## Being descended from Confucius

A couple of days ago, Victor Mair wrote about some provocative behavior on the part of "Kŏng Qìngdōng 孔庆东, associate professor in the Chinese Department at Peking University, who also just happens to be the 73rd generation descendant of Confucius (Kǒng Fūzǐ 孔夫子 ; Kǒng Qiū 孔丘), or at least he claims to be a descendant of Confucius."

In the comments, Victor names someone else who he believes to be a true descendant of Confucius, and notes that there is some doubt about Kŏng Qìngdōng's claim to this status.

Well, I'd like to come to Kŏng Qìngdōng's defense, at least on the specific and limited question of whether he is descended from Confucius. My standing to make this argument is based on the fact that I too am descended from Confucius. And I can prove it mathematically.

The basic argument was first made by Joseph Chang, in his 1999 paper  "Recent  common  ancestors  of all present-day individuals", Advances in Applied Probability, 1999:

Previous study of the time to a common ancestor of all present-day individuals has focused on models in which each individual has just one parent in the previous generation. For example, 'mitochondrial Eve' is the most recent common ancestor (MRCA) when ancestryi s defined only through maternall ines. In the standard Wright-Fisher model with population size n, the expected number of generations to the MRCA is about 2n, and the standard deviation of this time is also of order n. Here we study a two-parent analog of the Wright-Fisher model that defines ancestry using both parents. In this model, if the population size n is large, the number of generations, Tn, back to a MRCA has a distribution that is concentrated around lg n (where Ig denotes base-2 logarithm), in the sense that the ratio Tn / (lg n) converges in probability to 1 as n → ∞. Also, continuing to trace back further into the past, at about 1.77 lg n generations before the present, all partial ancestry of the current population ends, in the following sense: with high probability for large n, in each generation at least 1.77 Ig n generations before the present, all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.

In other words, there is a date in the past such that at that time and before, the human population can be divided into two groups: those who have no current descendants and those who have all currently-living people as descendants. For people living at or before that time, if they are the ancestor of any modern humans, then they are the ancestor of all of us.

How long ago is that threshold time? Well, Chang's 1999 paper shows that in a model with random mating,

in each generation at least 1.77 lg n generations before the present, all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.

where n is the effective population size.

And according to Jack Fenner, "Cross-cultural estimation of the human generation interval for use in genetics-based population divergence studies", American Journal of Physical Anthropology 128(2) 2005, tells us that

… absent of other information regarding ancient reproductive behavior, values of 25, 28, and 31 years should be used for the female, overall, and male generation intervals, respectively, for those studies in which a speciﬁc generation interval value (rather than a range of years) is appropriate.

Wikipedia tells us that Confucius lived between 551 and 479 B.C., and that his first child was born when he was 20, in 531. 2012+531 = 2543 years ago. And 2543/28 = 91 generations ago.

According to Chang's formula, 91 generations would guarantee full mixing in a population of 2^(91/1.77) = 2^54.4 = 1.93*10^16 = 19.3 quadrillion, which is many times the current population of the world, much less its population over the past 2500 years. Specifically, it's about 2.8 million times the current world population — this seems like plenty of headroom to allow for geographical and cultural barriers to mating.

But is it? I have to confess that Confucius and I are a slightly marginal case for a more realistic version of this argument. A more elaborate and realistic version is exactly the goal of Douglas Rohde, Steve Olson & Joseph Chang, "Modelling the recent common ancestry of all living humans", Nature 431, 2004. They did a variety of calculations or simulations based on models with a simplified but realistic geographic distribution of population over time, with conservative assumptions about migration, exogamy, and so on; they explicitly modeled overlapping generations and the production of offspring at different times in the life cycle; and in general they tried hard to construct a concrete and realistic model of the statistics of human descent on earth over the past few millennia.

These elaborations don't affect the main point — it remains true that

… there was a threshold, let us say Un generations ago, before which ancestry of the present-day population was an all or nothing affair. That is, each individual living at least Un generations ago was either a common ancestor of all of today's humans or an ancestor of no human alive today. Thus, among all individuals living at least Un generations ago, each present-day human has exactly the same set of ancestors. We refer to this point in time as the identical ancestors (IA) point.

