[I've posted below the response I gave to an email question about the claim--made by theistic evolutionists at the BioLogos site--that the human species did not begin as a single pair but as a population.]
Your question was whether science had proved as impossible the claim--made by Christians, Jews, and Muslims--that mankind descended from two original humans, Adam and Eve. In particular, you implied that three methods of assessing genetic diversity (as related in a BioLogos post) prove that humans alive today exhibit too much genetic diversity to trace to a single couple.
First of all, let me point out that there is no question of 'proof' here, in either direction. Science doesn't work that way, though the BioLogos folks may not understand such issues. (I, too, am a biologist, and never during my scientific training did I receive any instruction in the philosophy of science, even a basic understanding of what science is, what it can and cannot do. I believe that my experience is the norm today, and so Venema and Falk can be excused for a naive understanding on this issue.)
On large issues in the historical sciences (such as this one), there will generally be a wealth of evidence available and a variety of methods for assessing this evidence. In addition, there will be a wealth of relevant evidence as yet undiscovered. On such questions, science uses abductive reasoning, arguing to the best explanation of all the relevant available evidence. Where that task is difficult--often because the available evidence leads to contradictory conclusions--the good scientist seeks more, better, and clearer evidence and/or methods. And in such cases (even more than usual), the good scientist remains humble, seeking truth rather than trying to prove a theory he holds a priori. When a scientist takes a strong position despite such contradictory evidence, that dogmatism is usually an indication that he lacks the objectivity that accompanies scientific discovery. This sort of dogmatism is apparent in Venema and Falk's article.
At present, there are two lines of evidence that rather clearly point to this... that all humans alive today can be traced to a single female ancestor (through their mitochondrial DNA) and that all males alive today can be traced to a single male ancestor (through the DNA in their y-chromosomes).
Venema and Falk highlight three methods (of analyzing the genetic diversity of living humans) that temper the conclusion of the two studies above.
What are we to make of this? Each of these sets of evidence and the methods used involve assumptions. And each of these assumptions is itself open to scrutiny, testable (to some degree), and (unfortunately) often held with a degree of unexamined faith by its proponents.
I could stop there, leaving it as an entirely open question as to whether the Bible is believable or reliable on this issue. But more needs to be argued on the side of an historical Adam and Eve.*
For one thing, it seems pretty clear that the assumptions associated with the BioLogos claims are less certain and less well-supported than those associated with the y-chromosome and mDNA evidence. As just one example, a study of the genetics of a population of mouflon sheep refutes some of the assumptions of Venema and Falk's methods (method 1 in particular, but all three generally). In this study, a single pair of sheep was introduced to Haute Island (in 1957), and the descendent population grew to 700 and has subsequently fluctuated between 250 and 700. Mathematical models use to predict the present population's heterozygosity (based on the known heterozygosity of the original pair) underestimated it by a factor of four. Had the models been used as in Venema and Falk's argument--to estimate the number of founding individuals by measuring the diversity of the present population--they would have grossly overestimated. That is, this test case shows that genetic diversity increases (at least in sheep, and over a mere 50 years) in ways currently not understood by the relevant experts. Venema and Falk may simply be unaware of such problems with the methods they espouse; nonetheless, their dogmatism is unwarranted.
Secondly, given the vehemence and certainty with which evolutionists claim the truth of their macro-theory, it is rather odd that when such tests finally became available, the evidence led to a conclusion so similar to the Bible's proclamation. Although theists might argue about the details (one pair or a few thousand), there is no one left still arguing for the competing view of human origins, the multi-regional hypothesis (which claimed that Asian, Caucasian, and African peoples descended from different hominid species in different parts of the world). What is agreed upon by nearly all today is that the genetic evidence shows that all humans alive today are descended from a very small population (which may have even been a single pair) living in or near eastern Africa some 40-60,000 years ago. The scientific evidence leaves Genesis 1 and 2 as viable portrayals of the true situation. And where apparently contradictory evidence exists, the assumptions associated with it turn out to be problematic.
There is no scientific evidence that can prove the Bible to be true and reliable about the descendence of humanity from a single pair. Nor is there any scientific evidence that disproves it. As a scientist, though, I have found overwhelming evidence for the truth and reliability of the Bible with many of its other claims, and that evidence has come both from science and history. More importantly, however, I know from personal experience the truth of its central claim, that the holy Creator of the universe so loved His creatures that He sent His eternal Son to make a way for me, a far-from-holy creature, to have a relationship wit Him. In your continued search for truth, I hope you will seek and find this most important truth.
* The humans to which the y-chromosome and mDNA evidence points would not be Adam and Eve but (more likely) Noah and Eve. Biblically, the bottleneck for males was more recent, since all the males on the ark were related to Noah, whereas the four females on the ark were from different families. Interestingly, this aligns with the genetic data as well. The date for mDNA 'Eve' is earlier than the date for y-chromosome 'Adam' (Noah).