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#45
09-25-2012, 05:59 AM
 Aspidistra Member Join Date: Feb 2001 Location: Melbourne, Australia Posts: 4,434
Quote:
 Originally Posted by Blake I can't make sense of this. To start with, I can't see any possible way that every kid would share at least one parent with every other kid. It seems mathematically impossible since there are a minimum of 4 children, but a maximum of 2 permutations of parents John and Jane have a kid: Bob Kath and Ken have a kid: Carol Kath and John then have a kid: Ted Jane and Ken then have a kid: Alice Ted doesn't share any common parentage at all with with Alice. Ted's parents are Kath and John. Alice's parents are Jane and Ken. Ted and Alice are genetically utterly unrelated. In order to find a path from each living person to every other living person within this group, you will need to go back and find an ancestor that is shared by both Ted and Alice. If John's Grandfather and Ken's Great Grandfather are the same person, Engelbert, then you will have a path linking all these people. But that would make that Engelbert the MRCA . If we mapped out every lineage going back 4 generations, the only way we I can see that we could have enough people to connect everyone in at least one manner is if the MRCA occurred within four generations. I'm guessing I'm missing something here. Perhaps you are working form a position that "step sibling" or adopted sibling or other relationships that have no objective or genetic basis are sufficient to establish a relation chain. But I don't think that's what the OP wants. Since he is talking about incest, relationships that only exist culturally, with no genetic relationship at all, hardly seem to fit.
His point is valid, even though the example given may not work exactly. The simplest example of it that I can devise involves 15 people:

Generation 1:
Alan and Barb have two kids - Geoff and Heather
Carol and Doug have two kids - Ian and Jane
Emma and Fred have two kids - Karen and Luke

Generation 2:
Heather and Luke have a kid - Mark
Geoff and Jane have a kid - Nick
Ian and Karen have a kid - Olivia

Now Generations 1 and 2 die. Everyone left (Mark, Nick and Olivia) is a first cousin to any other person, even though the MRCA is more than 2 generations back - in fact, an arbitrary number of generations greater than two back, since we know nothing about the genetic separation between the people in gen1.

Obviously the modelling of this over the entire population of the world is incredibly complex, but I would pick 30 or less as the most likely number that constitutes a factual answer to the OP's question. 30 generations back gives you a number of ancestors (1 billion) which is roughly double the world population at the time (about half a billion or less in the 15th century) - I would call that more than enough to ensure that at least one of those ancestors was shared between every two people on earth, even if it's not the same ancestor for every pair.