Ok, let me try to put this in the simplest and quickest way I can.
Let's try with an hypothetical example. Say we had a dog and a donkey. A dog has 78 chromosomes (39 pairs) and the donkey 62 (31 pairs).
So the dog mounts the jenny and the jenny gives birth to this hybrid. And the hybrid is viable and it grows up. Now this hybrid is what is called heterozygous, meaning it has unpaired chromosomes. It has 39 chromosomes from its canine father and 31 from its equine (I guess that works for donkeys too) mother. Here's where the fun starts. This hybrid donkey-dog is going to start producing gametes. During meiosis, the chromosomes will be unpaired, alleles will not correspond and there will be utter chaos. Therefore, this process will be entirely unpredictable. During meiosis, a number of things might happen, such as fusing of chromosomes, splitting up of chromosomes, mutations of a multitude of genes, deletion and doubling of genes, you will get genes from the dog and donkey on the same chromosome doing god knows what. You could also get a diploid gamete with 35 pairs of chromosomes. This gamete could possibly be able to impregnate a donkey and thus create a triploid organism. The triploid organism could then be able to produce a haploid gamete of say 54 chromosomes and mate with another of its kind. Boom, you have a 54 pair diploid organism that can mate with its kind but is possibly highly sterile with donkeys and dogs and it has genes from both set into a completely novel karyotype that is reproductively stable. If you think this is just stories, all of these mechanisms have been documented and they happen all the time.
So from the perspective of the donkey, this new organism has many new genes courtesy of the dog, it has a completely different karyotype and is no longer able to reproduce with either the donkey or the dog. If this organism is able to survive within it's environment, you've got yourself a new "species"(species is a completely imaginary concept) with it's own completely novel characteristics and it all happened in only a few generations among only a few individuals, so finding the intermediate forms is near impossible in the fossil record.
This was just a really quick overview and I didn't go into detail with all the specifics. Read the book. From start to finish.
That's an awful lot of "mights" and "maybes", so to say.
And it posits a whole lot of interspecies "communication", as it were, that seems highly unlikely. I seem to recall reading about a number of people (throughout history) who have attempted to combine species with no success. Here, we are expected to believe that it occurs naturally in Nature? A lot, in fact? Enough so that there can be two products of such miscegenation that can interbeed together?
And notice, the very mechanism that should have prevented reproduction of the "donkey-dog" above, in the first place, is invoked for "stabilization", i'e. "a completely different karyotype that is no longer able to reproduce with either the donkey or the dog".
Sorry, it doesn't fly.
It certainly may be that some hyperdimensional engineer is toying with designs in some way similar to this, but I suspect that the "stabilization" principle is pretty much built in to the organism.
Geeze, neo-Darwinists will come up with the most ridiculous ideas to try to save their materialism.