Big Bang for beginners-4: The speed of cosmic evolution

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

For previous posts in this series, see here.

What may surprise people is how rapidly the universe went from a very hot initial state to one in which it was cool enough for atoms and molecules to form. If we push our theories back as far as we dare, bearing in mind that we have stretched them to the limits and that we may well be wrong in some aspects, the earliest time that we can speak of is 10-43 seconds after the Big Bang (called the Planck time). i.e., this is 0.0000… 0001 seconds (43 zeros in all, including the one before the decimal) after the Big Bang. In other words, it is a really tiny time. It is estimated that the temperature of the universe at that time was about 1030 degrees. That is 10 followed by 30 zeros, a really huge number.
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Big Bang for beginners-3: The basic story

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

For previous posts in this series, see here.

The starting point of the Big Bang story is a cosmic event that started out small and expanded rapidly (like an explosion). This event brought into being the universe we now inhabit and produced all the matter that our universe is presently composed of, though not in its present form. The time at the beginning is arbitrarily set to zero.

We do not know what happened right at the very beginning (at time zero by our convention) because our known theories are believed to not apply right at the beginning. So our story begins very shortly after the Big Bang occurred. It is believed that what existed then were quarks, gluons, electrons, and photons that were moving freely around in a hot dense gas called a plasma. (There were also a few other exotic particles that I will ignore as they are not central to a basic understanding of the evolution of the universe). As the universe expanded over time, these quarks and gluons and electrons and photons eventually became the ordinary matter that we now have. No new matter was created after the Big Bang, but the form that the matter took did change dramatically.
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Big Bang for beginners-2: The nature of energy

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

For previous posts in this series, see here.

In order to understand the Big Bang theory, we also need to have an understanding of the nature of energy in addition to that of matter that was discussed yesterday. The word ‘energy’ has a technical meaning in science but has also entered into the vernacular and thus has been used to mean many things. In everyday language, it usually signifies the source of the ability to do things, such as move objects or break them up or put them together. So gasoline provides the energy to run cars, coal the energy to heat things, and so on.
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Big Bang for beginners-1: The nature of matter

(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.)

I was recently asked by a relative to provide a simple explanation of the Big Bang theory ‘in words of one syllable’, i.e., without using jargon or esoteric scientific concepts and in a way that it could be understood by non-scientists. So here goes my attempt at fulfilling that request. In doing so I have tried to follow a paraphrase of Einstein’s dictum that says that when explaining something we should make things as simple as possible, but not simpler. In other words don’t distort in the search for simplicity. In trying to achieve this goal, I have created a multi-part series. (I promised my relative that my explanation would be simple, not short!)
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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.)
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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.

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.

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.

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!

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 <the previous two posts for some background.)

He assumed that the population is constant over time at some value N. He assumed that the generations are discrete and non-overlapping (i.e. mating took place only between males and females of the same generation). He also assumed that mating was random. In words, that there was equal probability of any one male in a generation to breed with any female of that same generation.

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

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

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

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

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

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

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

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

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

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

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

POST SCRIPT: File under things I don’t understand

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

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