# Count of ancestors exceeds world population?

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I've got a puzzle for the geeky genealogists.

The number of direct ancestors doubles every generation -- two parents, four grandparents, eight great-grands, etc. I have the names of all sixteen of my great-great-grands. Beyond them there are a few holes in the tree.

So with a doubling every generation in eleven generations we pass a thousand direct ancestors, in 21 generations we pass a million, and in 31 generations we pass a billion.

31 generations will take us back to about 1100 AD (to use round numbers). So in that year I have about a billion ancestors. Except the world population was only about 350 million. Hmm.

In my genealogy databaase there is one case where second cousins married. I can subtract two ancestors out of the great-grandparent generation. There is also the case where an ancestor had two wives. The great-grandson of the first wife married the granddaughter of the second wife. I can subtract one ancestor out of another generation. Those subtractions propagate back through the generations.

In those 31 generations that makes a difference of about 12 million ancestors, but the number of ancestors still tops a billion. (Aren't spreadsheets fun!)

I tried a mathematical experiment. What if a certain number of each generation were duplicates -- their descendants (along my direct line) intermarried and they didn't need to be counted twice in the number of ancestors. Such duplication is plausible in small communities with a lot of intermarrying. I started this in generation 11 and propagated it through generation 31. Yes, it helps -- the number of ancestors is no longer above a billion, but it is still at the level of world population.

I changed the number of duplicates to 4, then to 2. When half the ancestors in each generation were duplicates the number of ancestors in generation 31 were down to 2.5 million. Compared to the population of Europe (71 million in 1350 and where my ancestors are from) this begins to sound plausible in terms of population. Does it make sense in terms of a rate of intermarrying? Alas, my data of direct ancestors ends at about 1600.

The actual formulas:

Strict doubling:

cell A3 = A2 * 2

Accounting for duplicate ancestors

cell B12 = (B11 * 2) - (B11 / 2)

If I'm generation 1 then I determined generation 12 was born in 1600. For every generation further back I subtracted 25 years, so generation 28 was born in 1200.

Now on to the question that prompted all that musing. If my direct ancestors in 1100 numbered 2.5 million, what are the chances one of them might be a king?
I am somewhat new to this, but have been at it hard enough that I’ve read about pedigree collapse and in fact I can get back 30+ generations on some of my lines due to having royal ancestry. It is fascinating to be able to look back so far and to read about these people on Wikipedia LOL. Based on the pieces of the tree that I have a connection to that I know about, my parents are 18th cousins. I can see back through some of these very ancient lines where I am related to someone through both my mother and my father - a very real look at pedigree collapse for me. The math is interesting, too. I’d be curious to know just how few 28th great grandparents I actually have compared to what it I should supposedly have.
Have to say math has always been my poorest subject and this is way over my head.  I have a lot of French-Canadian ancestry and descend from over 50 families more then once (several three times), and that is just on this side of the "pond". One on my lines goes back into the nobility & royalty and at that point I start duplicating ancestors again, big time. I have not counted those dups.

See the article on why everyone on earth is your cousin (and in particular, the section on pedigree collapse): https://waitbutwhy.com/2014/01/your-family-past-present-and-future.html

by Dennis Wheeler G2G6 Pilot (585k points)
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Great article. Forwarding it to cousins who just couldn’t get the concept of “removed” in a recent conversation around the fire. Thanks, Dennis.
Your calculations leave out pedigree collapse.
by Doug McCallum G2G6 Pilot (556k points)
I'm not familiar with the term. Please explain.
So I Googled "pedigree collapse" -- and that looks to be the same as what I describe as duplicate ancestors. What I'm saying is even with pedigree collapse there is still a great number of ancestors. My formulas indicate there must be a great deal of pedigree collapse.
yeah, in my own tree, I've got a number of different cousins with common ancestors that follow from 3 to 5 separate paths because of pedigree collapse.

And the further back in time you go, travel was much more difficult, and people tended to marry within their own immediate communities, so neighbors and cousins, etc. And cousin marriages weren't frowned upon, like they are today (or the mid-1900s).
Paul, pedigree collapse is exactly what you are describing, and yes, the math proves that there had to be many occurrences.  There's a lot of info on the web if you look through all those hits you get when you Google the term.  For example, there were some societies and cultures in history where people were required to marry within their family, for example to preserve the purity of a "royal" blood line.  And in small rural communities before people had the capability to travel far, cousin intermarriages were not so rare.
Now that I know the term I'll be doing more research into the idea -- and maybe give my spreadsheet another workout.
Siblings mostly have the same ancestors. All my cousins share half my ancestors, etc. My father's pedigree collapses several times just between now and the American Revolution. Small communities see lots of it. My wife and I have been surprised that we only have 1 and maybe a second, common ancestor since Europeans started coming to North America.

Another way to look at it is in the number of people descended from the original Mayflower passengers.

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