In Ecology of the planted aquarium, Diana walstad outlines how it is possible to keep water well within the peramiters for keeping aquarium fish without water changes or filtration, but simply with plants and a high bioload.
this is done with fast growing stem plants aswell as heavy root feeding adsorbing neutrients from the substrate and oxygenating the substrate preventing too much matter rotting within the substrate.
she also freely admits that it dosent always look that pretty, especialy when the watter becomes full of tannins released from breaking down plant matter.
I have known several people who have tried this "natural approach" and failed drastically losing entire fish and plant stocks. In reality there are 3 ways to deal with the nitrate cycle in a fish tank.
1) low fish stock, highlevels of filtration, daily fertilisation, a neutrient rich substrate. and heavily planted. The highlevels of filtration mean more ammonia is processed by the filter bacteria than is adsorbed by plants meaning that when you test for nitrate when fertilising you get an accurate measure. and can ajust your fert routine according to the levels of niterate existing in the water column.
2) Denitrification equipment, There are various systems available some chemical some utilise bacteria. when i had a marine tank I successfully built a denitifyer that kept nitrates at 0. i had a 6ft long length of drain pipe capped at each end. I carefully coiled many many many meteres of 6mm air hose around the indise of the pipe leaving a gap up the middle. this was then filled with bioballs before the end was sealed.
the principle was that bacteria would adsorb all oxygen from the water on its way down the air tube and then denitryfying bacteria would take over and produce nitrogen gases thusly removing all nitrate from the water column.
3) Regular water changes and cleaning debris from your tank. Prevents nitrates building up and is the most simple and cost effective way to deal with the tank. I do mine weekly