In order to find the date of the most recent common ancestor (MRCA) of all the people living today, Chang started out by constructing a simple mathematical model of population mixing. (See here for some background to this post.)

He assumed that the population is constant over time at some value N. He assumed that the generations are discrete and non-overlapping (i.e. mating took place only between males and females of the same generation). He also assumed that mating was random. In words, that there was equal probability of any one male in a generation to breed with any female of that same generation.
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In 1999, Joseph T. Chang published a very interesting paper in the journal Advances in Applied Probability (vol. 31, pages 1002-1026) titled Recent Common Ancestors of all Present-Day Individuals. To understand the paper, it helps to reflect a little on the mathematics of genealogy.

One rock-solid fact of ancestry is that every person has two, and only two, biological parents. They in turn each have two parents so going back two generations gives a person four ancestors. If you go back three generations, you have eight ancestors and so on. Each generation that you go back doubles the number of ancestors in the previous generation.

We all know that this kind of geometric progression results in one reaching very large numbers very soon and by thirty generations, the number of ancestors one has acquired has ballooned to over one billion. In forty generations, we have over one trillion ancestors.

Conservatively allowing for each generation to span 30 years (which is a little large), going back thirty generations takes us back to about 1100 CE where the population was only about 300 million, and forty generations takes us back to 800 CE where the population was less than 200 million. (If we take each generation as averaging 25 years, 30 generations takes us back to 1250 CE when the population was 350 million and in forty generations we reach 1000 CE where the population was 200 million.)

Having more ancestors that the total population leads to the clear conclusion (which is not that surprising once one thinks about it) that all our ancestors cannot have been distinct individuals but were shared. In other words, my great-great-great-grandfather on my father’s side had to be the same person as my great-great-grandfather on my mother’s side, or something like that.

But the interesting point is that each one of us has over a trillion ancestors in just forty generations, which must mean that you, the reader, and I must have some shared ancestors, unless the huge population of your ancestors were entirely isolated from the huge population of my ancestors, with no mixing at all between them. Given the large numbers of ancestors involved, this kind of isolation seems highly unlikely unless there was some major geographical barrier separating the populations. We know that this is not the case, since by 1000 CE, people were able to travel pretty much all over the inhabited world, and all you need is just one person from my group of ancestors mating with one person from your group of ancestors to break the isolation, because then the ancestors of that pair are shared by both of us.

So if you and I (as just two people) share common ancestors, then we can see that if we go back far enough in time, all of us living on the world today should share at least some common ancestors. (See this post for a more rigorous argument for this.) One question that Chang was investigating was that of finding out, from among all the common ancestors, when the most recent common ancestor (MRCA) of all the people living in the world today lived.

The concept of the MRCA is interesting. My siblings and I share all our ancestors so the MRCA is not meaningful. The MRCA of my cousins and I (say) are the one set of grandparents that we have in common. As my current relatives get more distant, the MRCA goes back in time but it is not hard to see that an MRCA must exist for those who are commonly referred to as ‘blood’ relatives.

As another example, for those who take the Bible literally, definite common ancestors would be Noah and his wife. Since everyone except the two of them and their sons and their sons’ wives were killed by god in the flood, all the current inhabitants of the world should have Noah and his wife as common ancestors. But they may not be the MRCA because their sons’ descendants may also have intermarried, creating a more recent MRCA.

For those of us who accept evolution, it is not hard to get our minds around the concept of all of us having an MRCA, and the fact that we must have a shared ancestor in an earlier species has a pretty rigorous proof and is fairly easily accepted. What people thought was that this person probably existed around the time of our ancestor Homo erectus, perhaps a million years ago.

But when analysis was done on the mitochondrial DNA, and its mutation rate was used to triangulate back to the time when all the current mitochondrial DNA converged on a single individual, people were surprised that the calculations revealed that the MRCA deduced from this analysis, (nicknamed Mitochondrial Eve) lived much more recently, only about 140,000 years ago, probably in Africa. All present-day mitochondrial DNA is descended from this single individual. A similar analysis can be done for the Y chromosome to trace back to ‘Y-chromosome Adam’, and that person lived about 60,000 years ago (Richard Dawkins, The Ancestor’s Tale (2004), pages 52-55).

But as Dawkins cautions (page 54):

[I]t is important to understand that Eve and Adam are only two out of a multitude of MRCAs that we could reach if we traced our way back through different lines. They are the special-case common ancestors that we reach if we travel up the family tree from mother to mother to mother, or father to father to father respectively. But there are many, many other ways of going up the family tree: mother to father to father to mother, mother to mother to father to father, and so forth. Each of these pathways will have a different MRCA.