And more quantitatively:

With 5% of individuals migrating out of their home town, 0.05% migrating out of their home country, and 95% of port users born in the country from which the port emanates, the simulations produce a mean MRCA [Most Recent Common Ancester] date of 1,415 bc and a mean IA date of 5,353 bc. Interestingly, the MRCAs are nearly always found in eastern Asia. This is due to the proximity of this region to both Eurasia and either the remote Pacific islands or the Americas, allowing the MRCA's descendants to reach a few major world regions in a relatively short time.

Arguably, this simulation is far too conservative, especially given its prediction that, even in densely populated Eurasia, only 55.3 people will leave each country per generation in ad 1500. If the migration rate among towns is increased to 20%, the local port users are reduced to 80%, and the migration rates between countries and continents are scaled up by factors of 5 and 10, respectively, the mean MRCA date is as recent as ad 55 and the mean IA date is 2,158 bc.

Even under the second of these scenarios, Confucius lived about 1500 years too recently to be a Universal Ancestor of all contemporary humans. But I would submit that he's more rather likely to be among MY ancestors, since some of them lived in Anatolia and in the Crimea, much more accessible to East Asia than (say) the Amazon basin is. And as for Prof. Kŏng Qìngdōng, his case is surely an easy one. Within China, there's been more than enough mixing to ensure that by now, if anyone is a descendent of Confucius, everyone is.

When Chang's result was first published, I explained it to an anthropologist friend, who refused to believe it, raising the obvious objections about assortative mating, geographical barriers, and so on. So I coded up a simulation, much simpler and less realistic than the ones done by Rohde et al., but still having a hierarchy of population groups, with parameters to control the probabilities of mating outside one's native group at each level, the probability of migrations of different sizes and distances, etc. I got my skeptical friend to suggest numbers for these parameters. Like Rohde et al., we found that such additions had no effect on the qualitative conclusion, and remarkably little effect on the quantitative results.

On the basis of that experience, I'd be willing to bet a substantial sum that a realistic simulation of Chinese mating behavior over the past couple of millennia would prove the result that if anyone within that population is now descended from Confucius, then everyone is.

For those of you who still find these results hard to believe, it may help to keep in mind two things:

(1) This is about two-parent lines of descent. Single-sex lines of descent (as in the Mitochondrial Eve scenario and so on) work differently.

(2) This is about genealogy, not about genetics. For autosomal genes, each individual gets half at random from each parent, and so you can expect to inherit G/(2^n) genes with an ancestor n generations ago, where G is the total number of genes. The current best guess for G seems to be about 25,000. Thus someone who is a 73rd-generation descendent of Confucius can expect to inherit 25000/2^73 of the sage's genes.

25000/2^73 = 2.646978e-18

So such a person has about 3 chances in a quintillion of having inherited a single gene from their illustrious ancestor.

An entertaining summary of similar work for a popular audience can be found in Susanna C. Manrubia, Bernard H. Derrida and Damián H. Zanette, "Genealogy in the Era of Genomics: Models of cultural and family traits reveal human homogeneity and stand conventional beliefs about ancestry on their head", American Scientist 91(2) 2003. Their conclusion:

The next time you hear someone boasting of being descended from royalty, take heart: There is a very good probability that you have noble ancestors too. The rapid mixing of genealogical branches, within only a few tens of generations, almost guarantees it. The real doubt is how much "royal blood" your friend (or you) still carry in your genes. Genealogy does not mean genes.

1. ### Steve F said,

February 9, 2012 @ 6:26 am

This cropped up on an edition of QI where Stephen Fry pointed out that the whole panel – and all Europeans – are descended from Charlemagne. Link here

February 9, 2012 @ 6:30 am

My mother's family are Welsh, and my old gran used to tell me that I was 'lineally descended from Owain Glendŵr' and therefore rightful king of the British Isles. I always took this as standard grandparent-style hyperbole; the more so as, since growing up, I've rarely met a Welsh person who doesn't claim the same thing. But maybe it's both true and wholly unremarkable!

3. ### Paul McCabe said,

February 9, 2012 @ 7:43 am

I'd love to have a play with that simulation – do you still have the code? (that you'd be willing to share?)

