THIS BLOG HAS MOVED AND HAS A NEW HOME PAGE.

Entries in "Common ancestors"

December 31, 2009

Emotional reactions to Darwin

(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.)

There is no doubt that Darwin's ideas about evolution by natural selection carry a huge emotional impact. For many people the idea that "we are descended from apes" is too awful to contemplate and is sufficient reason alone to dismiss any claim that natural selection holds the key to understanding how we came about. (Of course, we are not descended from apes. The more accurate statement is that apes and humans share common ancestors, making them our cousins, but even this refinement does not take away the stigma that supposedly comes with being biologically related to animals such people consider inferior.)

This unease about being biologically linked to other species is widespread and transcends any particular religious tradition. In Sri Lankan rural areas, one would frequently see monkeys on trees by the side of the road. As children when we were passing them, almost invariably someone would point them out and say things like "Your relatives have come to see you." Similarly, if one said that one was going to visit the zoo, this would also result in the question as to whether one was going to visit one's relatives. This kind of humor among children was commonplace, and reflected a reflexive instinct that humans were superior to all other animal forms, and reinforced the belief that some sort of special creative process must have been at work to produce us.

But if the thought of being related to apes gives some people the creeps, imagine how much worse it will for them to realize that as we go farther back in evolutionary time, we are cousins to all sorts of life forms that might make people even more squeamish.

Reading Richard Dawkin's book The Ancestor's Tale (2004) I found that I myself was not immune from that kind of emotional reaction, even though I have no problems intellectually with accepting natural selection and all its consequences.

For example, I had little difficulty emotionally accepting that the apes and monkeys are my cousins, partly because, I suppose, that idea has been around for a long time and I have simply got used to it. Also a common ancestor to the humans and apes would not look very different from us now and is easier to envisage. But as the evolutionary clock went back in time, and I started imagining what my deep ancestors looked like, I had a variety of reactions.

The idea that I had common ancestors with dogs and cats and horses (those evolutionary branches separated from the human branch at about 85 million years ago (Mya)) did not cause me any problems. I kind of liked the idea that my dog Baxter and I can trace our separate lineages back to a time when we both had a common ancestor. It is clear that our common ancestor would not look much like present-day humans or dogs, but I cannot imagine what it might have looked like apart from having some of the common characteristics shared by dogs and humans, like being four-limbed, warm-blooded, invertebrates.

More annoying was the realization that the branch that led to the rodents like rats, squirrels and rabbits only separated from the human branch at 75 Mya, meaning that those animals that we consider vermin and would not think of having in our houses, actually have a closer relationship to humans (since our common ancestors lived more recently) than those whom we love and welcome into our homes as pets, like dogs and cats.

Somehow, the emotional reaction of finding oneself having common ancestors with dignified and majestic animals like whales (85 Mya) and elephants (105 Mya) is positive while being linked to things like snakes (at 305 Mya) felt kind of icky.

A hard bridge to cross (again I mean emotionally) was accepting that frogs and toads and salamanders shared a common ancestor with me at about 340 Mya, perhaps because I share the common perception that these animals are slimy.

Going back further, I had little negative emotional reaction to realizing that I had a common ancestor with sharks at 460 Mya but the thought that flatworms and I were related at 630 Mya was harder to take. I suppose that this is because sharks are usually perceived as admirable and graceful (if dangerous) animals while I have never liked worms, seeing them as somehow disgusting. Perhaps I will now have warmer feeling towards them, seeing that we are relatives.

Once I got over the emotional hurdle of being able to accept the fact that worms and I have common ancestors, the rest was pretty easy to accept, perhaps because the earlier life forms that our common ancestors took had to be so different that I could not really relate to them (let alone imagine them) in any way. Thus it was a breeze to accept that I am related (however distantly) with sponges, bread moulds, amoeba, and bacteria.

It was amusing to keep monitoring my emotional reactions as I read about the backward evolutionary journey. But like most difficult journeys, taking that first step is the hardest. And now I have a better understanding why many religious people simply cannot take that first step and acknowledge that chimpanzees are our cousins, in fact are the closest cousins we have in the animal kingdom, with our common ancestor living just 6 million years ago. Because once you accept that, then you have embarked on journey whose inevitable end is that you end up as one with a bacterium. It is hard to think of you being created in god's image after that.

