(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.

Because of the holidays and travel overseas where internet access will be sporadic, I am taking some time off from writing new posts and instead reposting some of my favorites (often edited and updated) for the benefit of those who missed them the first time around or have forgotten them. New posts will start again on Monday, January 18, 2009.)

In the previous post, I discussed the calculation of Joseph T. Chang in which he showed that the most recent common ancestor (MRCA) of all the people living today lived around 1100 CE, while around 400 CE everyone who lived then was either the ancestor of all of us or none of us. The date when this occurs is called the IA (identical ancestor) date.

Chang got these results assuming that the population is constant over time at some value N, that the generations (with each generation lasting 30 years) are discrete and non-overlapping (i.e. mating took place only between males and females of the same generation), and that mating was random (i.e., there was equal probability of any one male in a generation to breed with any female of that same generation.)

What happens to these dates if you relax these unrealistic assumptions? One practical difficulty of going to more realistic models is that exact mathematical calculations become impossible and one has to resort to computer simulations. This was done by Douglas L. T. Rohde, Steve Olson, and Joseph T. Chang and their results were published in the journal Nature (vol. 431, September 30, 2004, pages 562-566).

[Read more…]

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.

Because of the holidays and travel overseas where internet access will be sporadic, I am taking some time off from writing new posts and instead reposting some of my favorites (often edited and updated) for the benefit of those who missed them the first time around or have forgotten them. New posts will start again on Monday, January 18, 2009.)

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 <the previous two posts for some background.)

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.

Of course, none of these assumptions is realistic. The size of a population changes with time for a variety of reasons. People also do not mate at random, being more likely to choose from those nearby, and from people within their same groupings whether those be economic, social, cultural, class, religion, etc. And cross-generational matings are not uncommon.

But for the purposes of mathematical simplicity, and to get a rough idea of the timescales involved, Chang’s simple model is worth looking at because it enables him to do a rigorous mathematical calculation for the date of the MRCA. What Chang found, to everyone’s surprise, was that the date of existence of the MRCA of all the humans living today was very recent. He found that the number of generations that one has to go back to get an MRCA was log₂N, which stands for the logarithm to base 2 of the population size N. He further found that even though this was a statistical calculation, the result was very sharply peaked about this value, meaning that it was highly unlikely that the MRCA date would differ by even 1% from this value.

If you take a population N of size one million, the number of generations you have to go back to get to our MRCA is only 20. If you take a population of one billion, our MRCA existed about 30 generations ago, or around 1100 CE (for an average generation span of 30 years).

So according to Chang’s model, our MCRA lived far more recently than anyone had imagined, and way more recently than Mitochondrial Eve (~140,000 years ago) or Homo erectus (~250,000 to one million years ago). It is fascinating to think that every single one of us living today share at least one ancestor who was living in the Middle Ages. I have been wondering who that person was, and where he or she lived, and what he or she was like.

But that was not the only surprising thing that Chang found. Once you get an MRCA, then that person’s parents are also common ancestors for all of us, as are his/her grandparents and great-grandparents, and so on. In fact, just as the number of our ancestors increase rapidly as we go back generations, so do the number of our common ancestors once we go further back than our MRCA.

Chang found that if you go far enough back, you reach a point when every single person living at that time is either the ancestor of all of us or none of us (i.e., that person’s line went extinct). In other words, there is no one who lived at that time who is the ancestor of just some of us. It is an all-or-nothing situation with an 80% chance of the former and 20% chance of the latter. To be perfectly clear about this (because it is an important point), at one particular time in the past, 20% of the people who lived at that time have no descendants alive today. Each one of the remaining 80% of the people has the entire world’s population today as descendants.

So all of us have the identical entire set of ancestors who lived at that time. Chang calls that time the IA (standing for ‘identical ancestors’) time.

Using the same assumptions as before, Chang’s calculations for the number of generations to reach the IA date is 1.77log₂N. For a billion people, it amounts to about 53 generations ago. This works out to 675 CE for a generation span of 25 years and 410 CE for 30 years.

It seems amazing (to me at least) that all of us living right now have identical ancestors that lived so recently, roughly around the period when the Prophet Muhammad lived (570-632 BCE). In fact Mark Humphrys, a professor of computer science at Dublin City University in Ireland using a different technique estimates that Muhammad, the founder of Islam, appears on the family tree of every person in the Western world. (Thanks to commenter Steve Lubot for this link.) But it is important to realize that there is nothing special about Muhammad or about the Western world.

So taking Chang’s results at face value, all the people who fight over religion today are highly likely to be descendants of each and every religious leader who lived from the time of the Prophet Mohammed and earlier. So in a very real sense, they are killing their own cousins.

Of course, Chang’s results were based on a highly simplified mathematical model. In the next posting in this series, we’ll see what happens when we create more realistic scenarios of population changes and mating patterns.

POST SCRIPT: File under things I don’t understand

What is the book most often stolen by shoplifters at bookstores? The Bible.

The article also seems to suggest that shoplifting is a routine activity among young people of all social classes in the US, almost a rite of passage. Could this be true?

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.

Because of the holidays and travel overseas where internet access will be sporadic, I am taking some time off from writing new posts and instead reposting some of my favorites (often edited and updated) for the benefit of those who missed them the first time around or have forgotten them. New posts will start again on Monday, January 18, 2009.)

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 as recently as a thousand years ago, 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 all 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. 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 first cousins and I are the one set of grandparents that we have in common. As my cousins get more distant, the MRCA goes back in time but it is not hard to see that an MRCA must exist for those whom we commonly refer to as ‘blood’ relatives.

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 rigorous proof (see the previous post) 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: Praying for defeat of health care

Congressperson Michele Bachmann (R-Loony) leads a group of people in a creepy prayer. Watch Tony Perkins, head of the Family Research Council that organized the event, drink some coffee in the middle of the prayer. You shouldn’t have done that, Tony. Jesus just hates it when people eat and drink when they should be groveling before him. Actually, Tony seems to show a remarkable lack of enthusiasm, not standing up and holding hands at the end.

If the health care legislation is defeated, they will no doubt attribute it to their prayers. But what if the health care bill that they are earnestly praying against actually passes, what will they conclude? That god wanted it to pass? Nah. That god was playing golf at that time and so missed their prayer? Nah. That god wanted to punish Tony Perkins for drinking coffee during the prayer? Nah.

Like all religious people when their prayers are never answered, they will ignore the issue (since no one usually asks them because the faith of religious must not be disturbed) or they will say that god agrees with them (isn’t it amazing that god agrees with every religious person?) but that he has a cunning plan that we cannot fathom.

It is all so predictable.

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.

Because of the holidays and travel overseas where internet access will be sporadic, I am taking some time off from writing new posts and instead reposting some of my favorites (often edited and updated) for the benefit of those who missed them the first time around or have forgotten them. New posts will start again on Monday, January 18, 2009.)

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 either the ancestor of all of us or of none 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 the theory of evolution. 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: Best Christmas film

Forget It’s a Wonderful Life. See The Ref (1994) with Denis Leary, Judy Davis and Kevin Spacey. The language is too strong for children but it is hilarious.

I couldn’t find a clip from the film but here is Leary doing a Christmas TV program (language advisory).