Our normal concept of genealogy traces back through both sexes and thus the web of ancestral pathways becomes increases tangled and complex as you go back in time. As a result there is a greater chance of my ancestral pathways intersecting with the ancestral pathways of other people. It is thus reasonable to suppose that if we look at all these pathways, we will find a more recent MRCA than Mitochondrial Eve or Y-chromosome Adam. But this kind of calculation using mutation rates is not easy to do for things other than sex-specific chromosomes like mitochondrial DNA.

In order to try and fix the date of existence of the MRCA of everyone living today using the lines through both sexes, Chang used the tools of mathematics and statistics rather than genealogical charts or DNA mutations. And he found something very surprising, to be discussed in the next posting.

POST SCRIPT: If you live in fear, the terrorists have won

Tom Tomorrow points out the absurdity of people terrorizing themselves.

While doing some research on my ancestors last month, I made the surprising discovery that I am the direct descendent of Narmer, who was the first Pharaoh of Egypt and lived around 3,100 BCE. Narmer (thought by some to be the same person as Menes) was not your run-of-the-mill pharaoh. He is a bona fide Pharaoh Hall of Famer, credited with unifying the land that became Egypt and founding the very first dynasty. Of course, given the poor nature of record keeping back in those days one can never be absolutely certain of such things, but I am 80 percent certain that he is my direct ancestor.

How do I know this? I did not do an actual genealogy chart of my ancestors. It is a curious thing but people in Sri Lanka are nowhere near as enthusiastic about tracing their ancestral roots as the people in the US. I know who my grandparents are and I know some of their siblings but that is about it. I think that may be true for most Sri Lankans. I do not recall ever having discussions with anyone in Sri Lanka where people talked about ancestors farther back than three or four generations. It was not a topic of much interest.

Contrast this with America where people are fascinated with their ancestry and go to great lengths to trace back as far as they can, even hundreds of years. It is not unusual to have a conversation in America and for people to spontaneously raise the topic of where their ancestors came from and how far back they have tracked them. And people here are very excited when they find someone in their past who is famous (or even infamous) or had a role in some major historical event or is even just mentioned in some historical document.

Since thinking about my ancestors last month, I have been pondering why there is such a marked difference in interest in the two countries and have come up with some hypotheses, although I have no idea if these explanations are valid.

One possible explanation is that tracing one’s ancestors in Sri Lanka is likely to be a fairly boring exercise with little expectation of anything exciting turning up. After all, it is a small island nation that has a recorded history of about 3,000 years. I know the village where my paternal grandfather, for example, was born and raised. If you trace back farther you will likely arrive at another person in that same village or a neighboring village. If you go back yet further, it will probably be another person in that same village or region, and so on for generation after generation. The likelihood of finding something really surprising or interesting is small. Pretty boring stuff, hardly worth putting a lot of effort into.

In the US, it is quite different. As one goes back in time, one will fairly soon reach ancestors who came from another continent or came over with the early settlers or were members of a Native American tribe. All of these are sufficiently novel and interesting facts that may make worthwhile the hard work necessary in finding one’s roots.

Another factor is the quality of the recordkeeping as you go back in time. The structure of American and European societies was such that maintaining records was desirable. The fairly early adoption of a mercantilist society, capitalism, and private property ownership meant that you had to know who owned what and, most importantly, who inherited the property when someone died. This required that careful records of births and death be kept. This record keeping was also facilitated by church records. Since churches were institutions that also performed civil functions and married people, baptized their children, and buried them when they died, church records are rich sources of genealogical information.

Countries like Sri Lanka remained feudal until later and in many such societies land was either owned by the local feudal lord or held in common by the villagers, so questions of property inheritance were not major issues. Furthermore, Buddhist and Hindu religions (which are the main religions in Sri Lanka) are much less hierarchical in organizational structure than Christianity, and I believe their clergy do not have the same dual civil/religious role that Christian clergy have when it comes to marriages. So Buddhist and Hindu temples are not repositories of marriage, birth, and death records the way that Christian churches are.

A comprehensive mercantilist and capitalist economy came much later in Sri Lanka than in (say) Europe so one is likely to run up against a genealogical blank wall much sooner there, making the search for one’s ancestors a much more frustrating task. Coupled with the fact that the long history and relatively little migratory behavior, and it is easy to see why tracking one’s ancestors is not a particularly popular endeavor.

Even with good record keeping, tracing one’s ancestors is a time-consuming task, requiring that one spend enormous amounts of time and effort in libraries and other archival institutions, poring over old records, and following many false trails.

In tracing my own ancestors, I did not do any of that laborious detective work. So how is it that by merely sitting lazily at my desk in the US in front of a computer, I could state that I am 80% confident that I, a person of Sri Lankan origin, am in a direct line from the very first pharaoh of Egypt?

