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Comment by lolinder | Hacker News Reader

If you actually go back and look at who those people are, though, you likely don't have anything like as many as calculated, because your family isn't so much a tree as a DAG—there's plenty of duplication.

For example, my wife and I recently discovered that we're sixth cousins. This means that when our kids trace back their ancestry, there's an entire subtree on my side that is duplicated on her side, which dramatically shrinks the number of ancestors down from the theoretical maximum. And this is far from an uncommon occurrence—we most likely have many other subtrees in common that we simply don't know about.

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My parents are related through one set of grandparents four or five generations back.

My wife and I are related through the same grandparents.

These are weird, but it makes sense - we're from smaller towns, which were settled not that long ago in the grand scheme of things. If you trace enough of us back, we're all probably related.

But the seriously trippy part is - my younger sibling and their spouse are related through the same great(x4 or so) grandparents. The sibling is from a different country that isn't even close to where we're from. Like literally the other side of the planet.

It blew my mind.

If one of you is from one corner of the former British empire and the other from another corner, it becomes a lot less surprising. The British showed out everywhere the past ~400 years and often forcibly relocated certain subjects (e.g. the Irish).

My old man, bless him, found one instance of inbreeding going back to 1800 for each one and going back to 1700 on a few.

My son's mother's ancestry is very different from mine.

If anything I think we might live in period of the greatest number of long distance gene flow events in history. And I think this has been true for hundreds of years at this point.

EDIT: That's not to say inbreeding doesn't hugely reduce your number of ancestors, just that the modern world for many social groups has much less inbreeding than earlier societies.

OK, so this is the key assumption that does not hold up in the real world?

> With fully random matings the number of your ancestors doubles every generation.

No, because fully random would still cause duplication, because the population of Earth is finite not infinite. With matings specifically selected to create no common ancestors back to X generations, then you theoretically have 2^X ancestors.

I'm kinda grokking it but still have no clue how far off the calculation is. To go back to the blog title, are you saying that the number of your ancestors is more like hundreds rather than thousands? Or is it just impossible to even put a number behind it due to how complicated the real-world relationships are?

Edit: Just saw your other comment here. The answer seems to be more along the lines of "impossible to put a number behind": https://news.ycombinator.com/item?id=37387655

The latter. It's impossible to make any generalizable statement about everyone's ancestry, you really have to look at the family tree and count them up one by one.

People whose families have been in one place for generations are much more likely to have a smaller set of ancestors than people whose families migrated many times over the last few centuries. And any given person's family tree is likely to have some subtrees that were sedentary and others that migrated, further complicating any attempt at an abstract calculation.

Fully random only appreciably diverges from 2^n when 2^n becomes a sizable share of the world's population.

When the population is roughly 2^2n, you expect to lose one ancestor in that generation.

It absolutely does not. Going backwards in time like this, most people will have many generations where the number of their ancestors in that generation go down, not up.

For the majority of the past four thousand years, almost everyone lived in farming villages that had ~50-100 families living in them, and mostly married inside those communities. Even just going to a neighboring village for a bride was something that only happened occasionally, but even when that happened, it was almost always the same few neighboring villages. This means that when you trace ancestry backwards, you always end up related to everyone living in a few villages, and then every few generations this extends to a new village. Then if you are related to a successful trader or soldier or something, it will suddenly double the amount of ancestors in a generation, but I really need to stress that this is rare.

The introduction of the bicycle did a lot for reducing inbreeding in farming communities, because it was something that a normal people could own, and allowed day visits to neighboring communities. Before that, it was entirely ordinary to live and die without ever traveling more than 10 miles from the place where you were born.

I guess it doesn't, or you could go back to the time where the early human lived expecting an astonishingly high number too, or even before the big bang if you wanted.

We are all basically sixth cousins from what I've seen written.

As long as you're comparing two people from the same country and ethnic group (which tend to be the most common pairings for childbearing), it's pretty close to true. It doesn't work so well if you're comparing people on different continents.

A country is too big. The number of 6th cousins somebody has is on the order of thousands. If you're from a small town with stable population (people haven't moved in or out much for the last couple hundred years) you might be 6th cousins with pretty much everyone.

many earlier societies had traditions of inter-tribal wife-stealing .. farmer cultures with socially important grandmothers practiced social interchange.. meanwhile, opportunistic breeders often physically moved around and did not have stability patterns.. this is a massive subject, not possible to talk about without errant conclusions and misstated sub-parts, right?

None of that changes the math of how many cousins you have.

Agreed, sixth is too close to be "everyone" in a country, but the general principle is accurate: we tend to have closer common ancestors than we might think.

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