Subject: Re: I need information on 'Eve' Date: 5 Nov 91 19:49:10 GMT In article 4124@mrsvr

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From: Charles Geyer Subject: Re: I need information on 'Eve' From: charlie@umnstat.stat.umn.edu (Charles Geyer) Date: 5 Nov 91 19:49:10 GMT Organization: University of Minnesota, School of Statistics Message-ID: <1991Nov5.194910.18293@cs.umn.edu> Newsgroups: talk.origins In article <4124@mrsvr.UUCP>, barbiaux@links.uucp (Bill Barbiaux 4-6031) writes: > This is a request for information about the theory behind a PBS show > I saw awhile ago about what I'll call "genetic tracing", since I don't > know its real name. The show (possibly a Nova special) was about a > technique of genetic tracing which showed that all humans are > descendents of one female -- let's call her Eve -- and this woman > probably lived in central Africa, if I recall correctly. > > The reason I ask is that I was just in a discussion with several > Creationists, and one of them mentioned the show and stated how it > basically showed that the biblical creation story is true. I was > the only other person in the group who had seen the show, and being > the only evolutionist there, I showed how that same data fits quite > well with evolution. Someone else jumped to his defense, and > mentioned a couple articles she had recently read about this > technique, and the authors said that it causes serious problems for > the theory of evolution. She said one of the articles was in > "Science" magazine, I think. First, "Eve" is a notion based on inheritance of mitochondrial DNA (mtDNA), which (unlike nuclear DNA) is inherited entirely from the mother. So looking at mtDNA gives a family tree of "maternal inheritance". It only looks at the maternal lines. There is a similar concept of the Y-chromosome "Adam", but that work hasn't gone as far. Sequencing the Y chromosomes gives information on paternal inheritance. Now suppose we have mtDNA from a bunch of individuals today and we draw a "family tree" like this A ----- \ ----- / \ B ----- \ ------- / / C ----------- (just three individuals A, B, and C, here because character graphics is so limiting). Imagine a big tree with lots of individuals (20 - 30). What this tree says is that all of these individuals are descended from a common ancestor, say E if we label the internal nodes of the tree as follows A ----- \ D---- / \ B ----- \ E------ / / C ----------- and that A and B have a more recent common ancestor D, than either has with C. There was a mutation in E, after which there were two distinct lines, and a mutation in D, after which there were three lines. So far so good. No problems with evolution yet. Family trees are what it's all about, right? Now what about a stochastic model for this process? When was E (= "Eve") alive? This turns out to be a hard problem and simple solutions are available only under the simplifying assumption of constant population size. In that case the stochastic process (the connections of the tree, its "topology" and the branch lengths) is known as the "coalescent. The term and its theory were introduced by Kingman about ten years ago. Under those assumptions all of the tree topologies are equally probable and the times between branchings are exponentially distributed with times that depend on the number of individuals in the tree at that time (and the population size and the mutation rate, both of which are assumed constant). There is *always* a tree. Hence there is *always* an "Eve" (= most recent common ancestor via maternal lines). Even if the population size is *constant*. There were other individuals alive at that time, but their genes have been lost. They have no descendants (through the maternal line). Assuming that we know the population size and the mutation rate we can estimate the time back to E = "Eve" = the most recent common ancestor. This is what the "Eve" work does. Two things to note. 1. The only thing this really "proves" is that the coalescent coalesces. There is *always* a most recent common ancestor, regardless of the population structure. Especially note that *under the assumption of constant population size* there is an "Eve". So this work certainly does not even suggest that "Eve" was the only woman on Earth at the time. 2. The time back to "Eve" is a random quantity, which depends on the matings that have occurred over the years, how many offspring each produced, and what happened to them. If we look at the Y-chromosome Adam, this is a similar random quantity, perhaps with the same expectation, but the actual (not just expected) time back to "Adam" and "Eve" will differ, most probably by tens of thousands of years. They certainly are very unlikely to have been alive at the same time. Doesn't sound much like the couple in the garden of Eden, does it? -- Charles Geyer School of Statistics University of Minnesota charlie@umnstat.stat.umn.edu d

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