R
rossum
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Your understanding is incorrect. The existence of a Mitochondrial Eve is contingent on the fact that women tend to have more than one child:Consider all the humans alive today on Earth. Put them into a set S.
Next, consider the set of all those women who were the mothers of the people in the set S. Call this set S’. A few observations about this new set S’. It consists of only women (while set S consists of both men and women) – this is because we chose to follow only the mother-of relationship in going from set S to set S’. Also note that not every member of set S’ needs to be in set S – set S consists of all people living today, while some of the mothers of living people could have died, they would be in set S’ but not in set S. Third, the size of set S’ is never larger than the size of set S. Why? This is because of the simple fact that each of us has only one mother. It is however overwhelmingly more likely that the size of set S’ is much smaller than that of set S – this is because each woman usually has more than one child.
Repeat the process of following the mother-of relationship with set S’ to generate a new set S’’. This set will consist of only women, and will be no larger (and very likely smaller) than set S’.
Continue this process. There will come a point when the set will consist of smaller and smaller number of women, until we finally come to a single woman who is related to all members in our original set via the transitive-closure of the mother-of relation. There is nothing special about her. Had we chosen to follow the father-of relation, we would have hit the Y-chromosome Adam. Had we chosen to follow combinations of mother-of and father-of relations, we would have hit some other of our common ancestors. The only reason why the mother-of relationship seems special is because we can track it using the evidence of mitochondrial DNA.
Thus there must exist a single woman whose is the matrilineal most-recent common ancestor of every in set S.
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Also important to keep in mind is that while the final set S’* has only one member (the Mitochondrial Eve), she was by no means the only living woman on Earth during her lifetime. Many other women lived with her, but they either did not leave descendents or did not leave descendents via the matrilineal line, who are still alive today.
Source: What, if anything, is a Mitochondrial Eve?
The presence of other women at the same time is shown by the evidence for genetic bottlenecks in the human populations. This is determined by the amount of genetic diversity present - the smaller the population the less the genetic diversity. For example, Cheetahs had a severe genetic bottleneck during the last Ice Age. As a result they have a very low genetic diversity and it is possible to graft skin from one Cheetah to another without fearing rejection because they are all very closely related.
The amount of genetic diversity in human populations is too large for there to have been a bottleneck of either eight people (Noah and family) or two people (Adam and Eve) in the last seventy thousand years.
The smallest figure I have seem for a human genetic bottleneck is between 1,000 and 100,000 breeding pairs about 70,000 years ago, associated with the Toba catastrophe.
It is also worth bearing in mind that the Y-chromosome Adam (the patrilineal equivalent of the Mitochondrial Eve) lived between 90,000 and 60,000 years ago. Mitochondrial Eve lived about 140,000 years ago, so there were at least 50,000 years between them - they never met.
rossum
