Pedigree Collapse

[Arwald]

For a long time I've been interested in the exponentially-increasing nature of our ancestry. When I got into genealogy I wanted to know where every single branch went. And every branch splits into two. I uncovered all sorts of surnames that really meant nothing to our family.  I would draw charts of my ancestors but it became impossible to contain all the different branches. I recently discovered I am descended from two cousins who married each other in the early 18th century. So now I have a weird situation where I have the same people in more than one place in my family tree.

2 parents.
4 Grandparents.
8 Great-Grandparents
16
32
64
128
256
512
1,024
2,048
4,096
8,192
16,384
32,768
65,536
131,072
262,144
524,288
1,048,576
2,097,152
4,194,304
8,388,608
16,777,216
33,554,432
67,108,864
134,217,708
268,435,456
536,870,912
1,073,741,824
2,147,483,648
4,294,967,296
8,589,934,592
17,179,869,184
34,359,738,368
68,719,476,736
137,438,953,472
274,877,906,944
549,755,813,888
1,099,511,627,776
2,199,023,255,552
4,398,046,511,104
8,796,093,022,208
17,592,186,044,416
35,184,372,088,832
70,368,744,177,664
140,737,488,355,328
281,474,976,710,656
562,949,953,421,312
1,125,899,906,842,624
2,251,799,813,685,248
4,503,599,627,370,496
9,007,199,254,740,992
18,014,398,509,481,984
36,028,797,018,963,968
72,057,594,037,927,936
144,115,188,075,855,872
288,230,376,151,711,744
576,460,752,303,423,488
1,152,921,504,606,846,976

I'm sure you got the point a while ago, but as you can see, the numbers involved become astronomically large. I think that last number is 1 Quintillion, 152 Quadrillion, 921 Trillion, 504 Billion, 606 Million, 846 Thousand, 976.

The world population as of today is estimated at "only" 6.8 billion, and that is the highest it's ever been. Yet the further you go back in time, the more ancestors you need.

In the Middle Ages the world population was only 1 billion. But if we could trace our family tree back through 40 generations to arrive around the year 1000 AD, we would have 1,099,511,627,776 different ancestors living at that time - over 1000 times the population of the whole world. How does one resolve this?

Well sooner or later our ancestors have to have inbred. As you go further back in your family tree and climb up the bewildering array of different branches, you will eventually have to strike an example of cousins marrying each other, knowingly or unknowingly. This will mean that the same individuals will begin to occupy more than one "slot" in your family tree.

Theoretically everyone has 8 different Great-Grandparents. But if 2 cousins have children together, then their children will only have 6 different Great-Grandparents. They still have 8 "slots", but the same 2 people will occupy 4 of them.

As you get back to the point where there are over 1 Quintillion different "slots", many of those slots will simply be duplicating the same ancestors.

So if we could trace our ancestry over thousands of years, we would end up with a chart resembling a diamond shape. Our ancestors will double at each generation, until a point of critical mass is reached and we start to uncover inbreeding. Genealogists believe that this point is around the year 1200 AD. As far back as 1200 AD it is possible to have a different individual in every slot, but at that time it become a logical necessity to start to duplicate people.

http://en.wikipedia.org/wiki/Pedigree_collapse
http://www.straightdope.com/columns/read/412/2-4-8-16-how-can-you-always-have-more-ancestors-as-you-go-back-in-time

[Deb D]

Interesting concept, isn't it?

I have a similar situation, where cousins married ... but ... this has happened in virtually every branch of the tree.  My "diamond", therefore, would be considerably foreshortened, wouldn't it?

[Arwald]

Interesting concept, isn't it?

I have a similar situation, where cousins married ... but ... this has happened in virtually every branch of the tree.  My "diamond", therefore, would be considerably foreshortened, wouldn't it?

Yes I think that 1200 AD is just the absolute furthest. That's the point at which you would have to be descended from everyone living on the planet, which is not actually likely. I have already started seeing cousin marriages in the 18th century.

By our standards it seems dodgy, but there probably wasn't anything sick or sinister about it. In tiny rural communities where couples had about 10 children, you were probably bumping into cousins all the time and may not have known. They didn't exactly have much opportunity to meet new people. These families didn't move much.

[Nick29]

It's easily explained.   We all share common ancestors, if you go back far enough.  Out here in the Norfolk/Cambridgeshire Fens, where travelling any distance at all involved using a boat before the Fens were drained, repeated intermarriage between families did cause genetic problems in some cases. 

[msallen]

It doesn't have to be just first cousins marrying. I have numerous examples of 4th/5th/6th/more distant cousins marrying (including my parents who were 5th cousins once removed), and can trace descent from some individuals in the medieval period via a dozen or more routes.

It is almost certain that these relationships were not known of by the couple in the vast majority of cases; but in some others they were, and were even deliberate, in order to keep lands within familes.

[behindthefrogs]

This problem should be attacked from the opposite direction.

For example:

30% of the people in any one generation have no descendants who survived to have children of their own.

Most children were born to parents who lived within a particular community.

Similarly most children were born to parents who belonged to a particular ethnic or religious group. 

The result of this is that the potential number of ancestors for any one person is considerably less than the world population figues would suggest.

David

[ammonite]

Similarly most children were born to parents who belonged to a particular ethnic or religious group. 

however religions have changed over time and therefore people will have links to other religious or ethnic communities. Christianity is only a relatively recent concept so back to Roman times you have intermarriage there. 

So you end up taking the whole of the human race back into consideration.

[behindthefrogs]

I agree but the point that I was trying to make was that for fairly long periods of time a whole group of ancestors would have come from a fairly restricted community.  This reduces the frequently quoted possibility of being descended from nearly everyone in the world only thirty generations ago extremely unlikely, even though the theoretical number of ancestors would exceed the world population.

David