Thus I am somewhat sympathetic to those people who find Darwin's ideas hard to stomach and desperately seek to find a more palatable alternative. However, I think their task will prove hopeless, since the basic tenets of evolution are here to stay and so we may as well get used to it.

December 30, 2009

Looking for deep 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.)

Richard Dawkins in his book The Ancestor's Tale (2004) tells a fascinating story. He models his book on a journey that, rather than moving through space to a particular destination, is moving in the temporal dimension, going steadily back in time. He calls it a "pilgrimage to the dawn of evolution." He starts with present day humans and follows them back into history. One reason he gives for going back in time instead of starting at the beginning and going forwards as is more commonly done is to avoid a common trap of perception. When you tell the story forwards, it is hard to avoid giving the impression that life evolved purposefully, that human beings were somehow destined to be. This is counter to evolutionary theory that says that evolution is not directed towards any goal. It tells us how the present emerged from the past. It does not tell us how the future will emerge from the present.

Dawkins points out that the another advantage of telling the story backwards is that you can choose any of the current species and go back in time and tell pretty much the same story.

As I have mentioned earlier, we quickly (in just 2,000 years) reach the time when the most recent common ancestor lived and soon after that (about 5,000 years ago) reach a point when all our ancestors were identical.

But this convergence of ancestry is not just for humans, it is for all species. If we go far enough back in time, even my dog Baxter and I share the same ancestor, which I find a very appealing notion.

Anyway, here is a concise summary of the landmarks on this pilgrimage back in time, along with some other landmarks.

About 10,000 years ago, the agricultural revolution began and about 12,000 years ago saw the beginnings of language. About 160,000 years ago saw the beginning of what we would consider modern humans, and beyond that we start reaching the precursors to modern humans, a famous milestone being the fossil Lucy, dated to 3.2 Mya (million years ago).

As we go further back in time in this pilgrimage, other species start 'joining us' in our journey. What this means is that we reach times at which an earlier species existed which then split into two branches and diverged evolutionarily to what we see now. So if we go back further in time, we should cease to view the pilgrims on the journey as a combined group of humans and other species but instead see the travelers as that earlier common ancestor species. He calls these common ancestors 'concestors'. (Concestor 0 in Dawkins' scheme is the most recent common ancestor of all humans (or MRCA) that I have discussed earlier and who lived just a few thousand years ago.)

Going back in time, at 6 Mya we meet concestor 1 when we join up with the ancestors of chimpanzees. As we go even back further, we (and when I say 'we', I remind you that we should not think of 'us' as humans at this point but as the common ancestor species of humans and chimpanzees) join up at about 40 Mya successively with gorillas, orang utans, gibbons, and finally monkeys. Remember that the 'pilgrims' look different as we pass each concestor point.

Concestor 8 occurs at about 63 Mya when we join up with mammals like lemurs and lorises. (Just prior to this, around 65 Mya, was when all the dinosaurs went extinct.) As you can imagine, concestor 8 would not look much like present-day humans at all.

About 75 Mya, we join up with rats, rabbits and other rodents (concestor 10), at 85 Mya with cats and dogs (concestor 11), at 105 Mya with elephants and manatees (concestor 13), at 310 Mya with snakes and chickens (concestor 16).

At 340 Mya, we make a big transition when join up with the ancestors of amphibians, such as frogs and salamanders (concestor 17). This point marks the first time that animals moved out of the water.

Around 440 Mya we join up with various kinds of fish (concestor 20), and around 630 Mya with flatworms (concestor 27).

After various other species ancestors' join ours, the next big rendezvous occurs at about 1,100 Mya when we join up with the ancestors of fungi, such bread molds and truffles (concestor 34).

Some time earlier than that (passing the connection with amoeba at concestor 35) but before 1,300 Mya (it is hard to pin the date) is when the next major transition occurs when we join up with green plants and algae. This common ancestor is concestor 36.

At about 2,000Mya we arrive at concestor 38 where every species is now represented by a eukaryotic (nucleated) cell.

At about 3,500 Mya we meet up with our earliest ancestors, the eubacteria (concestor 39), the original form of life.

