This argument has descended into the absurd. I would encourage everyone to take a big step back and deal with the problems in their own camp. Back of a clearly unwinnable argument. There is plenty of blame to go around.
Let us keep in mind that one cannot claim to have ruled something out if one has not considered it. Science does not in any way consider the miraculous creation of Adam and Eve, so it unequivocally has not ruled it out. We can legitimately say that the DNA evidence appears to indicate a large population that shares common ancestry with the great Apes. However, if we believe that God exists and can do miracles, we cannot totally foreclose the possibility more has happened.
To shut down the sincere beliefs of others with the "findings of modern science" as some have done here is to misrepresent the claims of modern science, which does not consider miracles like the special creation of Adam and Eve. That is a scientific error. So, if you care about science, back off the clearly incorrect claims.
First off all, I want to thank @agauger for participating here. Do not underestimate the difficulty of arguing with a large number of people who disagree with you. This takes great bravery.
Second, @T_aquaticus is correct about this...
None of the model I have seen produced by the ID camp have explained trans-specific variability, as Ayala and others have unequivocally demonstrated in the data. This is appears to be a very strong hard stop lower limit on the total population of our "ancestors" (whether they be "human" or not) as we go back in time.
There is one effective rejoinder to this, that fits the evidence, but raises other questions. It is possible that Adam and Eve have different genomes in each egg/sperm. This may possibely solve the problem if Adam and Eve are situated far enough back in time, and if they have a large enough number of children. Fantastical, yes. But technically possible if we allow for one grand starting point miracle. I do not think @agauger can declare success here yet. It is not appropriate to declare success without doing the mathematical modeling, which they have planned to do but have not yet done.
This solution, however, does raise an important theological claim. Why did God make us in a way that looks like we evolved if we did not? The best theological response to this comes from John Sanford. He argues that God intentionally designed ambiguity, for a purpose, into creation. Perhaps he is wrong, but this is the beginnings of a coherent case that needs to be dealt with on those terms. That is a philosophical and theological argument that deserves consideration. Claiming falsely, however, that science has ruled his position out is not legitimate.
We are now in the realm of science-engaged theology, not science. Science makes no pronouncements here.
I do understand that there are theological agendas at play here. Some are on an agenda to affirm a historical Adam and Eve. Some are on an agenda to deny a historical Adam. Do not claim the authority of science for your agenda. ́[content removed by moderator]
Finally, I do not think @agauger (and Richard Buggs) has fully made her scientific case. Demonstrating that @DennisVenema may have slight overstated a point here or there, or explaining part of the patterns we see in the data, is not the same thing as presenting a cohesive mathematical model for all the data we can currently explain in evolution. I encourage @agauger to try, and will gladly acknowledge when they are correct.
However, there is a better option. As I have explained, and is widely accepted among BioLogos biologists,
Therefore, entirely consistent with the genetic evidence (Figure 1), it is possible Adam was created out of dust, and Eve out of his rib, 10,000 years ago in a divinely created garden where God might dwell with them, the first beings capable of a relationship with Him. Perhaps their fall brought accountability for sin to all their descendants.17 Leaving the Garden, their offspring blended with their neighbors in the surrounding towns.18 In this way, they became genealogical ancestors of all those in recorded history.19 Adam and Eve, here, are the single-couple progenitors of all mankind.20 Even if this scenario is false or unnecessary, nothing in evolutionary science unsettles this story. So, evolution presses in a very limited way on our understanding of Adam and Eve, only suggesting (alongside Scripture) that their lineage was not pure. Any case claiming that evolution itself requires more dramatic rethinks of Adam is in scientific error.
This would make Adam and Eve the first "humans" as we understand the meaning of "human" today, though we can imagine other types of God-Imaged humans before them (following the exegesis of @JohnWalton. Remember, that "human" is an ambiguous term was we move into the distant past.
There is exactly zero scientific evidence against this view. And it demonstrates exactly @agauger's point, that science has not ruled out a first couple.
To the regular commenters, why not give those with deeply held beliefs a way to affirm those beliefs in a manner consistent with our mainstream understanding of science? @agauger, also, I would love to hear what you do or do not find acceptable about this model. As I hear your position, I do not see a strong insistence against the notion that Adam's offspring ended up mixing with other lines (Genesis 6:2). I know first hand that many in the ID camp are comfortable with this solution.
Now please, everyone, stop with the needless fight. Do your best to understand and be understood. This is not about winning. Honesty is more important.