Sometimes, homeowners remove what's commonly known as a 'lolly column'. It's usually used to support a load from the floor(s) above. It's most unknowingly removed in order to finish the basement or to just make more room. Although the columns seem to be in the most inappropriate places (such as the middle of a room), they're there for a reason.
If you can take a look at the floor above and see adjoining rim joists, then a column was most likely removed. Sometimes, you can see a 'spot' where a square or round post use to stand. If your basement ceiling spans more than 12', you should have support somewhere. The best medicine would to have an architect or a structural engineer visit your house to inspect the load. From there, you can plan a solution. Since your particular problem is NOT a perimeter problem (hence, a between-rooms problem), chances are good that support is needed. An 'I' beam + the column sounds in order. Find out what the 'dip' is between the ends and the lowest point. You may have to jack up the floor a bit but slooooowly, and over time so you don't cause a new, major problem with the rooms above. This is why you need an engineer or an architect who's schooled in this stuff.
As Ron suggests, if you don't see an damage from insects, go from there. In any event, I'd still have an engineer look at it because no matter what, the floor has already dropped and needs to be pushed back up. My best to ya and hope this helps.