Dawkins' reverse story can be seen visually, told in a beer commercial in 50 seconds flat to the pounding beat of Sammy Davis Jr. singing The Rhythm of Life. (A minor quibble: There is one way in which this fun visual representation is not accurate. It shows three humans going back in evolution until we join up with ancestors of the present-day amphibians (concestor 17) in identical parallel paths. This is ruled out by the reductio ad absurdum argument written about earlier, where it was established that all present day humans must have had a single common ancestor in any earlier species.)

I must say that this book was an exhilarating journey. To see the whole of the evolution of life going backwards and merging together was a nice new way of seeing the process. Those of you who are interested in the grand sweep of evolution written for a non-specialist will find Dawkins' book a great resource.

POST SCRIPT: The Boxer

A live performance of Simon and Garfunkel singing one of my all-time favorite songs The Boxer.

December 29, 2009

Sexual selection

(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 a previous post, I discussed the fact that although all of us have the identical set of ancestors who lived just 5,000 years ago, this does not mean that we have the same genes. The fact that we are different is due to the fact that if most of the mating occurs within a group, then this can result in certain features becoming emphasized. In extreme case, this initial isolated mating pattern can result in a new species being formed that cannot mate with other groups that it could have done in the past.

I had always thought that the two organisms belonged to different species if they were biologically different enough that they either could not produce offspring or, as in the case of mules produced by horses and donkeys, the offspring were infertile and thus not able to reproduce.

But I learned from Richard Dawkins' book The Ancestor's Tale (2004) that two things can be considered different species even if they are perfectly capable of producing fertile offspring. All that is required for them to be considered to be different species is that they are not found to mate in the wild for whatever reason.

Normally, this happens when there is some kind of barrier that separates two groups of the same species so that they cannot mate. "No longer able to interbreed, the two populations drift apart, or are pushed apart by natural selection in different evolutionary directions" (p. 339) and thus over time evolve into different species. But the separation can also occur due to sexual selection.

He gives a fascinating example of this on page 339. He describes experiments done with two species of cichlid fish. The two species live together in Lake Victoria in Africa and are very similar, except that one has a reddish color and the other bluish. Under normal conditions, females choose males of the same color. In other words, there was no hybridization between the two colors in the wild, thus meeting the requirements for being considered different species. But when experimenters lit the fish in artificial monochromatic light so that they all looked dirty brown, the females no longer discriminated among the males and mated equally with both kinds of males and the offspring of these hybrids were fully fertile.

He also describes ring speciation using the example of the herring gull and lesser black-backed gull (p. 302). In Britain, these two kinds of birds don't hybridize even though they meet and even breed alongside one another in mixed colonies. Thus they are considered different species.

But he goes on to say:

If you follow the population of herring gulls westward to North America, then on around the world across Siberia and back to Europe again, you notice a curious fact. The 'herring gulls', as you move around the pole, gradually become less and less like herring gulls and more and more like lesser black-backed gulls, until it turns out that our Western European lesser black-backed gulls actually are the other end of a ring-shaped continuum which started with herring gulls. At every stage around the ring, the birds are sufficiently similar to their immediate neighbors in the ring to interbreed with them. Until, that is, the ends of the continuum are reached, and the ring bites itself in the tail. The herring gull and the lesser black-backed gull in Europe never interbreed, although they are linked by a continuous series of interbreeding colleagues all the way around the other side of the world.

Dawkins gives a similar example of this kind of ring speciation with salamanders in the Central Valley of California.

Why is this interesting? Because it addresses a point that sometimes comes up with skeptics of evolution. They try and argue that there is a contradiction if we had evolved from an ancestor species that was so different from us that we could not interbreed with that species. Surely, the argument goes, doesn't speciation imply that if species A evolves into species B, then must there be a time when the child is of species B while the parent is of species A. And isn't that a ridiculous notion?

The herring gulls and salamanders are the counterexamples in space (which we can directly see now) of the counterargument in time (which we can only infer). What it says is that as descendants are produced, they form a continuum in time. Each generation, while differing slightly, can interbreed with its previous generation, but over a long enough period of time, the two end points of the time continuum need not be able to interbreed.

Thus it is possible for an organism to be intermediate between two species.

