Off-hand thoughts on the subject, from a general network perspective. Consider what portion of the subject matter is relevant to the class of item you're tagging. So in this case, what about animals are we asking about? The best way to approach tagging is to approach it based on what the site content actually contains, rather than what it could contain.
From what I've seen so far, the majority of animal related questions are all about conditions and environments for raising animals (primarily for eventual dining). So in the big picture, the general category is about "raising animals".
It could be that really, this is the only (or only distinguishable and common) thing we will ask about animals. In which case, something as simple as animals can serve the general need - being more specific about it is unnecessary. Both the site topic and the presence of a good tag wiki will clarify that one would expect questions about sustainable means of raising animals, an act that itself is geared towards self-sustenance. It may seem generic but it is clear and demonstrative of its purpose.
If it is not the only class of questions we will have on animals, then a more specific tag would be necessary. Of the above case, there's probably a better term than "raising animals", that would be the general tag for that. Then, the other classes of questions would have their own relevant tag. There doesn't need to be a hierarchical "supertag" that would cover everything as a whole.
Note that either way, this doesn't affect some other narrow tags like aquaponics, which are happy to coexist with whatever we do because, while there is intersection, there are other components to these other tags.