Your definition of "species" isn't correct. It isn't even the general species definition taught in high school. You are so off on what defines a species and REFUSE the corrections I have made. Read this, not just the first few sentences, the whole thing, and educated yourself Defining a species yes, the next pages too, as much as you can stand to read.
-_- also, I mentioned natural hybrids. That is, hybrids that occurred without human intervention, when it comes to plants. Since the offspring of these hybrids (and ones we force to happen) begin to exhibit reduced fertility and failure to thrive, the hybrids themselves are not considered to be a bridge between species that should be considered the same. That is, they are genetic dead ends. Also, the unnatural hybrids we force to happen aren't a part of natural selection at all.
Was it creationists that showed that the birds could interbreed? No. Do the birds live on separate islands quite a distance away from each other, and are adapted to the specific environments on those islands? Yes, which is an indicator that they stay on those islands for the majority of the time. This makes interbreeding less likely. However, no one ever said that NONE of these species interbreed. A few of the scientists mentioned in your source (which I will address further) weren't even surprised by it.
Last sentence of your source: "Meanwhile Prof Andersson and his colleagues, despite having shown convincingly that the finches' family history is decidedly blurry, actually argue for the addition of three new species to the existing tally of 15."
Furthermore, if you had actually bothered to read the source, you'd know that cross-breeding events are not the norm. They don't do it enough to establish enough genetic drift to merge the populations. Do you know what genetic drift is and the significance of it?
And yet, their populations retain quite distinct physiological and genetic traits, suited to the particular island they are native to. The significance of that is that it indicates that interbreeding between the species is fairly restricted; that is, two birds of different species are far less likely to mate than birds of the same species.
It happens, and it is interesting when it happens. Hybridization that greatly impacts evolution. Some speculate that the red hair gene present in some human populations may actually have been inherited through a hybridization event with Neanderthals. Humans and Neanderthals aren't the same species, we even have their DNA to confirm that. Heck, that we have no Neanderthal mitochondrial DNA suggests that females from that cross were infertile (as mitochondrial DNA is inherited from the mother, not the father), and many humans don't have traces of Neanderthal DNA at all, thus genetic drift never encompassed the population (interbreeding was very uncommon).
Doesn't make the groups the same species, but it is fascinating nevertheless.
What part are you emptily claiming is nonfactual? That all finches aren't in the same genus? Because one quick google search would show you that finches all share the family level of classification, not genus. I count 51 different genus that finches belong to. Furthermore, not all finches have the same breeding season or are attracted to each other, thus they will REFUSE to mate. For example, male Goldfinches are yellow, and male House finches have portions of their bodies which are anywhere from bright red to pale orange or yellow. Female house finches will ONLY mate with the males with the most red coloration, and thus would have no interest in the bright yellow Goldfinch males. Additionally, the mating season for Goldfinches is much later in the year than House finches (which actually choose their mate in the winter prior to their mating season, during which Goldfinches happen to be at their most drab). These birds will NEVER interbreed. This is the barrier to reproduction known as sexual selection, and this is a valid reason to consider two populations separate species.
Tigers and lions have bred with each other in captivity. Emphasis on "in captivity". Any hybrid of two species that is the result of human intervention, just so you know, is irrelevant entirely to species classification. Any amount of hybridization that is too small to allow for fluid gene flow between populations long term prevents the populations from merging and thus they will continue to diverge until, eventually, they cannot mate. Any time the hybrids produced are infertile or have significantly reduced mating success (a common occurrence with bird hybrids), this prevents the populations from merging as these are mostly genetic dead ends.
Did you think that when I said all finches cannot interbreed that I was only referring to Galapagos finches? Because I wasn't. I was talking about all the finches in the world, of which many do not interbreed. But again, being able to breed and interbreeding enough to break the species barrier are two different things. You, apparently, cannot understand that. I refer you to this page specifically, text under the title "Reduction of gene flow"
Causes of speciation
What for? Taxonomy is an imperfect system, so it is not uncommon for labels to change. However, it becomes a huge pain in the butt because the dividing line between species becomes so blurry that whether or not two groups belong to the same species or not often becomes a matter of contention. Genus labels change a bit less frequently.