Coming back to the question of why we look so different if we all shared common ancestors so recently, it is likely that the kind of selectivity practiced by the cichlid fish has resulted in certain features being shared by groups that interbreed within a restricted domain bounded by distance and geography and culture, although the process has not become so extreme that we have formed into distinct species.

I apologize for boring those readers who had had a much more extensive biology education than I have because all these things which I have been writing about recently on evolution must be well known to them. But I find all this perfectly fascinating and novel.

December 28, 2009

Why we look different despite having identical 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 the previous post in this series, I reported on a paper by Douglas L. T. Rohde, Steve Olson, and Joseph T. Chang and published in the journal Nature that said that if we go back about 5,000 years, the ancestors of everyone on Earth today are exactly the same. This date is called the IA point, where IA stands for 'identical ancestors'.

One question that will immediately arise in people's minds is that if all our identical ancestors lived so recently, how is it that we look so different? If you take four people from China, Sri Lanka, Sweden, and Malawi, they are usually fairly easily distinguishable based on physical appearance alone, using features such as skin color, hair, facial features, etc. How could this happen if they all had identical ancestors as recently as 5,000 years ago?

The answer lies in the fact that while it is true that we all share the same ancestors, it does not mean that we all received that same genetic information from that common ancestral pool.

It is true that each of us gets exactly half our genes from our fathers and half from our mothers. But when we pass on our genes to our children, while each child gets exactly half from each parent, that does not imply that they get exactly one quarter from each grandparent. What is true is that on average each child gets one quarter of the genes from each grandparent.

The reason for this is because when a sperm or egg is formed, the genetic information (say in the egg formed in the mother) that goes into it undergoes a process of recombination in which the genes the mother obtained from her parents get mixed up before the transfer into the egg. It is thus theoretically possible, though unlikely, that a child will have zero genetic information from one of her four grandparents.

Furthermore, as we go down to the next generation, the average genetic information received by a child is now just one-eighth from any given great-grandparent. After many generations, even the average contribution of someone to each descendant approaches zero and it is not hard to imagine that some ancestors will have descendants who inherited none of their genetic information. In fact, as Rohde, Olson, and Chang say, "because DNA is inherited in relatively large segments from ancestors, an individual will receive little or no actual genetic inheritance from the vast majority of the ancestors living at the IA point."

Furthermore, "In generations sufficiently far removed from the present, some ancestors appear much more often than do others on any current individual’s family tree, and can therefore be expected to contribute proportionately more to his or her genetic inheritance. For example, a present-day Norwegian generally owes the majority of his or her ancestry to people living in northern Europe at the IA point, and a very small portion to people living throughout the rest of the world."

So even though we all have the same set of ancestors, the amount of genetic information received from any one ancestor will vary wildly from person to person.

As long as populations remained largely isolated, they could thus evolve different physical characteristics, although even a tiny amount of migration between populations is enough to create the early common dates of the MRCA (most recent common ancestor) and IA.

There are some factors that could shift those dates back further.

If a group of humans were completely isolated, then no mixing could occur between that group and others, and the MRCA would have to have lived before the start of the isolation. A more recent MRCA would not arise until the groups were once again well integrated. In the case of Tasmania, which may have been completely isolated from mainland Australia between the flooding of the Bass Strait, 9,000–12,000 years ago, and the European colonization of the island, starting in 1803, the IA date for all living humans must fall before the start of isolation. However, the MRCA date would be unaffected, because today there are no remaining native Tasmanians without some European or mainland Australian ancestry.

No large group is known to have maintained complete reproductive isolation for extended periods.

It seems to me that these results arguing for the fact that our most recent common ancestor lived about 2,000 years ago and that we all have the same common ancestors who lived just 5,000 years ago are pretty robust.

This has profound implications for origins myths and tribalism. Some people like to have a sense of racial pride by thinking that they represent 'pure' races. This research argues that this view is rubbish. None of us are 'pure'. We are all cousins with every other person on the planet.

December 24, 2009

More realistic calculation of the date of our most recent common ancestor

(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).

