There is no such process without species A becoming mutually infertile with at least one of its descendant species AA or BB. So again, you're dodging the question.
Maybe we're misunderstanding each other. You refer to species AA and BB as descendant of species A. They're not descendent, because AA and BB are not new species. They are different isolated groups of the original species A, who because of their isolation, over time, obtain changes in their alleles which do not produce infertility within the members the two groups. However, because of the isolation, the two groups diverge along different genetic paths until they reach a point where if they are brought together, they are no longer fertile. So, it's irrelevant that either group AA or BB might have become infertile with what was once the original species A, because no fertility with species A is necessary to produce AA and BB. It may be that group AA or BB might still be inter-fertile if brought together with original species A. But, that doesn't matter, because as long as AA or BB are not inter-fertile, they have speciated. As to what happened to the original species A, well, if both AA and BB have changed their genomes over time, it's likely that they will be phylogentically divergent as well, and thus species A will have become extinct as an artifact of the divergence.
Edit to previous post: "It may be that group AA or BB might still be inter-fertile if brought together with original species A. But, that doesn't matter, because as long as AA and BB are not inter-fertile with each other, they have speciated."
I appreciate the effort, but there still seems to be a logic problem in your argument. Perhaps you can explain how AA can be infertile with BB, while at the same time both AA and BB are fertile with a common ancestor, namely A.
It may be, it might be, perhaps, we postulate, we theorize, we think it is, we believe it is...anything but "we don't actually know."
Fertility with A is irrelevant to the outcome of the speciation. Example: suppose AA and BB comprise the entire set of A, such that no other A can possibly exist. At this point AA + BB ARE A, because that's all there is in the set of all A. Now change an allele in AA and change a different allele in BB. At this moment A is extinct, because there is no longer any A with which AA or BB could ever mate. Now, keep changing alleles in AA and BB, and allow the non-infertity creating alleles to propagate within each group, but don't ever allow any member of AA and BB to interbreed. Eventually, the two groups will bear less and less genetic resemblance to either A or to each other. And, eventually, their genetic resemblance will prohibit interbreeding. A is gone, and AA and BB, while descendant are phylogenetically distinct, both from A, as well as from each other. The result: A is extinct; AA is one descendant species; BB is another descendant species. No fertility between AA and A or BB and A was ever required to produce the two new species.
Still waiting for you to prove your above claim that neither the origin of biological life by chance or design can withstand scientific scrutiny.
ok.. enough bs.. where is the missing link or the magic hybrid??? put up or shut up!!! no more lame excuses.
No, infertility with A is required by definition. With any mutation effecting the fertility of an individual within either AA or BB, there is now a new group CC composed of only that member. Surely you realize that. Exactly, it is INFERTILITY between A and AA or BB that is required, as well as impossible. Also, the extinction of A does not solve the problem of its fertility with a supposed new species. They don't have to actually meet or otherwise coexist for the potential to interbreed to be a structural reality. You're still on square one.