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Genealogy, mathematics and a little DNA

How many ancestors did you have in the year 1000?

The places in your family tree double every generation. By the year 1000 they need billions of people, in a Europe of about 36 million. Where were your grandparents born? We start from there and go back.

Where your grandparents were born

If you know only one place, we use it for all four grandparents. The map runs from the Atlantic to Japan and down to southern Africa. The places you choose never leave your phone or computer.

Two parents, four grandparents, eight great-grandparents

Each generation doubles the number of places in the tree. At the tenth, around the year 1710, you have 1,024 places in the tree. At the twentieth, around 1410, more than a million. At the thirtieth, around 1110, more than a billion.

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The places in your tree, on paper. Everyone in Europe, as estimated by Colin McEvedy and Richard Jones (1978). The lines meet around the year 1230: before that, the tree needs more people than lived on the whole continent.

Around the year 900, the tree would need more people than have ever been born on Earth: about 117 billion, by the Population Reference Bureau's estimate.

The arithmetic is right. The wrong part is assuming that every place in the tree is a different person. When two of your ancestors themselves share an ancestor, one person fills two places. Further back, one person fills thousands of places, then millions. Genealogists call this pedigree collapse: the tree folds into itself.

Where your ancestors lived

Each square is a patch of land one degree by one degree. The brighter it is, the more of the people living there are your ancestors. Full colour means about four in five.

For a child born in 2010 with grandparents from Cluj, the model reaches three quarters of the people of Europe around the year 1020: that many were the child's ancestors.

Start from your grandparents, around the year 1950: four people, in the places you chose.

Model: 30 years a generation; population of each place from HYDE 3.2.1. One parent in ten is born outside the child's patch, mostly nearby, rarely hundreds of kilometres away. How it is calculated and how sure it is: see the method.

The first centuries look like an ordinary family tree: ancestors double and stay close to home. Before 1750, most couples were born within about ten kilometres of each other (Kaplanis and colleagues, 2018, from 86 million profiles on the genealogy site Geni.com). In the Bihor parishes studied by the Romanian historian Mircea Brie, around 1870–1910, between half and three quarters of marriages joined two people from the same village.

Then the patch widens. It takes only one person in ten per generation coming from elsewhere for your ancestors to reach most of the continent within a few hundred years: traders, soldiers, slaves, monks, brides from far away. In a community that married mostly within itself for centuries, an isolated mountain village or an island, the same ancestors repeat more often and the map widens later. Somewhere between the eleventh and the ninth century, depending on how close your grandparents' places are to the middle of the continent, the coloured share of Europe passes three quarters and then barely grows.

Why it stops at four in five

Run the map back as far as you like: in Europe, the coloured share never passes about four people in five. The Yale statistician Joseph Chang explained why in 1999. He imagined the simplest possible population: the same number of people every generation, each choosing two parents at random from the generation before.

How many children each person has varies by chance. Some have many, some none, and some lines die out. Chang showed that far enough back, about 80% of a generation are ancestors of everyone alive today. The other 20% are ancestors of no one.

There is no middle ground. For Europe, Ralph and Coop reckon that, as long as populations mixed enough, a person from a thousand years ago is either your ancestor, your neighbour's and your classmate's, or has no living descendants at all. Bernard Derrida and colleagues reached the same figure, 20.3%, by another route. Chang himself pointed out that his model has no geography: people do not mix at random across a continent. The map above adds geography and arrives, more slowly, at the same place.

How many ancestors do you share with the classmate next to you?

Choose where a classmate's or a friend's grandparents were born. Their ancestors appear on the map next to yours.

or:

Starting from two different places, London and Iași, the two children's ancestors become, going back, more and more the same people.

Your ancestors Your classmate's Both of yours

In the model, the maps merge. The genetic data say the same. In 2013 Peter Ralph and Graham Coop compared the genomes of 2,257 Europeans, 14 of them from Romania. Two Europeans from opposite ends of the continent, they write, are expected to share millions of genealogical ancestors from the last 1,000 years. South-eastern Europeans share many ancestors from the era of the Slavic and Hunnic expansions, about 1,500 years ago.

Not every ancestor left you something

A genealogical ancestor is not necessarily a genetic one. The DNA from each parent reaches you cut into pieces. Going back, the pieces are shared out ever more finely among your ancestors, but their number grows slowly, by about 33 a generation, while your ancestors double. Sooner or later there are not enough pieces to go round.

