@Byron and @Essjay: Is there no argument to suggest that, as your filter medium can contain large populations of the beneficial bacteria and much of the nitrogen cycle management depends upon the biological filtration of passing water over said bacteria, that the filter facilitates the flow of water over this bacteria? Meaning that the filter not only performs a mechanical filtration, but also biological filtration?
Certainly. Mechanical filtration is our aim, but realizing that biological filtration is bound to be present. However, in an established tank, the greater number of various bacteria will be in the substrate. You should be able to shut the filter off and remove it, with no harm to the fish. This argues against the common misconception that the filter determines the fish load. No. The aquarium's biological system (with no filter) determines the fish load. Over simplifying, but it gets one thinking.