The definition of species is based on individuals’ abilities to bread. How can this be known without actually testing it? Shouldn’t a test for species individuality require cross-breading with reasonably similar specimen until gene-exchange (via reproduction) is absolutely ruled out? There are some pretty similar “looking” species which can’t bread, and there are some pretty contrary “looking” animals (think two very different dogs), which can bread consistently (but I’m guessing would not if domestication were not popular).
Yes, of course we don’t know if two individuals can or cannot interbreed unless we test it. And even if most members of population A can’t interbreed with most members of population B, there’s no saying that there aren’t some members who can.
This wikipedia article could give you a quick rundown on the problem of how to identify what is and is not a species: Species concept - Wikipedia
One definition of species is “a population of organisms that can and do interbreed in nature and produce fertile offspring.”
That was the standard high school biology definition 20+ years ago, anyway.
The definition of species in terms of which organisms can interbreed with one another (and produce fertile offspring) is really only a rule of thumb. It is one of the more useful criteria of specieshood, that works a lot of the time, especially for higher animals such as mammals and birds, but even amongst them it does not always work perfectly, and for “lower” animals and plants, and even more for microbes, it is really only of quite limited use. After, all, lots of things don’t even reproduce sexually (and not just plants and invertebrates: there are the lesbian lizards of New Mexico and Arizona). The fact is, there is no simple, clear definition of “biological species” that correctly captures the way that biologists actually use the term "species, across the board, and the concept is at best a fuzzy one. In practice, in deciding whether two individuals belong to the same or different species, biologists use a whole lot of different criteria, and may give different ones different weighting in different circumstances. It takes deep expertise, and, indeed, expertise in that particular type of organism, to classify them (you wouldn’t want really to rely on a snake guy to tell you about species of lizards, for instance), and even then, in difficult cases there can sometimes be a good deal of ongoing disagreement between the experts.
On the other hand, yeast is the only organism that can bread. 
There are lactobacilli in sourdough!
Soooo tempted to bring up whole wheat vs. pumpernickel vs rye, but I’ll be nice. 
Soda can bread without any organisms.
The concept of species is an attempt to compartmentalise groups or populations of organisms that exist as a biological continuum - if not in the sense of an extant continuum right now, definitely a continuum across spans of time (the European badger of today is probably at least a little different from its ancestral counterparts, even if we think of them as a single species).
Nature is continuous and constantly changing, and won’t ever be properly and consistently described by a discrete, static system.
I don’t if this will be helpful, but to a certain extent, the term species and the boundaries are really just a linguistic thing and not something that’s “real” (for certain definitions of reality, anyway).
As an example, we all know the difference between a spoon and a fork… and yet, somewhere on the spoon-spork-fork continuum, we’ll run into places where we fight over whether something is more spoon or more fork.
Or how about gender/sex. Male and female seems very simple for the vast majority of cases. But for the statistical outliers, do you use genitals (which are often ambiguous) or chromosomes (which are not just a binary option) or psychology?
Then we have planets. Or not. Poor Pluto.
So we have a word “species” with such a plain, common-sense meaning when we look at the big picture differences between dogs and cats. Unfortunately, like any other word, the closer to a boundary you get, the more you realize how inadequate words are. At a certain point, a scientist has to define their own meaning, and you can see some of those variations in the Wikipedia article.
Researchers write journal articles and books and then they argue until consensus is reached. Or not.
Not really. Lions and tigers can reproduce, creating hybrids that are at least not sterile. But lions and tigers are still separate species.
There are species in the wild that don’t reproduce together due entirely to differences in behavior. It really doesn’t matter if they can if, in fact, they don’t. At least, that’s the case for some researchers.
Seriously, it’s all about the arguing. There are two species of taxonomists: lumpers and splitters. But although they can mate, and there are taxonomists who claim to be neutral, those are not hybrids.
And if you think that’s a mess, all of the other levels of taxonomy are even worse. The definition of a species might be a bit squishy, but the definition of a genus, or a family, is basically nonexistent. And don’t even get biologists started on subspecies.
Animal species makes perfect sense in comparison to bacteria and archaea, where there’s such promiscuous gene transfer between such unlike things that even analyzing the whole genome can’t solve disagreements on what the heck a species is or isn’t, or whether there’s a cluster or a continuum. Imagine if elephant shrews got their big noses because of gene transfers from elephants.
And salt rising bread doesn’t involve yeast. The leavening organism in that case is Clostridium perfrigens, which might give you pause when somebody suggests eating the stuff.
Well, ok, so yeast is not the only organism that can make bread. I guess you got me there.
The others didn’t, though. In the case of sourdough, although the lactobacilli may be in there contributing to the flavor, the recipe still relies upon yeast to make the stuff rise, and so make it “bready”. As for soda bread, if that does use any organisms it is no counterexample to my assertion.
My understanding is that species is a fuzzy thing. There are situations where species A can interbreed with species B, and species B can interbreed with species C. Yet, species A cannot interbreed with species C. That pretty much blows away the “interbreeding equals species” theory.
No, it’s not. If I’m in a freak steam roller accident tomorrow and my testicles are crushed I will be unable to breed with anyone. That will not make me a species of one.
No it shouldn’t, since, as others have pointed out, the definition of species is a population level definition, and it usually doesn’t matter if they can interbreed if extraordinary circumstances force them to, what matters is wheter the do interbreed in the wild.
And as others have also pointed out, quite often not even that.
Like thousands of other men, I have had the ‘snip’. Does this make us a sub-species?
Not quite. What matters is if they “regularly” breed in the wild. We know that wolves and coyotes interbreed in the wild, but not often enough that biologists put them in the same species. Same with polar bears and grizzlies. What constitutes “regularly” is, by necessity, subjective.
Not only that, it can beer too!! Good versatile stuff, that yeast.