I mentioned hybrid vigor in my prior post, what the heck? I guess you didn't know what that was, despite the meaning being fairly intuitive. That "increased health" doesn't always mean increased reproductive success, and only applies to the first hybrid generation, not the offspring of the hybrids. I hope you won't ignore that. My nepenthes hybrids with two different species in their lineage grow better than either parent. My hybrid with three different species in it's lineage grows about as well as a pure species. My hybrid with 4 species in its lineage is pretty lonely, though, since out of only a couple dozen fertile seeds out of the 100 seeds I received from that cross, only 2 made it to their first birthday, and only 1 is still alive. So many survived from the 2 species hybrid seed that I've had to gradually give them away over the course of 2 years to keep them from taking over my life. Yet, not every plant from that cross was a "winner"; there are always genetic failures, even in the best circumstances.
-_- I'm not ignoring it at all. Hybridization can be an important part of evolution. Heck, species populations separated from each other can actually MERGE through reproduction and genetic drift, becoming a new species generated through hybridization. However, the cross-breeding of the Galapagos finches hasn't been frequent enough to do that. Whether it be mating preference or that the birds don't fly to different islands much, the hybrids aren't numerous enough to begin breaking down the species distinctions between the finches. Like how wolves and domestic dogs sometimes have offspring with each other that is perfectly healthy, it's just not frequent enough.
I appreciate, however, that you have been listening to what I had to say about how the offspring had to be fertile. Now we can move on a bit to discuss some of the gray area that is "species", if you so desire.
I remind you that taxonomy is an imperfect system. Bacteria (and maybe archaea do it too, since they are also prokaryotic) can integrate genes from dead bacteria into their genome through contact. And those dead bacteria genes don't have to belong to the same species as the bacteria integrating them. As you can imagine, this makes bacteria taxonomy a huge pain in the testes, as well as determining bacterial evolutionary pathways. I don't think that will ever be completely worked out.
You do know that we willfully use an imperfect system for taxonomy, right? Hence why bacteria have species names, even though their taxonomy is so complicated. It's always been a work in progress, heck, in the beginning, one of the Kingdom classes was "mineral". Freaking nonliving rocks. The idea is to keep improving it, not leave organisms without labels until the system reaches some standard of perfection. It changes as needed as we go. That's why it's so complicated. It's also why the high school definition is only suitable for people not going into a biology field.
Your error is in thinking that the definition for species in animals is complete.
-_- I don't even know how you managed to get that from your sources, especially not the latter one, which proposes that genomic testing would be a more reliable and faster method of determining bacterial species taxonomy than the previous method of using the traits the bacteria have, such as their growth habits. As genetic testing has only very recently become cheap and relatively fast, it is thus quite recent that this method was applicable to improving the taxonomy of the many species of bacteria. I mean, using an old method in a lab, it can take hours just to get the DNA out of a cell, and that's the easy part. The first organism had it's genes sequenced in the same year I was born (and I'm only 22). It's a fairly new capability, so it is no shock that it is taking some time to root itself into various scientific disciplines. Your other source is just too old to be relevant to the genetic testing we can do now.
Well, this source is exceedingly outdated in terms of genomic studies, since it's from 2006
The bacterial species definition in the genomic era | Philosophical Transactions of the Royal Society B: Biological Sciences
And the other source you gave, which is from 2012 and a bit better in terms of being representative of the technology now, says the opposite of what you are claiming; that DNA tests would be very helpful with bacteria taxonomy.
Defining bacterial species in the genomic era: insights from the genus Acinetobacter
A personal recommendation: make an honest attempt to never use sources more than 5 years old when it comes to scientific fields, as our capabilities can change rapidly, and new discoveries are made every year than make the previous articles progressively out of touch. And absolutely avoid sources older than a decade.