As a first improvement, they divided the world into ten population centers (or 'nodes'): one each in North America, South America, Greenland, Australia, the Pacific Islands, and the Indonesian archipelago, and two nodes in Africa and in Asia. Within each subpopulation, they assumed random mating, but allowed for neighboring populations to exchange just one pair of migrants per generation. Their computer models found that the best way to accommodate varying populations was to take a fixed value N equal to the population at the time of the MRCA. They assumed N to be 250 million, which was approximately the global population in the year I CE.

Using this more realistic model, and a generation span of 30 years, they obtained the MRCA date as 300 BC and the IA date as about 3,000 BCE, both still surprisingly recent.

They then constructed an even more sophisticated and realistic model. They broke up the inhabited area into three levels of substructure: continents, countries, and towns. (These were not real places, of course, just models, but they used our knowledge of geography and migrations routes that existed before 1,500 CE to create their models.)

The model allowed for each person to have a single opportunity to migrate from his or her town of birth. Within a country, they could migrate to any other town. If the migrants went to another country, the probability of that occurring decreased with the distance to the new country. To go to another continent required them to go through certain ports, and so on. The model also incorporated our knowledge of the size of ports and when they opened up.

Generations could also overlap in this model and the birth rate of each continent was adjusted to match historical estimates.

After making all these sophisticated adjustments to make their model more realistic, they arrived at what they felt was a reasonable estimate for the MRCA and IA dates. It turns out that the MRCA lived around 55 CE and the IA date is about 2,000 BCE. They also found that our most recent common ancestor probably lived in eastern Asia, not Africa as had been commonly supposed.

So despite going to considerable lengths to simulate a realistic pattern of population growth, mating, and migration, the dates arrived at for the MRCA and the IA are still surprisingly recent.

(If the authors of the paper made their parameters very conservative, they pushed the date for the MRCA only as far back to 1,415 BCE and the IA date to 5,353 BCE.)

A little reflection should persuade anyone that this result that our most recent common ancestor lived as late as 55 CE and in just 2,000 BCE we had identical ancestors has profound implications for the way we view ourselves and our relationship with others. The authors capture the wonder of it all when they end their paper with the following comment:

[O]ur findings suggest a remarkable proposition: no matter the languages we speak or the colour of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who laboured to build the Great Pyramid of Khufu.

I find this amazing and remarkably encouraging. It should be more widely known. If more people realized how close we are to each other, perhaps we would stop killing one another and treat each other like the fairly close relatives we truly are.

POST SCRIPT: Is that the real reason for the season?

Stephen Fry tells us about this Roman god named Mithras whose life story shows a remarkable resemblance to that of Jesus. What a coincidence!

December 23, 2009

The most recent common ancestor of all humans living today

(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

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?

December 22, 2009

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.

December 21, 2009

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).

October 13, 2006

Looking for deep ancestors

Richard Dawkins in his book The Ancestor's Tale (2004) tells a fascinating story. He models his book on a journey that, rather than moving through space to a particular destination, is moving in the temporal dimension, going steadily back in time. He calls it a "pilgrimage to the dawn of evolution." He starts with present day humans and follows them back into history. One reason he gives for going back in time instead of starting at the beginning and going forwards as is more commonly done is to avoid a common trap of perception. When you tell the story forwards, it is hard to avoid giving the impression that life evolved purposefully, that human beings were somehow destined to be. This is counter to evolutionary theory that says that evolution is not directed towards any goal. It tells us how the present emerged from the past. It does not tell us how the future will emerge from the present.

Dawkins points out that the another advantage of telling the story backwards is that you can choose any of the current species and go back in time and tell pretty much the same story.

As I have mentioned earlier, we quickly (in just 2,000 years) reach the time when the most recent common ancestor lived and soon after that (about 5,000 years ago) reach a point when all our ancestors were identical.

But this convergence of ancestry is not just for humans, it is for all species. If we go far enough back in time, even my dog Baxter and I share the same ancestor, which I find a very appealing notion.

Anyway, here is a concise summary of the landmarks on this pilgrimage back in time, along with some other landamrks.

About 10,000 years ago, the agricultural revolution began and about 12,000 years ago saw the beginnings of language. About 160,000 years ago saw the beginning of what we would consider modern humans, and beyond that we start reaching the precursors to modern humans, a famous milestone being the fossil Lucy, dated to 3.2 Mya (million years ago).

