Nitrification

Here are a couple detailed descriptions of nitrification.
Nitrogen Cycle In Soil

and the video below

  Recently it was asked what happened to the Nitrate.  

I too wondered about this.  

This video will explain that phenomenon at about 10 minutes into the video. 

Bottom line for aquaponics is lots of air because we want the Nitrate.

Click This Link

or watch this

If you wish to watch one more with a humorous attitude I'd recommend this one ;-)