[(myl) Unfortunately, this was 10 years ago, which is like a century in computer years, and at this point it would be easier to re-write the program than to find it. But a simple simulation of that kind is not hard. Each generation consists of a set of (male and female) individuals, organized into communities (call them "villages") with some distribution of sizes, scattered in a 2-D space (and with further hierarchies of structure if you like). In each generation, an appropriate fraction of the females produce an appropriate number of offspring, choosing mates (call them "fathers" according to some stochastic algorithms (say, most likely to choose someone from the same village, with more distant choices exponentially less likely; you can enforce partial monogamy if you want; you can assign a distribution of relative attractiveness to potential mates; it's all in the mate-selection function. For the next generation, the (male or female) offspring stay where they're born, except that villages split with some probability; when a "village" splits, one of the results moves some random distance in some random direction, according to whatever scheme you want to impose. For each of the original "people" (or for a sample if you don't have enough memory or patience), you need to keep a bit vector representing his or her descendents in the new generation. Then you repeat the process, discarding the intermediate results if you want. Continue until all the decendance vectors are either all ones or all zeros; or retain some other summary statistics over the iterations. It winds up being a couple of pages of code in C, or whatever language you use…]

4. ### J.W. Brewer said,

February 9, 2012 @ 8:08 am

I could be wrong, but my impression is that the claim here (associated with the family name "Kong" and the general patrilineal tendencies of Chinese culture) is that the fellow is a direct male-line descendant of Confucius. Whatever the mathematical modeling of the most recent common male-line ancestor of all currently living humans may be ("y-chromosomal Adam"), it's a lot further back.

5. ### Victor Mair said,

February 9, 2012 @ 8:11 am

@J. W. Brewer

To which fellow are you referring, Kong Qingdong or Kong Decheng?

6. ### J.W. Brewer said,

February 9, 2012 @ 8:28 am

Prof Mair: I am happy to be corrected by someone like you with actual knowledge, but my impression is that Kŏng Qìngdōng is claimed to be a direct male-line descendant (a reputed status said by wikipedia to be shared by several million Han Chinese, but still less than 1% of the ethnic group), but that others dispute this claim. This status would seem very loosely analogous to being a cohen among the Jews or a sayyid among Arabs/Muslims. I suppose in those communities as well there must from time to time be false claims by people interested in some perceived incremental boost in social status (without even getting into the situation of the grandchildren etc. of false claimants who have no reason to know their inherited claim is inaccurate).

7. ### Kathleen said,

February 9, 2012 @ 8:36 am

I may be confused. I have no problem with the overall argument, but it seems to me there would have to be exceptions in the case of groups whose ancestors migrated out of Africa/Eurasia long before any of the dates mentioned. I thought immediately of American Indians. If current estimates are right, their ancestors crossed the Bering Strait at least 15,000 years ago, and possibly as far back as 30,000 years ago.

Now, it is obvious that between 1492 and the present, there has been significant mixing of peoples in America. But surely there must still be some people who are of entirely Native descent? If so, I don't see how they could have ancestors from Eurasia who lived about 5000 BC. Am I missing something, or are does this model suggest that all Native Americans (given 500 years of contact) also have European and/or African ancestry?

[(myl) In essence, yes. Note that it doesn't take much. If just one member of group A leaves just one child in group B, we just have to wait until that child's lineage either dies out or becomes universal, in order for group B to share all of group A's universal ancestors. In a small population, that doesn't take very many generations. And generally a majority of the population at any given point ends up being a universal ancestor.]

8. ### linda seebach said,

February 9, 2012 @ 8:57 am

I don't quite understand how to square this with the finding that populations outside Africa have a small percentage of Neanderthal genes (and some have Denisovan, too) but Africans do not. That would put the IA point well before the emergence of Homo sapiens, wouldn't it? In which case, the result may indeed be true but unremarkable.

[(myl) No; because this is about geneology, not genetics.]

9. ### Tim Silverman said,

February 9, 2012 @ 9:23 am

Thus someone who is a 73rd-generation descendent of Confucius can expect to inherit 25000/2^73 of the sage's genes.

25000/2^73 = 2.646978e-18

So such a person has about 3 chances in a quintillion of having inherited a single gene from their illustrious ancestor.

But wouldn't they inherit Confucius' genes through multiple routes? Otherwise, you could apply the same argument to everybody in the world alive at the same time as Confucius, and, since the population at that time was very much less than 1018, conclude that nobody has inherited any genes from the ancestral population?

