My biological maths doesn't go far beyond the Hardy-Weinberg equation, I'm afraid (though I read it in the literature in awe and wonder and understand more than I'm confident to discuss). The discussion here went a lot further than I'd intended by the single point I was making on nested hierarchies, which was this: for T Aquaticus's hypothetical Coyne, having stopped his theological reasoning, to present the simple fact of nested hierarchies as proof positive of evolution would be inconclusive, because before evolution they were considered the strongest evidence for the former ruling paradigm, the Creation of plenitude.
I don't know if any specific writing of Coyne was inTA's mind, but that bare claim has often been made before in discussions here: "There are nested hierachies, for which common descent is the only possible explanation". But that is simply not true.
Since the reply to me then was in essence "Creationism allows for anything so can be dismissed" I felt it necessary to give some of the history, and to add the qualification that, since nested hierarchies are never neat and tidy, the exceptions need to be explained under both systems, and further work has to be done to show why an evolutionary explanation is superior to that of Linnaeus and the entire scientific body of his day, beyond mere change of intellectual fashion.
(Let me expand that last bit: since naturalism has become the preferred metaphysical foundation for science, the principle of plenitude, based on non-naturalism, will always seem to make evolution the more plausible option now - but that's to base a decision on a choice of worldview, not on empirical science).
I also thought it was of interest to share how much fruit the older assumption had born in giving rise both to careful taxonomic classification and even many of the foundations for evolutionary theory, including (in Larmarck) seeking to explain both the hierarchies and the environmental contingencies that break them, and (in Darwin) to his insistence on gradualism, using the very motto of plenitude, Natura non facit saltus, as his own watchword. In other words, saying "Creationists can believe anything as long as Goddidit" doesn't answer the case at all.
Now, when one goes beyond saying that nested hierarchies themselves prove common descent, and come to mathematical treatments that give a good match, then one is into empirical science that may well setlle the matter - at least for those who understand the maths or accept the arguments on others' authority. Even so, our hypothetical Coyne would, to make his case watertight, have to do the work to understand any mathematical implications of the principle of plenitude in the light of modern data, and show how it doesn't work as well as the maths supporting an evolutionary explanation. You have to show how an old theory is less true than your own.
Nobody, as far as I know, is interested enough to do that - it's hard to imagine Coyne himself being other than dismissive of an older paradigm based on a different philosophical and theological background to his own. I myself regard the principle of plenitude, and the chain of being from which it derives, as untrue on, mainly, theological grounds. For that reason I prefer the common descent explanation - but then I'm not Jerry Coyne seeking to convince opponents the Evolution is True, or (come to that) BioLogos trying to show Special Creationists they have the wrong explanation.
Yet if I refute explanation A simply by saying I prefer explanation B for such and such reasons, so I don't need even to examine the case for A, I'm only persuading myself. I doubt any Creationists are likely to revive Aristotelian justifications in the near future, so in practical terms, the current climate may well make common descent the only sociologically viable explanation for nested hierarchies. But knowing there is an alternative explanation that has never been disproved ought to remind us how much science is linked to culture, and make us humble enough to think in terms of "best current option" rather than fact. One day, metaphysical fashions will change again, for sure.