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.