As we go further back in time in this pilgrimage, other species start 'joining us' in our journey. What this means is that we reach times at which an earlier species existed which then split into two branches and diverged evolutionarily to what we see now. So if we go back further in time, we should cease to view the pilgrims on the journey as a combined group of humans and other species but instead see the travelers as that earlier common ancestor species. He calls these common ancestors 'concestors'. (Concestor 0 in Dawkins' scheme is the most recent common ancestor of all humans (or MRCA) that I have discussed earlier and who lived just a few thousand years ago.)

Going back in time, at 6 Mya we meet concestor 1 when we join up with the ancestors of chimpanzees. As we go even back further, we (and when I say 'we', I remind you that we should not think of 'us' as humans at this point but as the common ancestor species of humans and chimpanzees) join up at about 40 Mya successively with gorillas, orang utans, gibbons, and finally monkeys. Remember that the 'pilgrims' look different as we pass each concestor point.

Concestor 8 occurs at about 63 Mya when we join up with mammals like lemurs and lorises. (Just prior to this, around 65 Mya, was when all the dinosaurs went extinct.) As you can imagine, concestor 8 would not look much like present-day humans at all.

About 75 Mya, we join up with rats, rabbits and other rodents (concestor 10), at 85 Mya with cats and dogs (concestor 11), at 105 Mya with elephants and manatees (concestor 13), at 310 Mya with snakes and chickens (concestor 16).

At 340 Mya, we make a big transition when join up with the ancestors of amphibians, such as frogs and salamanders (concestor 17). This point marks the first time that animals moved out of the water.

Around 440 Mya we join up with various kinds of fish (concestor 20), and around 630 Mya with flatworms (concestor 27).

After various other species ancestors' join ours, the next big rendezvous occurs at about 1,100 Mya when we join up with the ancestors of fungi, such bread molds and truffles (concestor 34).

Some time earlier than that (passing the connection with amoeba at concestor 35) but before 1,300 Mya (it is hard to pin the date) is when the next major transition occurs when we join up with green plants and algae. This common ancestor is concestor 36.

At about 2,000 Mya we arrive at concestor 38 where every species is now represented by a eukaryotic (nucleated) cell.

At about 3,500 Mya we meet up with our earliest ancestors, the eubacteria (concestor 39), the original form of life.

Dawkins' reverse story can be seen visually, told in a beer commercial in 50 seconds flat to the pounding beat of Sammy Davis Jr. singing The Rhythm of Life. (A minor quibble: There is one way in which this fun visual representation is not accurate. It shows three humans going back in evolution until we join up with ancestors of the present-day amphibians (concestor 17) in identical parallel paths. This is ruled out by the reductio ad absurdum argument written about earlier, where it was established that all present day humans must have had a single common ancestor in any earlier species.)

I must say that this book was an exhilarating journey. To see the whole of the evolution of life going backwards and merging together was a nice new way of seeing the process. Those of you who are interested in the grand sweep of evolution written for a non-specialist will find Dawkins' book a great resource.

POST SCRIPT: The Boxer

A live performance of Simon and Garfunkel singing one of my all-time favorite songs The Boxer

October 12, 2006

My ancestor Pharaoh Narmes again

I began this series of posts saying that I had discovered that there was an 80% chance that I was descended from Narmes, the first pharaoh of a united Egypt. As subsequent posts have indicated, I arrived at this, not by any detailed investigative work in tracking my lineage, but by depending upon the analysis of Douglas L. T. Rohde, Steve Olson, and Joseph T. Chang and published in the journal Nature.

After reading that paper, I became curious about who lived around the time of the identical ancestors and looked around to see if there was a named individual. I knew that writing was discovered around 5,000 years ago, so the time of the IA (identical ancestors) coincided roughly with the time that written records were starting to be kept. So there was a chance that there was a reliable contemporaneous written record of some person from the time of the IA. The chances were also great that the person whose life was recorded was likely to have been a big shot, a king or some such, whom people considered important enough to write about, on tombs and so forth.

I started investigating about who was the earliest named person we knew for sure existed. This ruled out characters from religious books like the Bible because those were written much more recently (around 900 BCE and later) and depended too much on legends and oral traditions that made them unreliable as history.

