Some surprising facts about ancestors

(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.

Our common ancestors

(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).

The age of the Earth-12: The final synthesis

(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.)

For previous posts in this series on the age of the Earth, see here.

The minimum age of the Earth kept getting pushed back as older rocks kept being found and methods of analysis improved with the invention of new instruments such as the mass spectrometer. The minimum age was raised to 1.90 billion years in 1935, 3.35 billion years in 1947, to 3.45 billion years in 1956.

But there arose a new problem. Astronomers had discovered that the universe was expanding and Edwin Hubble’s (1889-1953) discovery of the law now associated with his name enabled scientists to estimate the time when the universe would have begun, and they initially arrived at an age of 1.80 billion years (Jackson, p. 251). It was absurd to suppose that the universe was younger than the Earth and this caused some consternation. But as the reach of telescopes increased and greater and greater expanses of the vastness of the universe came under observation, the calculated age of the universe kept increasing, to 10 billion years by the early 1950s, to 13 billion years by 1958, and finally to the present value of 13.7 billion years. Thus the potential paradox of the universe being younger than the Earth was resolved.
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The age of the Earth-11: The Earth becomes very old again

(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.)

For previous posts in this series on the age of the Earth, see here.

The discovery of radioactivity and the associated concept of half-lives of elements opened up the possibility of determining the absolute age of rocks. This argument was developed by Bertram Boltwood in the very early 1900s and is the process now referred to as radiometry (Jackson, p. 237). The argument goes like this. Suppose a sample of rock is found to contain 100 grams of a parent radioactive material P and 300 grams of the stable final daughter element D in its radioactive series, and also suppose that the half-life of this decay has been measured to be 10 years. If we assume that the rock initially had only the parent element P and no D, then we can assume that rock sample initially had 400 grams of P, then after 10 years, it had 200 grams of P and 200 grams of D, then after another 10 years, it would have 100 grams of P and 300 grams of D, and so on. Hence the rock must have been formed 20 years ago.
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The age of the Earth-10: The revolutionary impact of the discovery of radioactivity

(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.)

For previous posts in this series on the age of the Earth, see here.

The dawn of the 20th century was an extraordinary time of ferment in science. In the case of physics, in addition to the turmoil over the age of the Earth, there was also the well-known crisis that the newly emerging models of the atom as a tiny positively charged nucleus and orbiting negative charges seemed to contradict the well-established theory of electrodynamics. Another crisis was that the ‘luminiferous ether’, the material believed to permeate all space and the carrier of light waves, seemed to be extraordinarily successful in evading all attempts at detecting its presence or its properties. In addition, the blackbody radiation spectrum seemed to defy understanding on the basis of what were thought to be well-established laws of mechanics and radiation.
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The age of the Earth-9: Biologists join the geologists against the physicists

(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.)

For previous posts in this series on the age of the Earth, see here.

In the case of biology, Darwin’s theory of natural selection had been in retreat during the latter half of the 19th century under the assaults of both physicists and some biologists. Fleeming Jenkin (a physicist, engineer, and collaborator of Kelvin) had, in a review of Origins, delivered a severe critique of Darwin’s theory. He pointed out that not only was the time available insufficient for natural selection to work, but that the then-dominant theory of ‘blending inheritance’ (which said that children had a mixture of the qualities of their parents) worked against Darwin’s theory, since even if one parent experienced an advantageous mutation, that person’s child would only have half of it because the other parent would not have it, the grandchild one-fourth, and so on. The mutation would thus get diluted and disappear over time, and not grow and dominate the population, as natural selection argued.
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The age of the Earth-8: Geologists at loggerheads with physicists

(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.)

For previous posts in this series on the age of the Earth, see here.

While Kelvin’s estimate of the age of the Earth was interesting in its own right and faced its own supporters and detractors, the undeniably important consequence of his work was that for the first time, pinning down an actual age for the Earth became a question that had the potential to be definitively answered, and this spurred the growth of an entire research area. What Kelvin did that was of immense importance were two things: he demolished the uniformitarians’ vague notions of an almost limitless time for the age of the Earth and established the importance of doing precise calculations; and he began the process, and highlighted the importance, of unifying scientific theories in formerly divergent fields, by introducing physics principles into geological studies.

Kelvin had arrived at an age for the Earth that made it very difficult for natural selection to succeed as a mechanism. Then, as now, results from physics tend to be regarded as on a sounder footing than those from other disciplines. Hence those other fields such as geology and paleontology and biology tend to try and conform to the constraints provided by physics, not the other way around. Kelvin’s estimate of 100 million years as the upper limit for the age of the Earth became part of the scientific lore and geologists and biologists scrambled to accommodate it by trying to find ways to modify their calculations to be consistent with this upper bound. They had some success since each of these calculations depended on many parameters whose values could not be determined precisely, and so there was some room for flexibility.