10 generations back you have 1,024 places in the tree. On average only about 475 of those ancestors left you any DNA at all.

The formula is the geneticist Graham Coop's, at the University of California, Davis, and counts only the 22 ordinary pairs of chromosomes. Twenty generations back, out of more than a million places, only about 1,300 ancestors left you DNA. In the year 1000 almost all your ancestors are genealogical only: none of their DNA need have reached you, yet without them you would not exist.

Are you descended from Charlemagne?

The British geneticist Adam Rutherford wrote in his book A Brief History of Everyone Who Ever Lived (2016) that anyone with European ancestry is also descended from Charlemagne. His argument is the one above. Charlemagne died in 814, about forty generations ago. If he has living descendants, and if Europe mixed enough, as Ralph and Coop's data suggest, then he is an ancestor of every European today.

It also works the other way, which is said less often. You descend from Charlemagne just as surely as from the unnamed farmer ploughing near Aachen that same year. And you probably carry none of Charlemagne's DNA: Rohde, Olson and Chang wrote in 2004 that from most ancestors that far back we inherit little or nothing genetically.

The same calculation run for all of humanity, with ports, caravan routes and the odd person crossing the Bering Strait, gave Douglas Rohde's team a surprisingly recent date. In their simulations, everyone alive today has exactly the same genealogical ancestors once we go back to somewhere between 5353 and 2158 BC. The authors themselves call the estimates "extremely tentative".

Ask your grandparents where their grandparents were born

One generation further up you have eight places on the map instead of four, and the first centuries of the map change. Beyond that, the answer is much the same for everyone around you. The people who lived in these places a thousand years ago and have descendants today are your ancestors, your classmate's, and those of whoever is reading over your shoulder.

For a lesson

Method and sources

The doubling is arithmetic: n generations back, the tree has 2n places. The years come from your birth year and 30 years per generation, the value Tremblay and Vézina (2000) recommend from 100 Quebec genealogies. In the same study the measured mean interval was 31.7 years: 28.9 through women, 34.5 through men.

Europe's population in the chart is McEvedy and Jones's estimate (1978), including European Russia: 36 million in 1000, 80 million around 1300, "nearer 60m than 80m" after the Black Death, 80 million in 1500. Maddison and HYDE give 32 to 39 million for the year 1000, depending on how much of Russia is counted. Between those years the chart joins the points on a logarithmic scale.

The map starts from the one-degree cells that hold the places you chose and goes back one generation at a time. For each cell the model keeps the share of its people who are your ancestors. Every ancestor has two parents. Nine parents in ten are born in the child's own cell. The tenth comes from another cell no more than 1,000 km away, picked in proportion to its population, with the chance falling by a factor of e every 250 km. A person is an ancestor if at least one link reaches them. In an isolated cell the calculation settles at exactly Chang's share, 79.7%.

The population of each cell comes from HYDE 3.2.1 (Klein Goldewijk and colleagues, 2017), from grids every hundred years to 1700 and every 50 years after that, summed into one-degree cells. The map runs from the Atlantic to Japan and from the North Cape to southern Africa. For a family that crossed an ocean in the last few centuries, choose the place they left from.

What is certain and what is not. The doubling, the populations and the 80% of Chang's model are arithmetic or published estimates. When a region fills in depends on how much people moved. Starting from Cluj, Europe reaches three quarters around the year 1020. If only one parent in twenty came from another cell, around 960; if one in five, around 1110. Starting from Lisbon, at the edge of the continent, the dates are about two centuries earlier. “Europe” in these calculations means the land between 10° W and 40° E and between 36° and 60° N. The conclusion for Europe, that everyone's ancestors are the same people about a thousand years back, rests on Ralph and Coop's genetic data (2013), not on the model alone.

The number of ancestors who left you DNA uses Graham Coop's approximation: the pieces of chromosome from one parent number about 22 + 33 × (k − 1) at k generations back, and the expected number of ancestors who left you DNA is 2k × (1 − e−(22 + 33(k − 1)) / 2k − 1). The X and Y chromosomes are not counted. It is an average: for a particular person the number varies.

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Published on 27 September 2026.