Marc Abramiuk of the Anthropology department at Case Western Reserve University suggested Narmes as a likely candidate for the honor of being the earliest known and named human being, and since he fitted into the IA period, I claimed that there is an 80% chance that he is my direct ancestor. (If any of you know of other named people who are candidates for the earliest known and recorded human being, please let me know. This is one genealogy search we can all contribute to, since every person we find from that time is likely to be the ancestor of all of us.)

Of course, there is no distinction to the claim that Narmes is my ancestor, since if that is the case, then he is also the ancestor of every other person currently alive. But that's fine by me. I don't want or need exclusive rights to him since having a famous ancestor confers no credit to me. Thinking that we are special simply because we belong to some particular group or are related to some particular individual is a symptom of tribal thinking.

Since I started on this study, I have become curious about the people who lived long ago and a bit surprised at how soon the track goes cold. The origins of written language pretty much sets the upper bound for reliable knowledge. If you think about it, given the vast ages of the Earth and the human beings that inhabit it, it is humbling to think of how little direct information have about our origins in terms of actual historical figures and recorded history, and how amazing it is that we have been able to figure out so much about the deep past using the tools of research and analysis.

This is the power of science, that we can use it to painstakingly reconstruct so much of our distant past by building carefully on what we know from the fields of archaeology, anthropology, biology, chemistry, physics, and mathematics. That interconnected web of knowledge serves as a filter that allows a lot of the guesswork and speculation and myths about our past to drain away, and leaves behind precious nuggets of hard knowledge.

In the next post in this evolution series, I will look at what we find when we go even further back in time.

October 10, 2006

Why we look different despite having identical ancestors

In the previous post in this series, I reported on a paper by Douglas L. T. Rohde, Steve Olson, and Joseph T. Chang and published in the journal Nature that said that if we go back about 5,000 years, the ancestors of everyone on Earth today are exactly the same. This date is called the IA point, where IA stands for 'identical ancestors'.

One question that will immediately arise in people's minds is that if all our identical ancestors lived so recently, how is it that we look so different? If you take four people from China, Sri Lanka, Sweden, and Malawi, they are usually fairly easily distinguishable based on physical appearance alone, using features such as skin color, hair, facial features, etc. How could this happen if they all had identical ancestors as recently as 5,000 years ago?

The answer lies in the fact that while it is true that we all share the same ancestors, it does not mean that we all received that same genetic information from that common ancestral pool.

It is true that each of us gets exactly half our genes from our fathers and half from our mothers. But when we pass on our genes to our children, while each child gets exactly half from each parent, that does not imply that they get exactly one quarter from each grandparent. What is true is that on average each child gets one quarter of the genes from each grandparent.

The reason for this is because when a sperm or egg is formed, the genetic information (say in the egg formed in the mother) that goes into it undergoes a process of recombination in which the genes the mother obtained from her parents get mixed up before the transfer into the egg. It is thus theoretically possible, though unlikely, that a child will have zero genetic information from one of her four grandparents.

Furthermore, as we go down to the next generation, the average genetic information received by a child is now just one-eighth from any given great-grandparent. After many generations, even the average contribution of someone to each descendant approaches zero and it is not hard to imagine that some ancestors will have descendants who inherited none of their genetic information. In fact, as Rohde, Olson, and Chang say, "because DNA is inherited in relatively large segments from ancestors, an individual will receive little or no actual genetic inheritance from the vast majority of the ancestors living at the IA point."

Furthermore, "In generations sufficiently far removed from the present, some ancestors appear much more often than do others on any current individual’s family tree, and can therefore be expected to contribute proportionately more to his or her genetic inheritance. For example, a present-day Norwegian generally owes the majority of his or her ancestry to people living in northern Europe at the IA point, and a very small portion to people living throughout the rest of the world."

So even though we all have the same set of ancestors, the amount of genetic information received from any one ancestor will vary wildly from person to person.

As long as populations remained largely isolated, they could thus evolve different physical characteristics, although even a tiny amount of migration between populations is enough to create the early common dates of the MRCA (most recent common ancestor) and IA.

There are some factors that could shift those dates back further.

