I was using the generic "produces fertile offspring" definition.
Also, is "species" an attribute of an individual entity?
Heck no -- individuals are members of a species, which is almost by definition a group thing.
It does bring up an interesting question, though: if species are separated by an inability produce fertile offspring, is it possible to be "the first of a new species?" If so, then it's not clear to me how that new species could possibly propagate beyond the first member.....
Note that under your definition, the ends of a "ring species" are different species. "Produces fertile offspring" (a reasonable definition) is not a transitive relation. It's possible that members of subclasses A and B can interbreed as can members of subclasses B and C, whereas subclasses A and C cannot. Were members of subclass B deleted (volcano, virus, grey wolves, fire ants, other disasters), A and C would now be separate under your proposed definition.
So, if two groups could produce viable offspring, but refuse to mate (for various reasons), would you consider them separate species.