## Ancestors

The most recent xkcd:

The business about eventually being either "an ancestor to all living humans, or none of them" might have been brought to mind by Adam Rutherford, "So you're related to Charlemagne? You and every other living European…", The Guardian, 5/24/2015.

But it's true, and as discussed in "Being descended from Confucius", 2/9/2012, the basic idea goes back to Joseph Chang,  "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 ancestry is defined only through maternal lines. 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.

A more elaborate and quantitatively realistic version of this model is explored in Douglas Rohde, Steve Olson & Joseph Chang, "Modelling the recent common ancestry of all living humans", Nature 2004. And the wording of the interviewee's "greatest strength" in panel of the xkcd strip suggests that Randall Munroe has read and remembers Chang's work.

Rutherford's Guardian article cites only Ewen Callaway, "Most Europeans share recent ancestors", Nature News 5/7/2013, which in turns summarizes (without linking or even giving a title! For shame, Nature!) Peter Ralph and Graham Coop, "The Geography of Recent Genetic Ancestry across Europe", PLoS Biology 2013. Ralph and Coop base their estimates on parameters derived from population genomic datasets, and cite the statistical modeling work of Chang et al.

## 12 Comments

1. ### Keith said,

July 3, 2015 @ 7:19 am

It seems to me that the statement [m]ost Europeans share recent ancestors depends entirely on the value of "recent".

K.

2. ### AndrewD said,

July 3, 2015 @ 9:47 am

"Rutherford's Gurdian article…"
Is this an oblique reference to a certain British newspapers reputation for Typo's?

[(myl) No, that would be "Grauniad" — this was just a slip of the fingers…]

3. ### Eric P Smith said,

July 3, 2015 @ 11:32 am

What bothers me is that there may soon come a day when I am an ancestor to all living humans and to none.

4. ### January First-of-May said,

July 3, 2015 @ 12:20 pm

A commonly mentioned corollary to the "either all or none" claim (and similar discussions) is that, if the figure in question still had descendants two or three generations later, then almost certainly the answer will be "all". However, there are still known cases where a person's descendants didn't die out until even later.
I won't list all the examples I know (there are some quite prominent ones, such as Abraham Lincoln and Sophia Palaiologina), just the most ridiculous one I've ever encountered: Charles de Gondi died in 1596. His last surviving descendant was, apparently, his great-great-great-great-great-great-granddaughter, Joana Bernarda de Sousa Lancastre e Noronha, who died in 1827.

Incidentally, a fairly similar argument comes up a lot in Harry Potter fics regarding the "heir of Slytherin" – that is to say, that given that Salazar Slytherin (ca. 10th century) still had surviving descendants in the 20th century (the Gaunt family), it was likely that a lot more people were descended from him than known officially (though, for obvious reasons, most of such people would probably have been non-magical).

5. ### Q. Pheevr said,

July 3, 2015 @ 12:26 pm

I'm already an ancestor to no living humans, unless the ancestor-of relation is reflexive. (Note to self: Check Higginbotham (1983).)

6. ### Eric P Smith said,

July 3, 2015 @ 1:08 pm

Any decent mathematician will define ancestor-of to be reflexive. Sorry, you'll have to wait a bit longer.
(Couldn't resist that: no offence intended!)

7. ### D.O. said,

July 3, 2015 @ 2:07 pm

Re: Charles de Gondi. I don't know the fella and his kin (never even heard of him before now), but some people tend to have sometimes children they are not ready to acknowledge. And as for the children themselves they have to be really wise to know their male ancestry.

8. ### Rubrick said,

July 3, 2015 @ 4:52 pm

Munroe's source could also have been Dawkins (The Ancestor's Tale, I believe).

In any case, thanks for covering this despite the lack of an obvious linguistic angle (other than similar techniques being used in historical linguistics). I love this stuff.

9. ### Viseguy said,

July 3, 2015 @ 11:21 pm

Just spent the last 10 minutes trying to figure out if Ig denotes base-2 logarithm, what lg n denotes. There's something to be said for serif fonts, or eyes with long arms.

10. ### MikeA said,

July 4, 2015 @ 12:45 am

What I'd like to know is which of the dozen or more candidates for U.S. president are descended from John Lackland, so I can get my bets down.

11. ### J. Goard said,

July 4, 2015 @ 1:18 am

Being an ancestor to all living humans sure sounds like a lot more when you don't appreciate your contribution diluting toward zero. Perhaps you ought rather to consider the average fraction of "you" that future people will be!

12. ### January First-of-May said,

July 4, 2015 @ 9:26 am

@D.O.:
Charles de Gondi isn't particularly important himself, but the line of his wife, Antoinette d'Orleans, was supposed to inherit the Principality of Neuchatel (and the Duchy of Estouteville, but the problem with that one was more a question of weird inheritance laws).
So, since that line died out in 1827, the claims passed to the descendants of Antoinette's younger sister Eleonore – by then the rulers of Monaco – who happened, in fact, to already have the Duchy claim anyway (while the Principality passed, back in the 1700s, to a very distant relative from a completely different line, apparently by popular opinion).
And yes, the sources are careful to state "no legitimate descendants", but best I can figure out, there are no known illegitimate descendants either.
That said, IIRC, basically the situation you described came up in the Lincoln case, so it's not that unlikely (of course, since nobody actually cared about the nonexistent Neuchatel claim, and in any case the 1820s didn't have the technology, we'll probably never know).

@MikeA:
If you didn't quite catch it from the article above: the answer is, probably all of them (as well as Barack Obama).
I don't recall if there are any African-Americans in the running; if there are, chances are they probably still have the descent (from master-slave relations if nothing else), but might not be able to trace it directly. (Apparently there are some white candidates who don't have a known traceable descent either.)
Reitweisner made a fairly complete listing of the 2008 candidates; some of these would still be active today.