Here’s an interesting Fermi problem I came up with a while ago that I’m having trouble doing. Since all people share a common ancestry, any pair of people can be described as being nth cousins (and maybe a few times removed, but I’m ignoring that for now). Since humans have only been around for a finite amount of time, there is an upper bound to n. What is it? I can’t seem to be able to come up with a simple population model to estimate with–I always run into a variant of the “I have 4 billion great[sup]30[/sup]-grandparents” paradox.
Anyone want to make an estimate of the “cousin-distance” between me and, say, a dog? a tree? E. Coli?
I once read in a trivia book that n<=41 - i.e. everyone is at least a cousin 41 times removed to everyone else, if not closer. I have no idea if that’s true, or how they came up with that, or where I read it, so I wouldn’t call that conclusive
There is (very controversial) evidence that mitochondrial Eve lived roughly 100,000 years ago. She is the most recent woman from whom we all descent exclusively through the maternal line. We’re talking 5,000 generations, or 5,000th cousins. There’s also Y-chromosome Adam, the most recent man from whom we descend exclusively through the male line. The last I heard, it was believed Adam lived longer ago than Eve. Then there are people from whom we are all descended but not through the exclusively male nor exclusively female line. These people probably didn’t live much more recently than Eve, and almost certainly no more recently than 40,000 years ago (roughly 2,000 generations).
People who are literally 41st cousins have a common ancestor 42 generations back (roughly 1,000 years). It is safe to say that a full-blooded Australian Aborigine and a full-blooded Bantu from Africa do not have such a close common ancestor.
But when figuring relatedness, multiple relations can have an additive effect. People who are first cousins on both the maternal and paternal side (double first cousins) are as closely related to each other as half-siblings are (but that doesn’t mean that they are half-siblings; there is a mailbag article that covers distinctions like this here). It is possible, because of the small size of the early human population, and the interbreeding that ensued over many hundreds or thousands of generations, that all modern humans are as closely related as 41st cousins, but not that they literally are 41st cousins.
As the OP alludes to, we must all be multiply related because there were not enough people living hundreds of generations ago to give us as many ancestors as we would otherwise predict.
In light of bibliophage’s comments, I would like to clarify the OP a little bit. I would like to define “nth cousin” as any pair of living organisms who, by heredity, share 1/2[sup]2n+1[/sup] of their DNA with each other. (I think this gets the common case right; please correct me if I’m wrong).
What I want to know is how to calculate the average and maximum n both within a population that actively interbreeds with each other (e.g. Europe or China) and populations that have common ancestors but which do not interbreed (e.g. native Australians and Africans, or mammals and reptiles).
It’s also possible that person A and B have a common ancestor 41 generations back, and person B and C have one at the same distance, and likewise person A and C, but that it’s not the same common ancestor in all three cases. The common ancestor for all three could be significantly farther back.
While you could, conceivably, figure out the “cousin-distance” to a dog (but I’m not goint to try it), I don’t think it’s well-defined for a tree or a bacterium. The common ancestor to either of those would have been asexual, so “cousin” loses its meaning. I think you’d have to stick to vertibrates.
Bobort, the problem with that definition is that it makes all living things on the planet siblings. Most DNA is common to all living things, and codes for things like breaking down sugar to form ATP and making more DNA. I’m sure that there’s a better way to phrase what you’re trying to say, but I’m not sure what it is…
