A common way to define species can be found on Wikipedia:
A species is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring
This got me thinking. Imagine the case where we have three "groups": A, B and C, where A and B cannot produce fertile offspring together (different species) but C can produce fertile offspring with both A and B.
Have this ever been observed? And how would you classify C?
What you describe is called a ring species. From wikipedia:
In biology, a ring species is a connected series of neighbouring populations, each of which can interbreed with closely sited related populations, but for which there exist at least two "end" populations in the series, which are too distantly related to interbreed, though there is a potential gene flow between each "linked" population.1 Such non-breeding, though genetically connected, "end" populations may co-exist in the same region (sympatry) thus closing a "ring".
Have this ever been observed?
While ring species is a classical theoretical concept, the cases of ring species is often open to some interpretation and limit case of what we want to call a ring species.
The question has been asked at Do ring species exist?, however the post is still left unanswered.
And how would you classify C?
There is no obvious simple way to answer that question. The concept of ring species just shed light into the fact that the concept of species is an outdated concept and does not have a good formal definition. For much more discussion about the concept of species you should definitely have a look at the post How could humans have interbred with Neanderthals if we're a different species?.
