billion ancestors, which is about ten times the population of the world at the time. This is very conservative, since several generations would be alive at the same time, which affects world population but not my ancestor estimate.
These means that the many of the ancestors you have who were alive in 1200 would be your ancestors many times over, through a variety of lines. This doesn’t mean that each of us is descended from everyone who was alive in 1200, but we need to allow some latitude.
You say that “most” of your ancestors from the past 200 years were from PA and “many” of them were from MA the 200 years before that. It seems likely they were from Europe for the 200 years before that, and then who knows for the 200 years before that? Can you really say for certain that not one of your ancestors is descended from Genghis?
Anyway, it’s just a thought experiment. I certainly don’t mean to imply anything about anyone’s family. In another thread, I cast doubt on the belief of some people that they are descended from Henry VIII, so maybe this is the flip side of that coin.
October 19th, 2009 at 6:56 am
I’m sure these calculations are fine as far as they go, but they misleading imply that Genghis Khan is something exceptional genealogically. Anyone alive at that time would have an enormous number of descendants today.
October 19th, 2009 at 7:20 am
Welcome, Peter Kauffner!
The idea that Genghis is something exceptional genealogically does not come from me, but from this study.
Actually, the study just identifies a common ancestor for a large population of Asian males, without identifying definitively who that ancestor is. But the article makes a very good case for Genghis.