10. ### Vicki said,

February 9, 2012 @ 9:43 am

Is there good evidence that any of us are descended from Confucius? Yes, he had a child. Did that child have children, and so on? My mother has two children; at this point it seems unlikely that she will have any grandchildren.

Linda–

The claims about Neanderthal and Denisovan genes are consistent with this, if the most recent common ancestor didn't happen to pass down any of their Neanderthal or Denisovan genes to most of their descendants. As the article notes, the chances of inheriting a specific gene from Confucius, or any other ancestor that far back, is slim.

11. ### Brett said,

February 9, 2012 @ 9:52 am

@J.W. Brewer: I think I remember reading about a study of cohanim genetics, which concluded that about half of Israeli men who claimed to be cohanim actually shared a common Y chromosome. So it would seem that over more than two millennia, there has been a substantial but not overwhelming insertion into the group of people who do not belong to the same male line of descent.

My wife has actually suggested that I should get tested, to see whether my own family's cohanim heritage is real. However, the prospect makes me uncomfortable, even though I don't take the religious aspects of my Jewish heritage seriously at all. It makes me wonder how people from China would feel if their claimed descent from Confucius were questioned.

12. ### HP said,

February 9, 2012 @ 10:23 am

@ Linda Seebach: John Hawks (one of the Neanderthal genome researchers) just put up a data-rich post on the distribution of Neanderthal alleles in modern human populations, including sub-Saharan Africans. tl;dr: It's always more complicated than the press release.

The Onion chimes in: 7 Million People Direct Descendent of Single Smooth-Talking Ancestor.

13. ### Terry Collmann said,

February 9, 2012 @ 10:31 am

Clearly, with that degree of dilution, it's "homeopathic" descent. You may not have any of Confucius' genes, but you have a memory of him in your water.

14. ### Jerry Friedman said,

February 9, 2012 @ 11:07 am

@Adam Roberts: As I understand "lineally descended", it means descended in the male line through oldest surviving sons (or branches of the family), that is, your grandmother was claiming that you were the rightful heir to Owain Glendŵr.

Without doing a calculation, I could easily believe that all people of Welsh ethnicity are descended from him one way or another.

15. ### J.W. Brewer said,

February 9, 2012 @ 11:42 am

Well, the distinctive thing about male-line descent for males (which I find fascinating because obviously the genetics weren't understood in the prior ages when patrilineality became an organizing principle for many although not all human societies), is that I do have (with whatever accumulated mutations etc.) the same y-chromosome as my n-greats-grandfather in the male line even if the odds are well below 50/50 that any of my other chromosomes-as-such were possessed by any other randomly-chosen ancestor from that generation. (It should be noted, however, that the inference you might have from 10th-grade biology that once you go far enough back that you have >46 ancestors-per-generation you must have at least some ancestors whose genes you have not inherited is oversimplified, because of chromosomal crossover a/k/a homologous recombination during the meiosis that produces gametes.) The kohanim research shows, if nothing else, that reputed paternity is not 100% equal to genetic paternity and that even low-frequency incidence of phenomena like cuckoldry or hushed-up adoptions can have significant cumulative effects over enough generations.

But it is not implausible that a high percentage of reputed male-line descendants of Confucius may share a y-chromosome just as with the reputed male-line descendants of Aaron. Someone did a study fairly recently about the far-flung locations in which the y-chromosome strongly associated with reputed male-line descent from Genghis Khan had turned up, including (if memory serves) in a mild-mannered CPA in Florida who had neither any visible phenotypic hint nor any family tradition of Mongol ancestry.

16. ### Jerry Friedman said,

February 9, 2012 @ 11:49 am

@MYL: I think a factor is missing from your estimate of the probably that Kong Decheng and Kong Qingdong have one of Confucius' genes. Aren't they very likely to be descended from him by more than one route?

