September 28, 2006
Some surprising facts about ancestors
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.