As for evolution by natural selection, this low upper limit for the age of the Earth caused serious problems. As a result of Kelvin’s and other people’s strong criticisms of the idea of an Earth that was hundreds of millions of years old, by the third edition of Origins, Darwin had abandoned his breezy calculation of a 300 million year old timescale for the formation of the Weald, done somewhat casually at a time when such an age seemed reasonable. Meanwhile Wallace published another book in 1880 that suggested that 200 million years was sufficient for evolution to have worked (Jackson, p. 193). By squeezing here and pinching there, it seemed possible (though just barely) to accommodate 100 million years as sufficient for natural selection to work, but only with great difficulty and at the risk of sacrificing plausibility.

By around 1880, an uneasy truce seemed to have been drawn among the physics, geology, and biology communities around a 100 million year old Earth. But it did not last long. Others came along who followed up on Kelvin’s methods and using more refined calculations and newer estimates for the parameters involved, arrived at even shorter ages of 40 million and then 20 million years for the age of the Earth. Most important among these was an 1893 calculation by Clarence King, the first director of the US Geological Survey who, again basically using Kelvin’s thermal methods, arrived at a figure of 24 million years. In a paper in 1897, towards the end of his long and illustrious career, Kelvin stated his conclusion that the Earth was between 20 and 40 million years old, with King’s value of 24 million being likely most correct.

This caused immense problems for the other areas of science. If it was true, then almost all of geology would have to be drastically re-conceptualized and the theory of evolution by natural selection would have to be thrown out the window, to be replaced by some teleological model of directed evolution that implied planning or design or some other form of supernatural intervention.

But geologists had had enough of conforming to the ever-increasing restrictive limits of the physicists and modifying their parameters accordingly. Their discipline had now been around for about a hundred years and the newer generation of younger geologists no longer felt like new kids on the block who could be pushed around so easily by the big physics bullies. They felt that 100 million years was as far as it was reasonable for them to go given their own methods of estimating the ages of geological features based on rates of formation and erosion and sedimentation. They dug in their heels and became more assertive, saying that the laws of geology were firmly enough established to rule out such a young Earth and boldly suggested that it was physics that had gone awry somewhere, even if they could not find fault in its calculations or point out where the problematic assumptions were.

Next: What about biology and natural selection?

(Main sources for this series of posts are The Chronologers’ Quest: The Search for the Age of the Earth (2006) by Patrick Wyse Jackson and Lord Kelvin and the age of the Earth by Joe D. Burchfield (1975).)

POST SCRIPT: If the shoe were on the other foot…

If there is one thing that The Daily Show is particularly good at it is showing how ridiculous something is by reversing roles.

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The age of the Earth-7: The Earth starts getting younger again

(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.)

For previous posts in this series on the age of the Earth, see here.

Darwin and Wallace published their theory of natural selection at a time when it seemed that they had all the time they needed for their theory of natural selection to work. But that window of freedom of long geological times was soon to close and, starting around 1860, newer estimates of the age of the Earth started to shorten it considerably. Part of the reason was undoubtedly a backlash to the success of Darwin’s theory of evolution that, within a decade of the publication of Origins in 1859, had persuaded almost the entire scientific community that evolution was a fact and that its basic idea that all organisms arose from descent with modifications from common ancestors was true.
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The age of the Earth-5: Christianity tries to deal with an old Earth

(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.)

For previous posts in this series on the age of the Earth, see here.

By the end of the 18th century, Enlightenment values had taken hold, science and rationality were on the rise, and religion could no longer rely on dogmatic assertions and threats alone to suppress ideas that it found unpalatable. So the strategy shifted to creating alternative narratives that had a scientific veneer that would make their religion-based conclusions more acceptable. That strategy has been the one that religions have followed ever since, right down to the present day, with intelligent design being its latest incarnation.
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The age of the Earth-4: The strategy of religions in response to scientific advances

(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.)

For previous posts in this series on the age of the Earth, see here.

The history of the science-religion conflict follows a standard pattern. Religions make claims that lie within the framework of science, saying those claims must be true because of their divine origin (because of revelation or religious texts). Then it fights any scientific advances that challenge those claims. Then when the evidence becomes too great and further opposition becomes ludicrous, they concede the point and retreat to a new line of defense. Then after some time has elapsed to allow people to forget its previous objections, religions argue that the very scientific discoveries that they once vigorously opposed now actually support their religious beliefs. They sometimes even go so far as to suggest that their religion actually predicted them. (The comic strip Jesus and Mo has something to say on this here, here, and here.)
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