[(myl) Of course — as I understand things, there are lots of highly conserved genes that everyone in China and indeed everyone in the whole world shares. But for the relevant sense of "inherit" to mean anything, we'd want to believe that some particular gene was actually transferred from parent to child down through the generations in a direct line from Confucius to whomever. Otherwise it would be like me saying "I have this bead that I inherited from Confucius", and then someone objecting "Um, wait, you bought that last week from a store that got it from a factory in Ireland that made it last year", and then me responding, "OK, sure, but Confucius had one just like it…"]

It seems to me that a first cut at this probability would be to estimate the Han Chinese population at Confucius' time. (If we give any weight to the tradition that he does have living descendants, we would use a smaller number.) The reciprocal of that number would approximate the probability that a given gene in a Han person came from Confucius. Then we can easily calculate the probability that at least one of the 20,000–30,000 genes came from him.

Taking 1,000,000 as a SWAG for the population in Confucius' time and 25,000 for the number of genes, I get a bit less than a 2.5% chance, and taking 10,000,000 I get a bit less than a .25% chance. Hm, that probably should have been obvious.

As far as descent in the male line goes, I went to a talk by a population geneticist about 20 years ago in which, as I recall, he said the rate of non-paternity (the biological father isn't the stated father) is about 5% in all studied human populations, regardless of culture. This casts some doubt on claims to be the 70-some-generation descendant of someone in the male line.

[(myl) I've heard an estimate, supposedly based on DNA testing, of 15%. I suspect that this is an exaggeration, but it wouldn't surprise me to learn that it's more than 5%. In any case, you're right: 0.95^73 is about two chances in a hundred of an unbroken real sequence; 0.85^73 is about 6 chances in a million.]

(On a related subject, the Wikipedia article on Owain Glyndŵr says all his legitimate sons died without issue, but he also had acknowledged illegitimate sons. This would affect a hypothetical claim to the British throne, I suppose, but it's still not non-paternity as long as he really was the father of those illegitimate children.)

17. ### Jerry Friedman said,

February 9, 2012 @ 11:58 am

Actually, my estimates are overestimates, since the whole point of this is that modern Chinese people are also descended from contemporaries of Confucius who lived in what are now Portugal and South Africa. But I think my estimates are closer than anything in the 1E-17 range.

18. ### Are we all descended from Confucius? « God plays dice said,

February 9, 2012 @ 12:37 pm

[…] Mark Liberman at Language Log asks this question, spurred by a Chinese professor's claim to be a 73rd-generation descendant of Confucius. His conclusion: well, yeah, but if anyone in China is descended from Confucius (and this is documented), probably everyone in China is. Given a long enough time this would be true with "China" replaced by "the world", but it probably hasn't been long enough. Share this:TwitterFacebookLike this:LikeBe the first to like this post. Categories Uncategorized […]

19. ### Jerry Friedman said,

February 9, 2012 @ 1:50 pm

@myl: Maybe I was unclear. I am talking about direct descent (that being the only kind). If Confucius is indeed an ancestor of all modern Han Chinese, which seems likely as you demonstrated, both of a modern Han person's parents would presumably descend from Confucius, all four of the person's grandparents would, and so on for some generations. This greatly increases the probability that the person has inherited one of Confucius' genes.

To put it another way, your estimate of three chances in a quintillion would be right only if a living person had 300 quadrillion different ancestors 73 generations ago. Of course the real number of different ancestors then can't be over some millions.

[(myl) Yes, OK, you're completely right that the likely existence of multiple lines of descent increases the probability substantially.. But let's also agree that the mere fact that someone is your ancestor (in the sense that there's at least one sequence of parent-child links between them and you) tells us essentially nothing about what or how many genes you share with them, at least once there's more than a couple of dozen generations involved.]

(One thing I'm leaving out is the possibility of recombination within a gene, which I'm not going to try to estimate right now. But it seems even more likely that modern Han people have at least part of a gene that they inherited from Confucius.)

By the way, my colleague who teaches human evolution just happened by. She strongly recommended John Hawks' blog, already mentioned by linda seebach.

Even more by the way, a problem almost as important as descent from Confucius is raised by Legolas's comment, "…is he not of the children of Lúthien? Never shall that line fail, though the years may lengthen beyond count." I've discussed this on the Net, taking the side that pretty much all living people would be descended from her, and Legolas's prediction would have been very conservative. However, he may have meant the male line. One thing is for sure: nobody has inherited his Y chromosome from Lúthien.

