Your family tree grows exponentially as you go back in time. Two parents, four grandparents, eight great-grandparents — the number of ancestors in each generation doubles. Go back a thousand years, or about 40 generations of 25 years each, and the arithmetic says you should have 2 to the power of 40 ancestors. That's 1,099,511,627,776, or about a trillion.
That is far more people than were alive a thousand years ago — estimates for the world's population around the year 1000 run from about 254 million to 400 million — and more than the roughly 117 billion people the Population Reference Bureau estimates have ever been born. So the slots cannot all hold different people. The same ancestors fill many of them, a pattern genealogists call pedigree collapse. This guide works out where the doubling breaks, shows how quickly the count of different ancestors levels off in a simple simulation, and sets out what population geneticists have estimated about when everyone's trees meet. Our ancestor count calculator gives the doubling for any number of generations.
Where the doubling runs out of people
The generation at which the doubling overtakes a population is fixed by arithmetic. The date it falls on is not, because it depends on how long a generation is. Counting back from 2026:
| Years per generation | 2n passes 400 million | 2n passes 117 billion |
|---|---|---|
| 25 | generation 29, around 1301 | generation 37, around 1101 |
| 30 | generation 29, around 1156 | generation 37, around 916 |
| 35 | generation 29, around 1011 | generation 37, around 731 |
Using four hundred million, the high-end estimate for the world's population in the year 1000, makes for a generous test. Even so, at 25 years a generation, the doubling overtakes the entire global population by about 1300. A cross-cultural study of generation intervals puts the average between about 28 and 32 years, so the real crossing sits somewhere inside the table rather than at either edge. Either way, well within the last thousand years the tree must be reusing people.
How collapse happens, one marriage at a time
The simplest case is a marriage between first cousins. First cousins share a pair of grandparents, so their child has only six different great-grandparents instead of eight: one couple appears twice, once through each parent. Every marriage between relatives removes more distinct people from the count. Over centuries, in any population of limited size, such marriages are inevitable, whether or not the individuals know they are related.
The most thoroughly documented extreme is Charles II of Spain, the last Habsburg king of Spain, who died in 1700. A 2009 study in the journal PLoS ONE reconstructed his ancestry through 16 generations and more than 3,000 individuals and calculated his inbreeding coefficient — the probability that the two copies of a gene he inherited came from the same ancestor — at 0.254. That is slightly higher than the 0.25 expected for the child of a parent and child, or of a brother and sister.
His tree shows collapse in a less obvious way than a missing great-grandparent. He had eight different great-grandparents, but two of his grandparents on his father's side, Philip III and Margaret of Austria, appear again among his great-grandparents on his mother's side, because his mother was their granddaughter. The authors found that marriages between close relatives explained only part of the figure; distant shared ancestry, accumulated over many generations, contributed about as much.
A simulated population
This isn't just a quirk of royal families. To see how fast this happens in a general population, we ran a simple model. It uses a population of a fixed size, and each person's two parents are drawn at random from the generation before. Starting from one person, the model counts how many different people appear in each generation of the tree.
| Generations back | 2n slots | Different ancestors, population of 10,000 | Different ancestors, population of 1,000,000 |
|---|---|---|---|
| 10 | 1,024 | 905 | 1,023 |
| 15 | 32,768 | 6,835 | 31,674 |
| 20 | 1,048,576 | 7,935 | 491,606 |
| 25 | 33,554,432 | 7,946 | 790,400 |
| 30 | 1,073,741,824 | 8,036 | 796,933 |
| 40 | about 1.1 trillion | 8,006 | 797,364 |
In the million-person population the count tracks the doubling closely for about fifteen generations, then bends sharply and stops growing. In both populations it levels off at about 80% of everyone alive in that generation. The other fifth never appear in this person's tree, however far back it goes.
That 80% is not an accident of the simulation. The statistician Joseph Chang proved the same result for this model in 1999: far enough back, a randomly chosen person is an ancestor of everyone alive today with probability of about 0.8, and otherwise an ancestor of no one alive at all. The fifth of the population missing from one person's tree is missing from everyone's, a result the simulation reproduces independently.
Real populations are not like this model. People mostly marry near where they live, and whole regions were isolated for centuries, which slows the mixing. The model shows the mechanism, not the timing.
When everyone's trees meet
The timing was estimated by Douglas Rohde, Steve Olson and Joseph Chang in Nature in 2004, with a model that added geography: people living on continents, mostly marrying locally, and occasionally migrating. They estimated two dates: when the most recent common ancestor of everyone alive today lived, and the "identical ancestors point" — the date before which every person who lived was either an ancestor of all of us or of none of us.
| Model | Most recent common ancestor | Identical ancestors point |
|---|---|---|
| Detailed simulation, low migration | about 1415 BC (average) | about 5353 BC (average) |
| Detailed simulation, higher migration | as recent as AD 55 | about 2158 BC |
The authors called their simplest estimates "extremely tentative," and the spread in the table shows why; the answer depends heavily on assumptions about migration. They also note that a population isolated for long enough — they give Tasmania as the example — pushes the identical ancestors point back to before the isolation began. In their simulations the common ancestors were nearly always found in eastern Asia, a result of the model's geography rather than a claim about any real individual.
What a family record can and cannot show
Being someone's ancestor in a family tree is not the same as carrying their DNA. DNA passes down in large pieces, and after enough generations most of a person's genealogical ancestors contribute none of it; the 2004 paper makes this point directly. So the arithmetic here is about descent, not genes.
It also explains something familiar from long written genealogies, such as Chinese clan records (族谱), which often trace a family back to a single distant founder. Whatever the documentary evidence for any particular line, the arithmetic guarantees that going back far enough, many lines converge on the same people. A claim of descent from one person who lived fifteen centuries ago is, in that sense, plausible for a great many people at once — even where no single line of the record can be checked.
How the numbers were worked out
The doubling and the crossing dates are arithmetic, counted back from 2026 at the stated generation lengths. The population figures are from the Population Reference Bureau's estimate of how many people have ever lived, and from the range of published estimates for the year 1000 compiled in standard references. The generation interval is from a cross-cultural review in the American Journal of Physical Anthropology (2005). Charles II's figures are from Alvarez, Ceballos and Quinteiro in PLoS ONE (2009). The 80% result is from Chang's 1999 paper in Advances in Applied Probability, and the common-ancestor dates from Rohde, Olson and Chang in Nature (2004); both papers were read in full.
The simulation was run on 21 September 2026: one starting person, parents drawn uniformly at random from a population of fixed size in each earlier generation, and a count of distinct individuals per generation, for populations of 10,000 and 1,000,000. Another random seed moves the figures slightly but not the shape of the result.
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