Pedigree collapse calculator: ancestor slots against world population

The calculator does two jobs. The upper part doubles your ancestor slots, generation by generation, and sets each total beside an estimate of the world's population at the time, to find the generation where the slots outnumber everyone alive. The lower part, under "Collapse in your own tree", measures repeats in a real family tree: give it a generation and the number of different people you have found there, and it returns the share of slots filled by people who appear more than once.

Slots, not people

Call your parents generation 1, your grandparents generation 2, and so on. Everyone has two parents, so generation g has 2^g places: 2, 4, 8, 16, 32. Genealogists call them slots, because nothing guarantees a different person in each one. Adding the generations together gives every slot from your parents up to generation g:

2 + 4 + 8 + ... + 2^g = 2^(g+1) - 2

Check it at generation 3: 2 + 4 + 8 = 14, and 2^4 - 2 = 16 - 2 = 14. The table's column "All ancestors to here" is this sum. The table lists every generation up to 10, then every fifth, and the chart draws slots and population on a log scale, where steady doubling shows as a straight line.

From generations to dates

The tool places generation g at your birth year minus g times the generation length. How long is a generation? Jack Fenner (2005, American Journal of Physical Anthropology) estimated human generation intervals from marriage and childbearing ages in nation states and in hunter-gatherer societies. He concluded that male lines run about 31 or 32 years per generation, female lines 25 to 28, and both sexes together 28 to 30, and the genealogical studies of Iceland and French Canada that he compared gave similar figures, apart from a longer male interval in the French Canadian data. The default of 30 years sits at the top of his overall range. The menu runs from 20 to 35, so a straight surname line can be tried at 31 or 32 and a mother-to-daughter line at 25 to 28.

Where the slots overtake the world

The population figures come from Our World in Data's long-run series, which combines the HYDE 3.3 reconstruction, Gapminder and the UN's World Population Prospects 2024. The tool stores eighteen values, rounded to the nearest million: 1000 BCE, year 0, 500, every century from 1000 to 1700, every fifty years from 1750 to 2000, and 2023. Between them it draws straight lines. Figures for the medieval world are reconstructions with wide uncertainty, so read them as orders of magnitude.

Worked example: the default setting

The tool opens with a birth year of 1990, 30 years per generation and 40 generations charted.

1. Generation 28 lands in 1990 - 28 × 30 = 1150. It has 2^28 = 268,435,456 slots. 1150 is halfway between the stored values for 1100 (398 million) and 1200 (445 million), so the population is 398 + 0.5 × 47 = 421.5 million. Slots are still fewer than people.
2. Generation 29 lands in 1990 - 29 × 30 = 1120, with 2^29 = 536,870,912 slots. The population is 398 + 0.2 × 47 = 407.4 million. The slots now outnumber everyone alive, and the tool reports: by generation 29, around 1120, about 537 million slots against roughly 407 million people.
3. The slots from generation 1 to 29 add up to 2^30 - 2 = 1,073,741,822, about 1.1 billion.
4. The last charted row, generation 40, falls in 790 CE: about 1.1 trillion slots against about 294 million people.

Generation 29 falls between table rows 25 and 30, so read the crossover from the sentence above the table. Try other generation lengths and the crossover stays at generation 29 for every option in the menu; only the date moves, from 1410 at 20 years to 975 at 35 years. Across those dates the tool's population figures all lie between 2^28 and 2^29, roughly 268 to 537 million.

What collapse means in a real tree

The crossover is a ceiling, not a forecast. Real families married within a parish, a valley, a faith or a trade, from pools far smaller than the world, and cousins married, so the same people fill several slots long before generation 29. That is pedigree collapse, also called implex. The tool measures it as:

collapse % = (slots - different people) / slots × 100

The default is generation 5, your great-great-great-grandparents: 32 slots, 30 different people. (32 - 30) / 32 = 2/32 = 6.25%.

One way to get those numbers: your parents are third cousins. Third cousins share a couple four generations above each of them, which is generation 5 for their child. That couple fills four slots, each partner twice, so 32 slots hold 30 people. Their own parents repeat in generation 6, where 64 slots hold 60 people, and the share stays at 6.25% upward unless other loops add to it. Our explainer on pedigree collapse follows a first cousin marriage the same way.

Two cautions when you enter your own count. Only repeats count as collapse: if you have identified 20 of 32 people and the rest are unknown, the unknown slots are gaps, not repeats. And a number larger than 2^g is cut back to 2^g, which shows as zero collapse.

Questions

Does 6.25% collapse at generation 5 mean my parents are related?

Not necessarily. Parents who are third cousins give that figure, but so does a grandparent whose own parents were first cousins: their shared couple also sits at generation 5 for you and fills four slots. In the first case your inbreeding coefficient from that loop is 2 × (1/2)^(4 + 4 + 1) = 1/256; in the second it is 0, because the loop closes above your grandparent, not between your parents. The percentage counts repeats and does not say where they occur, which is why Wright's path method, set out in the coefficient of relationship, worked out by hand, is the better guide to genetic effect.

How exact are the population numbers?

They are estimates, and the tool draws straight lines between the stored years: every ten years since 1900, every fifty or hundred before that. In the twentieth century that tracks Our World in Data's yearly series closely; in earlier centuries the gaps are wider, but the crossover does not depend on the fine detail, because by then the ancestor slots are doubling far faster than any population could grow.

What generation length should I choose?

For a mixed tree, 28 to 30 years follows Fenner's overall estimate. For a line through fathers only, try 31 or 32; through mothers only, 25 to 28. Your own records are better still: average the gaps between parents' and children's birth years along the line you are studying.

Can I find how two people in the collapsed part of my tree are related?

Yes. Count the generations from their shared ancestors down to each of them and enter the two counts in the cousin calculator.