I read in the Linguistics section on the Wikipedia page for American Sign Language that ASL was "proven [to be a natural language] to the satisfaction of the linguistic community by William Stokoe, and contains phonology, morphology, semantics, syntax and pragmatics just like spoken languages" (emphasis mine).
Are these elements, of phonology, morphology, semantics, syntax, and pragmatics, generally accepted as the necessary and sufficient components of a natural language? Would a constructed language which developed such features be accepted as "natural"? (Note that American Sign Language itself would be an ambiguous case, being a systematically modified version of Old French Sign Language, a signing language which developed "in the wild", so to speak, in the deaf community in Paris well before the French Revolution.)
To consider a somewhat flippant example: what would be the necessary conditions, linguistically (as opposed to sociologically) speaking, for either Esperanto or Klingon to develop dialects which would be considered natural?
Edited to add: I am accepting Alennano's answer as being the most factually correct with respect to what it means for a language to be "natural"; but I also think that, from the answers and comments, the question of whether a language is "natural" is completely beside the point on a matter of linguistics, except inasmuch as the vast majority of "vernacular languages" happened to evolve more-or-less organically most of the time from a prehistoric origin.