i thought i would ellaborate on this:
waste is excreted by the fish in the form of;
1. solid waste that is broken down into ammonia by waste assimilating (mostly heterotrophic) bacteria AND
2. ammonia or urea
that ammonia is then taken by Autotrophic bacteria along with oxygen, and carbonate or bicarbonate and converted by oxidation into nitrite and CO2.
(autotrophic bacteria are bacteria that use INORGANIC carbon, such a carbonate and bicarbonate)
The resulting nitrite is then taken by another strain of Autotrophic bacteria (of which there are many) along with oxygen, and carbonate or bicarbonate and converted by oxidation into nitrate and CO2.
And there ends the Autotrophic bacteria's job, again, these guys adhere to substrates/biological media/live rock and use INORGANIC carbon, they dont float around in the water column and heterotrophic bacteria can. Heterotrophic bacteria will create biofilms and adhere to substrate as well, sometimes even smothering out nitrifying bacteria.
For reference, there are also Heterotrophic bacteria (those that use organic carbon) that can also digest ammonia and nitrite, but noweher near as effectively.
This nitrate, through the process of being digested/converted/oxidised by the autotrophic bacteria has had bicarbonate and carbonate bound to it, and therefore, when heterotrophic denitrifiers (such as bacillus denitrificans) take that nitrate, organic carbon and sometimes oxygen (sometimes not as denitrification will also occur in anerobic zones with little oxygen present, and these bacterias will not use oxygen for respiration), they digest it back into nitrogen gas, and spit out the carbonate and bi-carbonates consumed during the production of the nitrate during nitrification by the ammonia and nitrite oxidizing bacteria.
This is why finding the "sweet spot" in relation to flow and tumbling the biopellet is important. You want to create;
1. an environment with enough oxygen in most parts of the reactor so all the heteortrophic bacteria feeding on the organic carbon ( both aerobic/oxygen dependant and anerobic/oxygen non-dependant) have an enivronment that is tolerable to them i.e. just enough oxygen for the aerobic but not too much oxygen for the anaerobic
2. fast enough flow to effectively "sheer" the bacteria and the biofilms off of the outside of the pellet for harvesting by the protein skimmer, but not too fast that it either sloghs them off altogether or creates an environment too rich in oxygen for the anerobic bacteria to survive. NOTE: keeping a biofilm thin is called "biofilm control" and is a process used and applied in the application of MBBR's or moving bed bio-reactors such as filters using the Kaldnes media. the thinner the biofilm and the better it is controlled/exfoliated the younger the biofilm is, the younger the biofilm, generally the more effcient it is as when bacteria gets olders and biofilms get thicker, older bacteria does not do as good of a job as younger bacteria does, and thicker biofilms have trouble getting suffcient oxygen.
3. big enough reactor : System size : volume of biopellet ratio so that dwell time is sufficient to allow contact of waste products with the bacteria for efficient removal.
4. and of course, a big enough skimmer, this is the same as my theory that less is more when dosing bacteria into a liquid bacterial driven system using Vodka, VSV, NO3:PO4X or similar products, if you add to much at once, the bacteria go crazy and reproduce quickly, and without a skimmer big enough to remove the bacteria qucik enough, the bacteria die and break down into nutrient, compounding the problem. its the same with biopellet, if you create and sheer more bacteria that you can remove, the same thing will happen. For what its worth i also use a pro-bitoic bacteria with biopellet, and well as liquid based organic carbon driven systems.
Hope this clears this up a bit.