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Originally posted by dashen
You should divide it every average generation. For instance, every 40-60 years you should kill off that generation, as that was the average life expectancy for the past few thousand years so every generation or so. Also you must factor in plagues, wars, and mass deaths every so often to account for population dropoffs. Then maybe you might start arriving at some interesting numbers. Also, many children over time have been born illegitamately, so factor that in too. Moreover, tracking back bloodlines will yeild many sources coming back to many differing reigions. Also, perhaps starting this equation solely from the bottom is erroneous. If you start with the assumption that ensuing generations came from a small limitied population perhaps you should work the equation from both ends as to meet in the middle. Hope this helps some how.
[edit on 10-6-2009 by dashen]
Originally posted by dashen
reply to post by spy66
That's why i think that there is reason to start with a hypothetical minimum of original points at the top of the equation, and you at the bottom and work your way to the middle. Logically it should look like a bell curve over time. And yes, you should very well expect much incest going back, that is how thing get back to normal after population dropoffs happen. And I do not mean proper incest, but first cousins reproducing will make a larger dent in the equation than you think.
[edit on 10-6-2009 by dashen]
Originally posted by GEORGETHEGREEK
reply to post by spy66
There is a multitude of factors omitted here that make your initial assumptions poor in calculating with any degree of accuracy.
I will not even get into the trouble of mentioning the first couple one that sprung into my mind since it very soon become chaotic and its almost impossible to render a mathematical formula that represents reality/history.
However statistics which is a science by its own right may give you a hand of help when considering this more thoroughly.
Another hand of help i would suggest is using the knowledge of the human genome through the knowledge of DNA as a tool. I have read an article on DNA and all the past of our history it unfolds to us.
My guess is getting to study what the DNA has to offer in finding the answer you are seeking. I think it will complement your requirements if it does not fulfill them all together!
Take care !
Originally posted by jimminycricket
Well, just a simple look at it, would be..
You need 2 people to make you..
They needed 2 to make each of them...
and so on, so it's a
2 ^ N issue
If we go back 8 generations,
2 ^ 8 = 256
If we go back 50, it's
2 ^ 50 = 1125899906842624
Of course there are many other things to take into account, as you say, like inbreeded, deaths, multiple children and so on, but if we say 50 generations at average age 25 of giving birth, that's only 1250 years...
I rushed a little on the math here, excuse me if I'm not quite spot on, but I think what you are asking for is the
2 ^ N
part.
Originally posted by jimminycricket
Sorry, I edited my post a few times to try and make it clearer, I'm not very good at explaining math.
basically, you substitute N for your number of generations, and you can use a calculator to work it out, most calculators will have a button, usually marked as x ^ y, power, or exponent.
numAncestors(descendant, n)
if descendant.visited == true return 0
descendant.visited = true
if n == 1 return 1
return numAncestors(descendant->mother, n-1) + numAncestors(descendant->father, n-1)
Originally posted by tmk81
Someone posted a similar question here: Population Numbers: Something is not right here.
Here is what I have learned about this problem:
Ancestors from different lines are not necessarily unique as pairing of relatives could allow for less than the upper bound of 2^(n-1) ancestors in the nth generation (assuming the first generation is oneself); for example, the ratio could be 510:1 in the 10th generation if there are two cousins in the 8th generation. This is known as pedigree collapse [1].
As a previous poster has mentioned, a way to visualize this is to follow two lines on a family tree; going back far enough these lines will intersect at a common ancestor. These intersections cause a divergence from the geometric progression 2^(n-1) and eventually the tree collapses to an identical ancestors point which for the current world population has been estimated to be between 5,000 and 15,000 years ago [2,3] with a population between < 1 million and 25 million [4,5].
Here is a recursive procedure to calculate the number of ancestors in the nth generation:
numAncestors(descendant, n)
if descendant.visited == true return 0
descendant.visited = true
if n == 1 return 1
return numAncestors(descendant->mother, n-1) + numAncestors(descendant->father, n-1)
As seen in this procedure, common ancestors result in some parents not being counted for a given generation i.e. pedigree collapse. If the theory of evolutionary common descent is correct then for large enough n (which depends on the variable rate of pedigree collapse) the tree collapses to the last universal ancestor or to an ancestral gene pool [6].