Nobody in my past was hugely famous, at least that I know of. I vaguely recall that an ancestor of mine who shipped over on the Mayflower distinguished himself by falling out of the ship and having to get fished out of the water. He might be notable, I guess, but hardly famous. It is much more fun to think that I am a bloodline descendant of Charlemagne. And in 1999, Joseph Chang gave me permission to think that way.

Chang was not a genealogist who had decided to make me his personal project. Instead, he is a statistician at Yale who likes to think of genealogy as a mathematical problem. When you draw your genealogy, you make two lines from yourself back to each of your parents. Then you have to draw two lines for each of them, back to your four grandparents. And then eight great-grandparents, sixteen great-great-grandparents, and so on. But not so on for very long. If you go back to the time of Charlemagne, forty generations or so, you should get to a generation of a trillion ancestors. That’s about two thousand times more people than existed on Earth when Charlemagne was alive.

The only way out of this paradox is to assume that our ancestors are not independent of one another. That is, if you trace their ancestry back, you loop back to a common ancestor. We’re not talking about first-cousin stuff here–more like twentieth-cousin. This means that instead of drawing a tree that fans out exponentially, we need to draw a web-like tapestry.

In a paper he published in 1999 [pdf], Chang analyzed this tapestry mathematically. If you look at the ancestry of a living population of people, he concluded, you’ll eventually find a common ancestor of all of them. That’s not to say that a single mythical woman somehow produced every European by magically laying a clutch of eggs. All this means is that as you move back through time, sooner or later some of the lines in the genealogy will cross, meeting at a single person.

As you go back further in time, more of those lines cross as you encounter more common ancestors of the living population. And then something really interesting happens. There comes a point at which, Chang wrote, “all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.”

In 2002, the journalist Steven Olson wrote an article in the Atlantic about Chang’s work. To put some empirical meat on the abstract bones of Chang’s research, Olson considered a group of real people–living Europeans.

The most recent common ancestor of every European today (except for recent immigrants to the Continent) was someone who lived in Europe in the surprisingly recent past—only about 600 years ago. In other words, all Europeans alive today have among their ancestors the same man or woman who lived around 1400. Before that date, according to Chang’s model, the number of ancestors common to all Europeans today increased, until, about a thousand years ago, a peculiar situation prevailed: 20 percent of the adult Europeans alive in 1000 would turn out to be the ancestors of no one living today (that is, they had no children or all their descendants eventually died childless); each of the remaining 80 percent would turn out to be a direct ancestor of every European living today.

Suddenly, my pedigree looked classier: I am a descendant of Charlemagne. Of course, so is every other European. By the way, I’m also a descendant of Nefertiti. And so are you, and everyone else on Earth today. Chang figured that out by expanding his model from living Europeans to living humans, and getting an estimate of 3400 years instead of a thousand for the all-ancestor generation.

Things have changed a lot in the fourteen years since Chang published his first paper on ancestry. Scientists have amassed huge databases of genetic information about people all over the world. These may not be the same thing as a complete genealogy of the human race, but geneticists can still use them to tackle some of the same questions that intrigued Chang.

Recently, two geneticists, Peter Ralph of the University of Southern California and Graham Coop of the University of California at Davis, decided to look at the ancestry of Europe. They took advantage of a compilation of information about 2257 people from across the continent. Scientists had examined half a million sites in each person’s DNA, creating a distinctive list of genetic markers for each of them.

You can use this kind of genetic information to make some genealogical inferences, but you have to know what you’re dealing with. Your DNA is not a carbon copy of your parents’. Each time they made eggs or sperm, they shuffled the two copies of each of their chromosomes and put one in the cell. Just as a new deck gets more scrambled the more times you shuffle it, chromosomes get more shuffled from one generation to the next.

This means that if you compare two people’s DNA, you will find some chunks that are identical in sequence. The more closely related people are, the bigger the chunks you’ll find. This diagram shows how two first cousins share a piece of DNA that’s identical by descent (IBD for short).

Ralph and Coop identified 1.9 million of these long shared segments of DNA shared by at least two people in their study. They then used the length of each segment to estimate how long ago it arose from a common ancestor of the living Europeans.

Their results, published today in PLOS Biology, both confirm Chang’s mathematical approach and enrich it. Even within the past thousand years, Ralph and Coop found, people on opposite sides of the continent share a lot of segments in common–so many, in fact, that it’s statistically impossible for them to have gotten them all from a single ancestor. Instead, someone in Turkey and someone in England have to share a lot of ancestors. In fact, as Chang suspected, the only way to explain the DNA is to conclude that everyone who lived a thousand years ago who has any descendants today is an ancestor of every European. Charlemagne for everyone!

If you compare two people in Turkey, you’ll find bigger shared segments of DNA, which isn’t surprising. Since they live in the same country, chances are they have more recent ancestors, and more of them. But there is a rich, intriguing pattern to the number of shared segments among Europeans. People across Eastern Europe, for example, have a larger set of shared segments than people from within single countries in Western Europe. That difference may be the signature of a big expansion of the Slavs.

Ralph and Coop’s study may provide a new tool for reconstructing the history of humans on every continent, not just Europe. It will also probably keep people puzzling over the complexities of genealogy. If Europeans today share the same ancestors a thousand years ago, for example, why don’t they all look the same?

Fortunately, Ralph and Coop have written up a helpful FAQ for their paper, which you can find here.

[Update: Adjusted the estimated generations since Charlemagne to thirty. Corrected Ralph’s affiliation.]