If a group of humans were completely isolated, then no mixing could occur between that group and others, and the MRCA would have to have lived before the start of the isolation. A more recent MRCA would not arise until the groups were once again well integrated. In the case of Tasmania, which may have been completely isolated from mainland Australia between the flooding of the Bass Strait, 9,000–12,000 years ago, and the European colonization of the island, starting in 1803, the IA date for all living humans must fall before the start of isolation. However, the MRCA date would be unaffected, because today there are no remaining native Tasmanians without some European or mainland Australian ancestry.

No large group is known to have maintained complete reproductive isolation for extended periods.

It seems to me that these results arguing for the fact that our most recent common ancestor lived about 2,000 years ago and that we all have the same common ancestors who lived just 5,000 years ago are pretty robust.

This has profound implications for origins myths and tribalism. Some people like to have a sense of racial pride by thinking that they represent 'pure' races. This research argues that this view is rubbish. None of us are 'pure'. We are all cousins, and fairly close ones at that.

October 02, 2006

Realistic calculation of the date of our most recent common ancestor

In the previous posting, 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).

As a first improvement, they divided the world into ten population centers (or 'nodes'): one each in North America, South America, Greenland, Australia, the Pacific Islands, and the Indonesian archipelago, and two nodes in Africa and in Asia. Within each subpopulation, they assumed random mating, but allowed for neighboring populations to exchange just one pair of migrants per generation. Their computer models found that the best way to accommodate varying populations was to take a fixed value N equal to the population at the time of the MRCA. They assumed N to be 250 million, which was approximately the global population in the year I CE.

Using this more realistic model, and a generation span of 30 years, they obtained the MRCA date as 300 BC and the IA date as about 3,000 BCE, both still surprisingly recent.

They then constructed an even more sophisticated and realistic model. They broke up the inhabited area into three levels of substructure: continents, countries, and towns. (These were not real places, of course, just models, but they used our knowledge of geography and migrations routes that existed before 1,500 CE to create their models.)

The model allowed for each person to have a single opportunity to migrate from his or her town of birth. Within a country, they could migrate to any other town. If the migrants went to another country, the probability of that occurring decreased with the distance to the new country. To go to another continent required them to go through certain ports, and so on. The model also incorporated our knowledge of the size of ports and when they opened up.

Generations could also overlap in this model and the birth rate of each continent was adjusted to match historical estimates.

After making all these sophisticated adjustments to make their model more realistic, they arrived at what they felt was a reasonable estimate for the MRCA and IA dates. It turns out that the MRCA lived around 55 CE and the IA date is about 2,000 BCE. They also found that our most recent common ancestor probably lived in eastern Asia, not Africa as had been commonly supposed.

So despite going to considerable lengths to simulate a realistic pattern of population growth, mating, and migration, the dates arrived at for the MRCA and the IA are still surprisingly recent.

(If the authors of the paper made their parameters very conservative, they pushed the date for the MRCA only as far back to 1,415 BCE and the IA date to 5,353 BCE.)

A little reflection should persuade anyone that this result that our most recent common ancestor lived as late as 55 CE and in just 2,000 BCE we had identical ancestors has profound implications for the way we view ourselves and our relationship with others. The authors capture the wonder of it all when they end their paper with the following comment:

[O]ur findings suggest a remarkable proposition: no matter the languages we speak or the colour of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who laboured to build the Great Pyramid of Khufu.

I find this amazing and remarkably encouraging. It should be more widely known. If more people realized how close we are to each other, perhaps we would stop killing one another and treat each other like the fairly close relatives we truly are.

September 29, 2006

The most recent common ancestor of all humans living today

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.

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 log(2,N), 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 is only 20 to get to our MRCA. 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 in Chang's model, our MCRA lived far more recently than anyone had imagined, and way less than Mitochondrial Eve (~140,000 years ago) or Homo erectus (~250,000 to one million years ago). It is kind of fascinating to think that every 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 1.77log(2,N), which means that 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: Clouds

Flying to Los Angeles last week, I saw some beautiful cloud formations from above. But none of them matched the beauty of those shown here.

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.

September 27, 2006

My ancestor Narmer, the first Pharaoh of Egypt

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.

russellteapot2.jpg

September 26, 2006

Our common ancestors

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.