How do you know if your aquarium is below, at, or over capacity regarding population?

Well, there are many factors that have to do with how you can stock your tank. The most common rule used is the one inch of fish per one gallon, but this is not always the best rule of thumb used for there are some fish that are so messy as in waste that the rule of thumb cannot apply "safely". It all has to do with what your tank can handle as in waste, not capacity. For example a 50 gallon aquarium will sefely hold 35 to 40 inches of fish (keeping in mind the full size of the adults, not juviniles). If you stock your tank to the full ammount it can hold you could very well be overstocking. Now unless you want to do large water changes within your aquarium every week you should almost always under stock your aquarium.
*The stronger your filter the more your tank can hold.

Thank you.