elt@astrovax.UUCP (11/19/83)
------------------------------------------------------------------------------ How surprising is it that we should all have a common female ancestor on our pure maternal line within the last few thousand or tens of thousands of generations? Are there any reasonable explanations of this fact? I can think of at least a few: 1) It could be natural selection. If a mutation in mitochondrial DNA gave its possessor a slightly improved chance of survival (=successful reproduction in this context), this could account for the preponderance of that persons descendants. Note that a favorable mutation is much more effective for mitochondrial characteristics than it is for normal genetic characteristics; this is because it is passed on purely and absolutely without dilution by sexual reproduction to all of one's descendants. Thus, a mutation which conferred only a 1 part in 2000 advantage could snowball into a factor of ~100 advantage in 10,000 generations. 2) It could be the result of ordinary statistical fluctuations. The number of offsprings one has in later generations is subject to some sort of geometric (as opposed to arithmetic) random walk process. If our common female ancestor happened to have an unusually large number of female descendants among her children, grandchildren, great-grandchildren, etc. for a few generations then she might have achieved her dominance purely by good luck. I am not sure what one would expect for the results of such geometric random walks; does anyone know if this is a solved problem? It would seem to imply something about the number of people living as a function of the number of generations back one goes. 3) It could be the result of the extinction of all but one line of human descent through statistical fluctuations in a zero growth population. Any population of N individuals which is in steady state (i.e., ZPG) will eventually go extinct due to a fluctuation which takes the population through zero (if there are no restoring forces which couple dN/dt to N). The typical time for this to occur is N generations. In particular, a population consisting of N asexually reproducing individuals will after N generations have a probability of 0.368 of extinction, an equal probability of only having the descendants of one of the original individuals still living, and a probability of 0.264 that the descendants of two or more individuals are still going. Thus, if conditions of order ten thousand generations back were such that the human population were at ZPG with a few thousand individuals, the common female ancestor result would not be unexpected. This explanation would also imply that the ZPG period lasted long enough for there to have been a fair chance of extinction. 4) Perhaps the simplest explanation would be that the race nearly did go extinct for some reason, and that at some point the total female population was very small. In fact all of the above explanations work best if the species was reduced to at least a fairly small population at some point. I wonder if it could be more than a coincidence that the estimated epoch for this common female ancestor (50,000 to 500,000 years ago) agrees roughly with that of the Ice Ages. Please recall in thinking about the above, that *only females* count in these arguments. All terms such as "population", "descendants", "offspring", etc. refer only to women who may be regarded as reproducing asexually for these purposes. Males are sterile and irrelevant by-products from the point of view of mitochondria. Nevertheless, if explanations 2, 3, or 4 were correct, we could very well have a common male ancestor on our purely paternal lines, but there would be no way to find out unless Bill Sebok's Y-chromosone trick could be made to work. Ed Turner astrovax!elt P.S. Some might think it wise to wait and see if the common female ancestor result is really true before worrying about it so much, but I think this approach would be contrary to the spirit of net discussions.