Ancestors and population paradox: exponential growth

If I have 2 parents, and each of them have 2 parents, each generation back has double the number of members. Thus there are 2^n members n generations ago. 10 generations ago there were about one thousand (1024) people, 20 back were 1 million, and 30 back were 1 billion.

If each generation is about 25 years, then 30 generations ago is around 750 years ago, or around 1250 AD. The entire world population is estimated to be around 300 million people around 1300 AD.

This implies that the number of people in my family tree 30 generations ago (1 billion) is larger than the number of people who existed (0.3 billion).

Does that means that I am equally likely to be descended from everyone who lived 700 years ago?

We’re all cousins!

If my wife and I have 2 kids, and they each have 2 kids, and they each have 2 kids….

My dad, a human geneticist from Honolulu, is visiting me in Seattle. He (and my mom) broke the two kids per family rule: he had five boys.

Comments

• Anonymous
  July 11, 2004
  Too many factors to easily compute this way. For example, what if one woman had a child each with two different men? Those children would share an ancestor, and would make it three people in the previous generation rather than four. Think about polygamy, harems, etc, where one man may have children on many different women. If the group is large enough, that would equal little more than one person in the previous generation (the mother) for each child, since the father would factor out of the equation (see the large portion of Asian people with DNA that can be traced back to Ghengis Khan -- he was prolific enough to essentially wipe himself out of the equation).
  

• Anonymous
  July 11, 2004
  30 generations back there were an unknown number of family members because the ones you calculated were still not born yet. The number you calculated must be the number of members at this moment of time if no one died during the 30 generations. I like to meet your 750 year old grandfather! If someone is married 6 times or they have 10 childeren doesn't influence calculations. The real factors are diseases like the "Black disease" killing 1/2 of earth population at ones.
  
  

• Anonymous
  July 11, 2004
  Some of us are from outer space.
  Really.

• Anonymous
  August 02, 2004
  The comment has been removed

• Anonymous
  August 03, 2004
  The comment has been removed

• Anonymous
  August 05, 2004
  Your also missing another key element - ALL of those people weren't alive all at one time.

• Anonymous
  May 25, 2006
  Today’s sample shows how to create a web crawler in the background. This crawler starts with a web page,...

• Anonymous
  May 27, 2008
  The comment has been removed

• Anonymous
  October 28, 2008
  Your reasoning is seriously flawed. You seem to be under the 'delusion' that all those people were distinct, ruling out the trivial cases like cousin marriages.

• Anonymous
  December 15, 2008
  Hello I am struggling with this notion of not enough ancestors for the decendants. I undersatnd cosuins marrying cousins but in the end are we all traced back to a few common ancestors? So in the end we all are related? What did that person meanthat some of us come form space. Does DNA testing show how many common ancestors there are in the world? blaketaylore@yahoo.com blaketayore.com

• Anonymous
  January 10, 2009
  The comment has been removed

• Anonymous
  January 10, 2009
  The comment has been removed

• Anonymous
  June 08, 2009
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• Anonymous
  June 09, 2009
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• Anonymous
  February 08, 2010
  This exponential theory is fundamentally flawed - it assumes that all couples will have 1 child. If this was the case humans would get extinct. You would need 10 trillion people 1000 years ago to have a population of 6 billion today which after a generation would be 3 billion (as 2 will only create 1 desendant)and after 1000 years there would be no one left. (numbers not precise - only used to illustrate the point). Instead the population is always increasing because people have more than one child so form a population of 300 million 1000 years ago we are now 6 billion. (again rough numbers) To make it really clear, think of it this way, if a couple has 10 children then the 10 children will have come from 2 parents - according to the flawed logic of this article they would have come from 20... Its really simple, no aliens or inbreeding...

• Anonymous
  September 10, 2010
  The comment has been removed