Inches to gallons, and creating a midget fish? The full explanation...
When asking about proper stocking rates for both fresh and salt water aquariums, the most often offered yet most misunderstood advice is the phrase "one inch of fish to a gallon of water" (or, in salt water circles, one inch of fish to three to five gallons of water). This mini-article will properly explain the basis behind the phrase and how it translates into deciding upon stocking rates for your aquarium (from a biological load and water quality perspective only - behavioral issues are not discussed but may have to come into play, such as territory requirements of the particular species). This is not scientifically exact, but it is a very good guideline/rate calculating system to use to ensure that the starting hobbyist won't crash their tank by stocking it with a load greater than the tank environment can easily handle and process.
Definition of an inch
This refers to a freshwater fish that at one inch long has the same body mass as a livebearer, like a molly, or a tetra, meaning a fish that is about 1/2 inch thick, and 1/2-3/4 inches tall. The saltwater equivalent would be a small damselfish, like the blue devil damsel, that is about 3/4" tall, and 1/2" (app) thick.
Meaning of a gallon
The gallon is the amount of water needed to sufficiently dilute the waste level the fish creates, to enable it to be comfortable, until the filtration can break the wastes down into less poisonous substances. So, a 1" long molly will need a gallon of water to dilute it's urine, CO2, and fecal matter to a level it can "deal with" until the wastes get carried to the filtering process (whatever that may be). A 1" damsel will need 3-5 gallons of water for the same "comfort level".
What does all this mean?
NOW, keep in mind the whole body mass issue mentioned above. If we take a different type of fresh water fish, like an Oscar, for example, we can see that the load factor, or biomass, per running inch, is not the same as a molly. The Oscar is both thicker and taller than the molly is, and represents a far higher load factor. (Think of how many mollies can fit into the space occupied by the Oscar's body - it will take at least 20-30 mollies, to equal the body mass of a 5" long Oscar, if they were fit next to and stacked upon one another like sardines). Every running inch of Oscar is at least twice as thick as a molly and quite a few times (15-20 times the height for an adult Oscar) taller. A 5" long Oscar would require a 20-30 gallon tank, ALL BY ITSELF, for proper comfort and life support-with filtration. A full grown Oscar can completely fill a 75-100 aquarium by itself, from a carrying capacity standpoint.
Metabolism also plays a role for the determination - a sedate fish will place less load factor on a system than an active fish will, per the same amount of biomass, as the more active fish needs to eat more, and will produce more waste, to support the same amount of actual biomass.
The same rules apply for a saltwater tank, though the ratios are a bit different, and the metabolism factor also needs to be considered. For example, a Tang requires far more space and swimming room than it's body mass alone would lead one to figure - they require very large amounts of oxygen, and release larger amounts of CO2, per unit of body mass, than a lionfish does, for example, and their behavior demands lots of swimming room.
Can a cube create a midget? (The "tank size affecting fish size" myth exposed and explained)
Many years ago, before the underlying concepts of waste management in closed systems and how they affect growth rates in fish were understood, people who kept aquaria didn't really understand the need for performing water changes. They also noticed that fish tended to stop growing at an earlier age in smaller tanks, than they did in larger tanks. This lead to the erroneous assumption that the physical size (dimensions) of the tank determined the physical size of the fish. Nothing could be further from the truth.
All animals will reach the size they grow to as a function of their genetic potential and their ability to take advantage of that potential. To illustrate, let's look at people - even siblings grow up to be different heights because the genes that determine growth rate and final size are different for everyone. As long as one receives proper nutrition and exercise, and is kept in good health, one will reach the maximum height that one's genes will allow for. Raising a child in a bathroom, will not turn them into a midget, as long as they get proper diet and perform calisthenics/exercise, have access to good fresh air and water to breathe and drink, (though they may go mental from boredom ;p ), and aren't subject to re-breathing their own CO2, or re-consuming their own waste. Also to illustrate, if you try to keep an elephant in a 6'x6' cube from birth, it will not become a cube shaped elephant measuring 6'x6' as an adult. You will end up with a busted cube. ;p
If an Oscar is kept in a 20 gallon tank, that is then plumbed/piped into a 1000 reservoir system, it will reach a foot long in spite of the physical size of the tank-since it's wastes are not building up in the system to the point of interfering biologically with it's growth potential. Alternatively, you can achieve the same result by performing daily water changes. One of the main waste products that fish produce is an anti-growth hormone, the function of which is most likely to ensure that the largest fish from a group of offspring, get a better survival chance than their slower growing siblings, to help increase the percentage of faster growing (and therefore better suited for survival) offspring in successive generations. This is often observed in closed systems.
When rearing fry:
Out of any group of fry, a small percentage will always start to grow faster than the rest of the group, and that smaller percentage will ALWAYS remain the largest. If the larger fry are then removed, another amount of fry will then "spurt" in growth, while the remainder does not, and so on. This is due to the presence of that anti-growth hormone. Again, water changes, or a corresponding increase of waste dilution ability due to an increase in water volume, will mitigate the effects and concentration of the levels of that hormone in the water.
The bottom line is that the physical dimensions of any aquarium have nothing to do with the end size of a fish, the management and water quality do. :)