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Old December 14th, 2012, 05:16 PM   #1

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The Ancestor Paradox and Pedigree Collapse


A person's ancestry forms a binary tree. Each person has two parents, four grandparents, eight great-grandparents, sixteen great-great grandparents, etc. The number of individuals in this tree grows exponentially and will eventually become impossibly high. For example, go back 40 or 50 generations and an individual will have a trillion ancestors more than all the people that have ever lived.

To resolve this paradox, Pedigree Collapse has come forth as an explanation. As explained by Wiki:

Quote:
This [ancestor] paradox is explained by shared ancestors. Instead of consisting of all unique individuals, a single individual may occupy multiple places in the tree. This typically happens when the parents of an ancestor are cousins (sometimes unbeknownst to themselves). For example, the offspring of two first cousins has at most only six great-grandparents instead of the normal eight. This reduction in the number of ancestors is pedigree collapse.
Pedigree Collapse is also discussed in this Family Tree Article:

Quote:

What is Pedigree Collapse?

By Diane Haddad
How many ancestors you have doesn't seem like a difficult question, yet genealogists have been attempting to answer it for years. You should be able to double the number of ancestors in each generation (two parents, four grandparents and so on) for 1,024 ancestors in 10 generations. Go back 40 or 50 generations, though, and this formula results in more than a trillion ancestors -- more than the number of people who've ever lived.

What gives? The explanation is pedigree collapse. Rutgers University professor Robin Fox has estimated that 80 percent of historical marriages have taken place between second or closer cousins, causing the same folks to occupy multiple spots on pedigree charts. That means your family tree starts shrinking once you've gone back so many generations.

This genealogical shrinkage makes you cousins with just about everyone. English genealogist, physicist and computer programmer Brian Pears says that "If every single marriage was between second cousins, then 30 generations ago [residents of Britain] would all have needed exactly 4,356,616 ancestors -- still more than the English population at the time."

In 1215, an estimated 2.5 million people lived in England. Pears concludes that each of England's residents in 1300 was an ancestor to nearly every modern Brit. (See his "ancestor paradox" essays here.)

Scholarly research backs him up: In a 1980 Genealogical Demography article "Ancestors at the Norman Conquest," demographer Kenneth Wachter calculated that out of the 1.11 million residents of England at the Norman conquest in 1066, about 86 percent are ancestors to all current residents of England.

In a 1999 paper, Yale University statistician Joseph Chang used a mathematical model to show how all modern Europeans, except recent transplants, have a common ancestor who lived about 1400. Go back to 1000, and 20 percent of adult Europeans alive then have no descendants today, while each of the remaining 80 percent is an ancestor of every European alive today. (See The Atlantic's website for more details.) That's a lot of cousins to look for.

In other words all of us living today are the product of some kind of incestuous relationship in our past, most likely marriage of first cousins.
It appears that all Europeans have at least one common ancestor. However, it is evident that all of us living today are the products of perhaps multiple incestuous relationships, most likely between marriages of first and/or second cousins. It's something to think about and ponder.

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Old December 14th, 2012, 06:02 PM   #2

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This subject has fascinated me since I first heard of it a few years ago. I tend to bring it up when someone makes a claim like "I'm related to William The Conqueror" or some other historical figure as if this is something special. My reply is usually "You and millions of others" before explaining the ancestor paradox and deflating their ego a little.
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Old December 14th, 2012, 06:16 PM   #3

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Originally Posted by Belgarion View Post
This subject has fascinated me since I first heard of it a few years ago. I tend to bring it up when someone makes a claim like "I'm related to William The Conqueror" or some other historical figure as if this is something special. My reply is usually "You and millions of others" before explaining the ancestor paradox and deflating their ego a little.
I could not figure out this ancestor paradox, but this evening I read this article about Pedigree Collapse. It would appear that all European wars were and are nothing more than family squabbles.
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Old December 14th, 2012, 07:25 PM   #4

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Quote:
Originally Posted by Aulus Plautius View Post
I could not figure out this ancestor paradox, but this evening I read this article about Pedigree Collapse. It would appear that all European wars were and are nothing more than family squabbles.
Including WW1 and II
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Old December 14th, 2012, 07:48 PM   #5

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Originally Posted by Ancientgeezer View Post
Including WW1 and II
The interesting thing from the American perspective is how many Americans were actually deployed fighting their cousins or relatives etc. There were thousands of German and Austrian Americans deployed to Europe to bring down "the Hun."

People with such American names as "Eisenhower" (originally Eisenhauer).

That's the thing about America. No matter whose side we take in European wars, somebody is going to end up fighting their distant (sometimes not so distant) family members.
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Old December 14th, 2012, 09:07 PM   #6

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This is true for all wars since we are all one species descended from people in southern Africa somewhere. All people are related.
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Old December 14th, 2012, 11:27 PM   #7
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If we only see it from a "mathematical" point of view a person 1000 years ago or even less could be an ancestor to all humans. I have sometimes read about mithocondrial studies, that some researchers draw a lot of conclusions from. Like "we all come from an africasn mithocondrial "Eve" long time ago - or man "Y-chromosome Adam". But since many familieas have only kids of one sex, boys or girls, such conclusions seems a bit risky to me, but perhaps there is some good explanation they are valid?
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Old December 15th, 2012, 12:42 AM   #8
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Quote:
Originally Posted by Belgarion View Post
This subject has fascinated me since I first heard of it a few years ago. I tend to bring it up when someone makes a claim like "I'm related to William The Conqueror" or some other historical figure as if this is something special. My reply is usually "You and millions of others" before explaining the ancestor paradox and deflating their ego a little.
It sounds to me more like you are fascinated by feeling superior to others.
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Old December 15th, 2012, 02:54 AM   #9

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Everyone being related is by no means a practical reality outside of mathematical equations - because if we look at it realistically, the majority of our ancestors are from the same general areas, with the theoretical number being fulfilled by almost every single one of them fulfilling many (thousands of) places in your ancestor tree, through layer upon layer of incestuous relationship (not necessarily known to them, btw, since few peasants could trace their lineage too far back anyways).
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Old December 15th, 2012, 04:14 AM   #10

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I never ever gave a thought to this and it rather appears very interesting and why I overlooked such a thought puzzles me now ?
So after understanding the logic and interpreting the maths in it , it becomes simpler to explain the existing equality in humans and the fact that none is born inherently great .
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