Aquaponics refers to any system that combines conventional aquaculture with hydroponics in a symbiotic environment. Are there publications on the application of material flow analysis and/or life cycle assessment to aquaponics ?
There are very few publications on aquaponics at all, and most of those available are from an agricultural economics and sustainability standpoint. You may be able to find some data on material flow or system life cycle within these publications, but they will be unsubstantiated by any references, and you will need to discern what is and what isn't reliable information.
If you wish, start with the work of Dr. Rakocy. If you have already reviewed all of this information and find it lacking, then I would like to encourage you to generate the information you require yourself, to the benefit of our field of study.