That’s the story for the next posting.

POST SCRIPT: Russell’s teapot cartoon

Here is another cartoon from the creator of the blog Russell’s Teapot. His cartoons are also a weekly feature on MachinesLikeUs.

Darwin’s theory of natural selection implies that we are all descended from common ancestors. Most people who have doubts about the theory tend to think that this is a proposition that we can either choose to accept or deny. After all, no one was around to see it, were they?

But Richard Dawkins’ excellent book The Ancestor’s Tale (2004) gives a surprisingly rigorous argument (on page 39) that back in the distant past, we must have all had common ancestors. He is such a good writer, both stylish and concise, that paraphrasing him would be a waste of time and I will give you an extended quote:

If we go sufficiently far back, everybody’s ancestors are shared. All your ancestors are mine, whoever you are, and all mine are yours. Not just approximately, but literally. This is one of those truths that turns out, on reflection, to need no new evidence. We prove it by pure reason, using the mathematician’s trick of reductio ad absurdum. Take our imaginary time machine absurdly far back, say 100 million years, to an age when our ancestors resembled shrews or possums. Somewhere in the world at that ancient date, at least one of my personal ancestors must have been living, or I wouldn’t be here. Let us call this particular little mammal Henry (it happens to be a family name). We seek to prove that if Henry is my ancestor he must be yours too. Imagine, for a moment, the contrary: I am descended from Henry and you are not. For this to be so, your lineage and mine would have to have marched, side by side yet never touching, through 100 million years of evolution to the present, never interbreeding yet ending up at the same evolutionary destination – so alike that your relatives are still capable of interbreeding with mine. This reductio is clearly absurd. If Henry is my ancestor, he must be yours too. If not mine, he cannot be yours.

Without specifying how ancient is ‘sufficiently’, we have just proved that a sufficiently ancient individual with any human descendants at all must be an ancestor of the entire human race. Long-distance ancestry, of a particular group of descendants such as the human species, is an all-or-nothing affair. Moreover, it is perfectly possible that Henry is my ancestor (and necessarily yours, given that you are human enough to be reading this book) while his brother Eric is the ancestor of, say, all the surviving aadvarks. Not only is it possible. It is a remarkable fact that there must be a moment in history when there were two animals in the same species, one of whom became the ancestor of all humans and no aardvarks, while the other became the ancestor of all aardvarks and no humans. They may well have met, and may even have been brothers. You can cross out aardvark and substitute any other modern species you like, and the statement must still be true. Think it through, and you will find that it follows from the fact that all species are cousins of one another. Bear in mind when you do so that the ‘ancestor of all aardvarks’ will also be the ancestor of lots of very different things beside aardvarks[.]

There is one aspect of this argument that is crucial and that is that our common shared ancestor Henry that Dawkins is talking about has to have lived at a time when he was of a different species from us, since the reductio argument he is using depends crucially on the unlikelihood of species evolution following separate but parallel tracks to arrive at the same species end point. Since all humans are descendants of this single animal Henry, we conclude that all the early humans must be the ancestors of all of us. So when Dawkins talks of us all sharing the same ancestors at some point, he means human ancestors, since all humans evolved from Henry’s line.

Of course, as time progresses, the human species descended fro Henry produced more descendants who then produced yet more descendants and so on, and there must come a time when the lines diverged so that not everyone living at later times is the ancestor of all of us, but only some. That transition time is called the identical ancestors (IA) time. i.e., Earlier than that, every human was the ancestor of all of us or none of us (i.e., their line went extinct). After the IA time, people share only some ancestors.

It is not hard to see that as time progresses even further, there will come a time when we all share just one common human ancestor, referred to as the most recent common ancestor or MRCA. After that time, everyone living today no longer shares a common ancestor.

I don’t know about you, but to me there is something extraordinarily beautiful about this idea that at one point in time we all shared the same single ancestor, and that some time further back, everyone who lived at that time was the ancestor of all of us. It seems to be such a decisive argument against tribalism. It is hard to maintain the idea that some groups of people are ‘special’ in some way, when we not only all descended from a single animal Henry, but that at a later time we all shared the same set of human ancestors. Not only that, but we are also cousins of all the species that currently exist.

No wonder some religious extremists are afraid to have their children learn this theory. It is so captivating one can see how it would fascinate and draw in anybody who begins to think seriously about it.

Having established that we have both an MRCA and a time where all our human ancestors were identical (the IA time), this raises the question of when these dates occurred.

And therein lies another surprise, to be discussed in an upcoming post in this series.

POST SCRIPT: We’re number 1?

Comedian Lewis Black tries to help Americans to see themselves as others see them.