Principle Three: Everything is Cyclical.
Everything is cyclical. In the planted aquarium, little goes to waste. As molecules, nutrients and even 'toxins,' enter the environment, these elements are converted by the various bacteria, plants and animals into usable material.
Two Easy Examples:
1.) Toxic (to animals) ammonia is taken in by bacteria, which then convert the toxic ammonia into slightly less toxic Nitrite. Then another type of bacteria converts this Nitrite into Nitrate, which is safe for animals. Another avenue is the plants themselves uptake this ammonia and use it for growth - as a nitrogen source. The plants 'filter' out this toxic environment and make it live-able to animals.
This very process makes life possible in the aquarium. Without the nitrifying bacteria, animal life cannot live long term. The animals will literally kill themselves as when they intake food they produce ammonia.
2.) Plant cells absorb Co2 and through photosynthesis produce oxygen. This oxygen is then usable by bacteria and animals to breath. Through Cellular Respiration at night, plants take in oxygen and produce Co2. Additional oxygen at night, which can enter the system either through surface disruption (lifted lily pipe) or air stone, is greatly beneficial to the growth and wellness of plants.
Ammonia: decomposing organic matter (soil, fish waste, rotting leaves, etc)
Oxygen & Co2: absorbed into water via contact/mixing with air, cellular respiration (co2 producing, oxygen intake) of plants, fish, etc. Oxygen through Photosynthesis (co2 intake) and surface disruption.
Oxygen used by: bacteria, fish, plants, shrimp, etc.
Co2 used by: plants primarily
Light energy, nutrients, gasses (co2, oxygen), trace minerals, molecules (ammonia, etc) are all taken in by plants. It's best to imagine plants as a factory which takes in these raw materials, and then out puts a product: in this case, more plant matter, which is an embodiment of energy in the aquarium. It's stored energy that's used to 1.) Grow more plants, 2.) filter more water and remove toxins, making the environment more suitable for life.
Bacteria, in basic terms, convert an even more -raw- source of energy: normally unusable elements like Ammonia, or Nitrites, etc to perform still even more layers of filtering power to the ecosystem. Other types of bacteria even break down waste components (soil sediments, solid wastes, etc) and "purify" these elements out of the system. In modern day sewage treatment plants - one stage of turning raw sewage into useable, clean water, is a bacterial filter which literally moves the sewage up and down until it breaks down.
Fish take in food, remove pests (such as various water insects / pests that eat plants), and by processing these elements into waste, the plants and bacteria then feed off them as a source of phosphorus, this is a vital component of aquarium balance!
Shrimp such as Amano's, and fish such as otocinclus cats also eliminate "pest" algae which infest plants and "choke out" their growth through invasion of the system. They act as a barometer of control over algae to keep it in check, which keeps the system healthy by way of keeping the plants healthy. Amano shrimp especially, also act as "filters," by removing and eating dead animals, which as they decompose after death release ammonia into the system. Then these algae eating, animal decomposing critters digest and produce waste, they provide a source of food for the plants.
Algae is the result of imbalance. Algae is nature's control factor for uptaking left over elements that go unused by other organisms.
Refer to Principle #2 Law of Minimums and Principle #1, Malthusian Organisms.
See, because plants, bacteria, fish etc only intake the exact amount of nutrients, light, co2, etc components which they need to grow to the least common denominator (example 2 light, 1 co2 2 Micro nutrient, 2 macro nutrient, = growth only to one).
In the last example, we would have 1 left over light, 1 left over micro nutrient, 1 left over macro nutrient. This leads to excess in the system.
This excess has to be taken in by something. Algae is what results. They use all the left-overs and infest the system based on 'whats left over.'
They're kind of like pigeons or rats in NYC, which thrive on the left-over food and trash of human occupation on Manhatten.
This is why, in the popular E.I. Method, the simplest technique is to over dose everything as much as possible, and use Co2 as the barometer for growth. In that dosing method, the underlying philosophy is that it's simpler to control only one element: Co2, than it is to precisely balance all the other elements.
A more advanced approach is to incrementally bump up each individual factor based on feel and observation; which requires a bit of experience with knowing how things grow and knowing when to up things at what time as it's not approximate.
This is also why when you overfeed the fish, algae appears.
You must feed enough to have happy and healthy fish, but not so much that there's excess and left over, which will contribute to algae.
You should be seeing patterns here now: behavior of organisms and growth with Principles #1 and #2, and the nature of the ecosystem (Principle 3, cyclical) and how this puzzle fits together.
In theory it would be possible to make something self sustaining, but not to the scale in which even the largest aquariums are, primarily because of Principle 4, as well as to grow plants to the extent to which we want them to be grown (and not just scraggly things growing randomly), we have to supplement with nutrients (which are not naturally available in the environment, except with what aqua soil and root tabs provides) and Co2 (which would require much more ground water and surface exposure to air to get suitable levels in the aquarium to grow like we do as quickly as we do).
Self-sustainability 100% is not possible. We must renew water, nutrients, etc. over time. Now, we can, however, get very close to self-sustainability by applying these principles and giving a little extra work up front to achieve balance.
Once balance is achieved, you are at about 80% self-sustainability.