Doesn't it mean that she left "no currant descendants" through an unbroken mother to daughter line? She may well have descendants alive but there may have been a generation of all males between her and us. Correto?
"Eve" is the one that
did leave descendants. Her contemporaries that didn't have the particular neutral mutation patterns in their mtDNA that we see today are the ones that didn't. And yes, there could very well have been a "break" in the non-Eve lineages where only males were produced. The .pdf I referenced has a couple of nice diagrams showing how this could happen.
Is there an initial population size where, over enough time, you MUST get down to a single Y ancestor and singe mtDNA ancestor showing in the resultant population? In other words, is this result just what you would expect if the human (for example) population stays not "too" large for long enough?
Not really. I'm not expert at this (pop gen was my second worst course in school, and I have attemptd faithfully to avoid it since), but my understanding is that initial population size doesn't matter - eventually every lineage will coalesce. Remember, we're tracing polymorphisms back in time from current populations. Additionally, it doesn't matter much what the size of the sample of modern populations is - the statistical variance based on sample size, which is usually 1/
n, is only 1/log
n with coalescent theory (don't ask me why). So either way you look at it, population size doesn't matter.
I see this happening by pure chance as once a line happens to encounter an all male (for the mtDNA) generation it is gone and over time we would expect the number of threads of mtDNA to dwindle.
Yeah. The whole concept arose out of pop gen attempts to model random drift.
Has there been any pop. gen work on this?
Tons. Here's a good review: Rosenberg NA and Nordborg M, 2002,
Geneological trees, coalescent theory, and the analysis of genetic polymorphisms, Nature Reviews 3:380-390. That review covers most of the studies up to that point (2002).