20. ### Trond Engen said,

February 9, 2012 @ 3:39 pm

@Jerry: You're probably long past this now, but the cumulative migration effect (using Mark's initial configuration) since the days of Confucion would be mN = m1^N = 0,9995^91 = 0,956 . Hardly enough to change your estimate. This reduced number would even be on the conservative side, since it ignores feedback effects from migration. But clearly it won't matter either way against the expected mis-estimates of the migration factor and the number of generations.

21. ### Victor Mair said,

February 9, 2012 @ 3:40 pm

from Richard Villems

The abstract formulas of genetics are of course rather simple, but I cannot find them of any use for any concrete problem. Rather than to argue that "shared ancestry" means millions of different tiny pieces of autosomal DNA shared in between any extant pair of persons (not very informative to my mind), it is much more productive to discuss, in this context, haploid genomes. It is highly likely that Confucius carried one of the typical for East Eurasia hg M mtDNA. Its split from largely West Eurasian hg R mtDNAs is anything around 50 – 60 kiloyears ago. Straightforward and unambiguous – I share matrilineal ancestry with Confucius at the level of macro-haplogroup L3 and the MRCA of L3 is perhaps 60 – 70 KY old – divided to 25 will give 2,400 generations ago.

22. ### Trond Engen said,

February 9, 2012 @ 3:41 pm

Heh! The subscripts worked in the preview, but not in the published comment.

23. ### Jerry Friedman said,

February 9, 2012 @ 7:28 pm

@myl: Thanks for your comment. I definitely agree that having gotten an unknown fraction that might be around a millionth of your DNA from someone, or even your whole Y chromosome, doesn't tell you anything.

@Trond: In fact, I didn't see that calculation (which may actually overestimate the migration effect, since it estimates emigration from China, but immigration from the less densely populated surrounding regions may well have been less). Thanks for pointing it out. Certainly I should have seen that the uncertainty due to migration is far less than others in my estimate. (Though I did eventually observe based on Kong Qingdong's picture that he probably has a great deal of East Asian ancestry :-)

@HP: Sorry, I see you were the one who mentioned John Hawks.

24. ### Steve Morrison said,

February 9, 2012 @ 8:50 pm

@Jerry Friedman: Some of the kings of Númenor lacked male heirs, and one Ruling Queen had no children at all. Since the first king was Lúthien's great-grandson Elros, it's hard to see what the "Never shall that line fail" statement means unless it refers to all descendants, in which case it's pretty trivial. I've discussed this on the Internet (and Usenet) myself, and no one has ever found a good answer.

25. ### Brett said,

February 9, 2012 @ 9:50 pm

@Steve Morrison & Jerry Friedman: I also had wondered about that line from Legolas. I don't think it's possible to discern what the speaker was really thinking, but the line does play a dramatic role. The question of who is entitled to claim descent in various lineages is a recurring theme in The Lord of the Rings and in the back story. This includes questions of whether female lines of descent are as important as male ones

26. ### Jerry Friedman said,

February 10, 2012 @ 2:08 pm

@Steve Morrison and Brett: I had indeed forgotten about Elwing, the Ruling Queens, and the dispute with Arvedui. Since we're doing genealogical geekiness (or I am), it's actually possible that Aragorn is descended from Elros in the male line, through some cadet branch of the family that was passed over in favor of the first Ruling Queen.

Also, I suppose one could take Legolas as prophesying that Sauron wouldn't win the war and exterminate all the descendants of Lúthien.

The further questions this raises would probably be better discussed elsewhere. (Allowing for the possibility that the same is true for the questions I've already raised.)

27. ### SimonMH said,

February 11, 2012 @ 11:36 am

@ Tolkien fans. The genealogy is not consistent, but we can forgive a few slips for dramatic effect. Gimli's "Till now I have hewn naught but wood since I left Moria" at Helm's Deep is untrue, but would you want to change the line?

28. ### Steve Morrison said,

February 11, 2012 @ 3:59 pm

@Jerry Friedman, Brett: We could perhaps take it to rec.arts.books.tolkien ?

29. ### Jerry Friedman said,

February 12, 2012 @ 12:40 pm

@Steve Morrison: rec.arts.books.tolkien works for me.

30. ### Steve Morrison said,

February 13, 2012 @ 3:06 pm

I've started the thread on Usenet now. For anyone who lacks newsgroup access, it can be followed at Google Groups and anyone with a Google account can use it to post as well. Sorry for the delay; I've had some troubles with a changeover to a new OS.