> The classic concept says that [a species] is a group of organisms with similar physical and genetic characteristics that can reproduce with each other in nature and produce fertile offspring,”

The fact this is a gross simplification that doesn't reflect reality at all is already discussed at length in the Origin of Species. "Species" is a human abstraction with no real biological reality. Almost "species" can breed and create fertile offspring with other "species". Of course as genetic distance increases the chances are increasingly unlikely, but there are some real wild cards out there.