Interesting can 'o worms you are opening. I think by 'natural' you mean low tech as in fewer artificial filtering monitoring and control systems like skimmers, resins, ph monitors and dosers etc.
Do a search on skimmerless. There is also a very good thread on the Marine Depot forums in Borneman's forum on skimmerless tanks.
I am currently running such a system. The only filtration I do is carbon, when I remember to change it that is and a sand bed.
My current system consists of 2 interconnected 40g tanks with one being a refugium. The primary occupants are seahorses and it is an algal dominated system; the antithesis of what people here consider successful. It is, however, a very appropriate system for the animals I am keeping.
I have tried keeping a few corals in the tank, but it is very hard to keep them from being overun by algae.
The goals of my system were to create an environment that my seahorses would be happy and healthy in and to produce as much live food for them as possible.
Given that one of the horses is a natural, in-tank recruit from one of the many spawnings, and that he has survived for two years and produces his own fry now, I think I have a very successful 'natural' tank. Note that he feeds only on the live food produced by the tank.
Eric Borneman runs a similar multi tank system that is coral domintated. If your goal is to keep stony corals than at a minimum you need to resort to 'artificial' methods of calcium replenishment as the species density in our sysems is infinately higher than in the ocean.
By the way, neither Eric nor I do water changes either.
There is much opinion and very little research on such sytems.
Also, every system has limitations.
As you rightly pointed out, the only truely natural system is the ocean. It is, after all, an open system
Fred