I drew this figure to address the question -> What is a species? Is it a human construct? Nope! Species are real. But discovering them is not an exact science. This sometimes causes scientists to freak out and creationists to laugh at us for trying. This relates to the fact that somewhere in the world, at this exact moment, a hard working systematist is temporarily losing his/her mind, trying to determine if the thing on the slab is a member of Species A, B, or New (species identification problem). Meanwhile, also at this exact moment, in a time zone where its 3am, another scientist is rocking back and forth and talking to himself. He hasn't had fresh food in days and he kind of smells. He's certain that he's discovered a new species but he can't finalize its description because he keeps finding exceptions his own rules (species diagnosis aka delimitation problem). Meanwhile, also at this exact moment, evolutionary biologists are arguing and clashing against each other with makeshift weapons like the fight scene in Anchorman, unable to agree about what a species actually is (species concept problem).
The Figure: Each twig represents an individual organism. Meeting points represent mating events. Colors represent morphological variation. I made it to demonstrate why there are so many different species concepts and delimitation schemes out there. It's not because we're stupid. It's because one mold (concept) does not fit all life. It's also because our perception is limited. It's almost impossible to observe a species in the literal sense because, 1) few natural scenarios allow us to observe every individual at a given time, and 2) species are temporally transient and eventually go extinct. To literally observe a species, the observation period must begin before or during the shift towards evolutionary independence, and end when independence is lost or terminated. Independence ends due to; 1) coalescence via hybridization, 2) lineage sorting, or 3) an extinction event.
So.....This doesn't mean that species aren't discoverable. They are totally discoverable! That's all that I wanted to say. <3 Dani