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Archiver > CUBA > 2001-09 > 0999880185


From: "Hilda B. Pomares" <>
Subject: [CUBA-L] Are we all related?
Date: Fri, 7 Sep 2001 12:29:45 -0400


I found this article and thought you would like to see it.
Regards
Hilda
So is everybody related, then?If one calculateds the number of ancestors, then it is evident that this number increases strongly (exponentieally) with the number of generations. In generation 10 we have room for more than 1000 ancestors, generation 20 contains more than a million, and in generation number 30 we will have passed the 1000 million (some people say milliard, other billion) mark. 30 generations ago, that would have been around the year 1250, we did not have that many human being walking on earth! The solution to this paradox is of course that in the older generations, there will be more and more ancestors from which we descend in multiple ways. We are being saved by inbreeding, so to say.
The nicest result of this paper is that the authors have looked at S(n), the part of the individuals from the oldest generation that is not related to a child (chosen beforehand) from thae last generation. This has been done for a population of 32768. (This is equal to the numer of ancestors in generation 15).

When n = 1, then S is almost equal to 100%. In the oldest generation we have 2 ancestors (the parents), and we have 32766 persons from which the child does not descend. In a pedigree without any "inbreeding", a child in the youngest generation only has 1024 ancestors (this is about 3% of the total) in generation 10, so we have approximately S(10) = 97%. But then things change fast, because we are getting nearer to generation number 15. For n = 15, about half of the people in the oldest generatino is an ancestor, at generation 20 this number has grown to 80%, and then it stops.

Even if we let the simulation run indefinitely, still S = 20.3% will be the limit. This is telling us that one fifth of the people from the oldest generation does not have descendents at present, these branches have died out. The larger the number of persons in the group, the longer it takes to reach this limit, but it can't be avoided. We have to conclude that we are not related to all people, but we are related to a large portion (80%)of the people that lived long ago!




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