Nitrification is used in both aquaponics and wastewater treatment to convert ammonia to nitrates. This wastewater training video does a good job explaining how nitrification works. One thing to note is that nitrifying bacteria can live suspended in aerated liquid (mixed liquor) as seen in the video or as a biofilm growing on media.
The dissolved oxygen, and pH ranges discussed in the video are for wastewater treatment and not aquaponics. Target values that are commonly used for aquaponics.