As long as aliens don’t kill off a significant fraction of human females or we don’t kill ourselves in the billions, future MtEve for all future humans won’t exist.
If technologically advanced aliens do invade earth, MtEve will most likely come from North America or some parts of Europe since that’s where the best weaponry and militaries are. My continent won’t survive an alien onslaught.
It is more like a dynasty.
So the current MT Eve will always be an ancestor of everyone’s MT, but the individual that people will call MT Eve in 7022 will be another woman because MT Eve is the individual that is the most recent common ancestor of everyone’s MT. Her mother, great grandmother gr…. are also ancestors and were once MT Eve themselves
Strictly speaking not all the females in that lineage would have been MT Eve since it changes on the extinction of alternative lineages, which doesn’t happen every generation.
Kind of like a dynasty 
I’m trying to understand the statistics here. Is this correct?
For mitochondria (as for Y chromosomes) we can neglect the possibility of recombination. Concerning any woman alive n generations ago, for n > some not very large number it will almost certainly be the case, either that her line of descent has died out, or that every person now alive is descended from her (apart from possible quibbles about effectively isolated populations).
Now consider her all-female line of descent. In any generation, there is the possibility that it will become extinct, and is possibility is much greater than the possibility of extinction of her line of descent as a whole. For this reason, the number of women with descendants in the all-female line will be decreasing fraction of the population as we go back in time, so that almost certainly, far enough back, we are back to a single one, and all current mitochondrial diversity has arisen through mutation since her.
And (here I find myself in the ridiculous position of disagreeing with Joe) this is true of mitochondria, but not of cytochrome C, since the DNA encoding for cytochrome C may well have undergone recombination many times.
Have I got it (more or less) right?
If we consider, not the whole cytochrome C gene, but one site in it (say site 17), then we can ignore recombination. Its genealogy is then a tree which has a common ancestor copy, like Mitochondrial Eve but involving gene copies in both females and males, and about 4x as deep in time.
OTOH, those with the deadliest weapons may find themselves the target of the same. Africa could be relatively safe.
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