+1 on the idea of a sump in the basement. From that picture, the space under the tank could be the perfect spot for a sweet little fish room!
Taunting aside, I agree with what others have already said, it is probably ok. To be sure, you need to do some more engineering. Your tank, with water, rocks, sump, stand, etc could weigh in anywhere between 1200-1500 pounds (saltwater weighs about 8.5lbs/gal, rock weighs more, the tank will add to that, etc). That is a lot of weight in a very small footprint.
Generally speaking, floor systems are designed to carry 10psf dead load + 40psf live load. Dead load usually represents stuff you probably already have in place, like floor covering; so you should be planning for 40psf x 10sf = 400lbs! Your tank is way over that. Fail? No, because I said "floor systems" - it is more complicated than just taking in to consideration a single large point load at any given spot on the floor. Residential floor systems are designed for deflection at full load, usually measured as L/360 (L=length, in inches of the span). Have a 10' span? Your floor is designed to flex no more that 1/3" under full load. have a 30' span? Now your floor will be designed to flex as much as 1" under full load. Note that "full load" means that the weight is evenly distributed, not all sitting as a large point load in one spot.
Real life enters the picture. If you place a heavy load near the center of that 10' span, you may see 1/3" deflection. Place that same load at the perimeter of the floor, especially perpendicular to the joists, the less deflection there will be. And in your case, if those partitions in the picture were added later or not included in the design of the floor, then they may increase the load rating for your floor because they effectively shorten the span.
If it were me, I'd want to know the overall span of your floor, what the depth of those joists is, what the joist spacing is, whether those partitions are load bearing or not, and how far apart they actually are. Your joists should also be stamped with the load rating information for them, which will help you do some math.
But like I said at the start, you are probably ok. If you want to skip all of the engineering and just test it for peace of mind, figure out a way to load the floor at that spot with 1000lbs, and measure the deflection. First measure the distance from the bottom of that joist under your proposed tank location. Then, say, get 3 trash cans (the 44 gallon brutes would be best), and just fill them up with fresh water. Ok, that's about 1000 lbs (figuring 40 gals in each brute). Measure the distance from the joist to the basement floor again. Take the difference, and that's your deflection. Then determine what your allowable deflection is by taking the entire span length, in inches, and dividing by 360. If it's close, you could be pushing it- but I bet you will find that it isn't even close ...
