Problem:
A more entertaining phrasing of the question would be "what would a marine ecologist put into a perfect aquarium?"

I was reading about Prochlorococcus, among other photoautotrophs, and found that they seem to get their nitrogen from ammonia, which must be produced by some other organism. This set me off wondering what different species I would need in a hypothetical aquarium (how big that would have to be is another question, I guess), such that a sustainable ecological equilibrium occurs (one different from everybody dead, I guess), only requiring sunlight and air from the outside.

I realize that I'll have to put other components like iron etc in the water, but let's say I only put some fixed amount in during setup. What exactly that would have to be is probably another can of worms, so let's keep that out of this question as much as possible.
Question: Has there been research towards such model ecosystems, and are there known minimum configurations?

It's hard to give an authorative "no" to this answer. But maybe there's research that looked for such a system and failed, or maybe marine ecologists use model cultures in their labs that show instabilities (meaning the culture dies, you have to replace the water, or keep adding fertilizer, or keep removing some waste) which allow some generalizations.
Please suggest your opinion.