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Thursday, May 28, 2009

Determing Average Number of Descendants

Dianne asked
In studying a certain ancestor of mine, I determined the need to know the following: How many others have this same man as their ancestor? Or how many descendents on average would one ancestor have after nine generations?
Dianne, it is impossible to calculate an average number of descendants. Let me give you some examples of the difficulties in working out such a mathematical result:

1) We have no way of knowing how many children each generation will have
2) We have no way of knowing how many of the children in each generation live to adulthood
3) We have no way of knowing how many of the children in each generation married and had children or conversely how many lived to adulthood and did not marry and have children.
4) Not every person in each generation will have the same number of children

So how do you determine what numbers you will use for your calculation? Answer: You can't.

Putting it another way, let's assume that Ancestor A has 4 children - B, C, D & E. (of course he could have had 1, or 6 or 12 or..... do you see the difficulty already and we are only at Generation 1)

If each of Ancestor A's 4 children had 4 children that is 16 people in Generation 2

What if Ancestor A's 4 children had 10 children each? That is 40 people in Generation 2!

What if Ancestor A's 4 children only had 1 child each - then we only have 4 people in Generation 2.

What if Child B had 4 children and Child C had 2 children while Child D had 8 and Child E had 10? Now you have 24 people in Generation 2.

And so we are in trouble right at the start. With each succesive generation you cannot assume that each person had the same number of children! And the more generations you use (you wanted 9) the more variable the numbers become.

Now, if you chose to say "I am going to assume that each generation had 4 children. How do I determine how many descendants this makes after 9 generations" then, you can do that by simply mulitplying 4x4x4x4 and so on, 9 times. The answer then is 262,144 descendants.

But to show you the huge difference depending what number of children you decide to use, if you chose to assume that each generation only had 2 children, your result after 9 generations would be 512.

I hope I've convinced you that it is impossible to determine an average number of descendants for one person.

1 comment:

  1. Actually, it is possible within certain limitations. Say if you had an ancestor, who had emigrated and came to a land were records were poorly kept or non-existence and for whom during the previous six generations prior to emigration excellent records were kept (baptisms and wills). You could (using the good records) compute the average number of children (and depending on how extensive the records were, how many children in each generation had children also) per generation. Then, using your averages (with margins for errors), you could develop an algorhythm to determine a probable number of descendants.
    The caveat here is that these conditions would need to be met and that's an unusual scenario. Also, it could only give you a probable estimated number of descendants. There would still be a lot of contingent factors, but it would constitute a good, rough sketch because it is based on a set of known data, namely the good records prior to emigration.