Every time there's a discussion of Adam and Eve, someone who doesn't understand the biology will inevitably bring up ‘Mitochondrial Eve’ (or sometimes ‘Y-chromosomal Adam’) as though this is somehow relevant to the Biblical fictional characters.
It has been shown by geneticists that all living human beings on the face of the earth today, based on their mitochondria in our cells, are descended from the same woman. There is literally a mother somewhere in the distant past of the entire human race. Scientists have called her the Mitochondrial Eve. They don’t think that this is the Eve of the Old Testament because they would say this woman was just one of probably thousands of women who existed at that time but remarkably if there were all these other thousands of women their descendants have all died off somehow in the course of history and everybody that exists today is a descendant of this woman who actually lived at some time in the prehistoric past.
Craig can rarely be accused of getting the science correct, and this is no exception.
Mitochondria reproduce themselves asexually and are inherited solely from mother to child; sperm do contain mitochondria, and these do enter the egg, but it turns out that in humans and most animals, the paternal mitochondria are tagged and destroyed, leaving only the maternal ones in the offspring. Accordingly, each female line of descent represents a tree of mitochondrial populations, which can be reconstructed by tracking the individual mutations in the mitochondrial genome.
Craig's fundamental mistake here is in conflating “descendants” and “female-line descendants”. ‘Mitochondrial Eve’ was just one woman out of many thousand alive at the time, and most of those women are also ancestors of everyone now alive, it is simply that the lines of descent to us from those other women all contain at least one male, breaking the line of mitochondrial inheritance but not that of the nuclear genome, which derives from both parents.
One simple way to understand how this works is by analogy with surnames. If we assume an idealized version of the English surname tradition, in which all children take their father's surname and no surnames are ever invented or changed, then surname inheritance works exactly like mitochondrial inheritance except with the sexes interchanged. So, out of my 16 great-great-grandparents, while I'm a descendant of all of them, I only take my surname from one of them, namely my father's father's father's father; as we trace ancestry further back, the number of people who are my ancestors in each generation increases, but there remains exactly one person in each generation who determines my surname.
A consequence of this is that surnames go extinct over time. In every generation going into the future, unless the population is exponentially increasing at an unsustainable rate, then the probability that in some generation, all holders of a particular surname are female (and thus fail to pass it on) converges to 1 eventually, for all surnames except the last surviving one.
For exactly the same reason, the existence of a ‘Mitochondrial Eve’ (henceforth MEve) in any real sexually-reproducing population is a mathematical certainly (the only way to avoid it would be to allow unbounded exponential growth, which is clearly impossible). The only question is how far back you need to go.
If we trace back all ancestors, not just female ones, then as the number of ancestors increases in each generation, an odd thing happens: at a certain point in the past, everybody now alive turns out to have exactly the same set of ancestors in that generation. This is called the “identical ancestors point” and for humans it may have been as recently as 8,000 years ago (though there is considerable uncertainty). This is more than an order of magnitude more recent than when MEve lived; so we can be absolutely certain that in her time, everyone then alive was either the ancestor of everyone now alive, or nobody now alive.
How do we know that the other women alive at the time also left descendants (just not in the unbroken female line)? That's shown by the studies (which use nuclear DNA, not mitochondrial) of past effective population size. One woman can't have descendants from more than a dozen or so men, which would mean a population bottleneck much more than 100 times smaller than the one which we actually observe (the human effective population size has never been below about 5,000).
Exchange sexes and all the arguments above apply to Y-Chromosomal Adam too. While some earlier studies placed YAdam and MEve at very different time periods, more recent ones give date ranges for them that at least overlap. However, this does not mean that they were actual contemporaries; we're talking time periods of thousands of generations, making it highly unlikely that YAdam and MEve were actually alive at the same time.
There is a real howler in the Q&A part of Craig's post:
Question: I don’t believe it is in this article that you mentioned in Science News but other articles have mentioned that the geographic location has been narrowed down. I don’t know if anyone else has more information on that but other articles I have read have narrowed it down to somewhere in that Middle Eastern region. They do that through lineage and they finally get down to that area. They can only narrow it so much.
Answer: Obviously we are talking here rough estimates of age and region but nevertheless it is very provocative, I think, and welcome news.
The location where MEve lived is known with some certainty from the distribution of mitochondrial haplotypes: she lived in East Africa, possibly the African Great Lakes region (modern-day Kenya, Uganda, Tanzania, DR Congo, etc.). In particular, MEve lived before the migration of modern humans out of Africa. No study has ever suggested the Middle East as a possible location.
So Craig's answer here is one of two things: either he knows nothing and is bullshitting, or, far more likely, he knows perfectly well that the questioner is wrong (seriously: that MEve lived in Africa is one of the most widely-known facts about her) but he's being ‘economical with the truth’ because (a) apologetics and (b) his post at Talbot School of Theology which has this ‘faith statement’:
The Scriptures of the Old and New Testaments are without error or misstatement in their moral and spiritual teaching and record of historical facts. They are without error or defect of any kind.
More Misrepresentation of Minimal Population Size
Craig in the other answers goes on to cast doubt on those studies that estimate minimum population sizes. First, Craig starts by misrepresenting the actual minimum sizes from the studies: he says “two thousand”, when in fact the usual minimum figure is more like 5,000 to 10,000. Second, he fails to point out that these are effective population sizes, not census sizes; effective population size is smaller than census size often by orders of magnitude (the effective size is the population size that would produce the observed degree of genetic mixing, according to some model, assuming they had discrete generations and perfectly random assortative mating; since real populations mate in ways that produce less mixing, the real population size is larger). Third, he claims that variation in mutation rate could change the results; but the change required is more than three orders of magnitude, and this discounts the fact that there are several techniques for estimating minimal population sizes and most don't depend on mutation rate. In fact similar results are obtained from studies that use Alu insertions or linkage disequilibrium.
(For a full account of what Craig gets wrong, Dennis Venema has a long series at Biologos starting here.)