Pacu, Colossoma macropomum
There are lots of things which do have an impact on growth.
Aquarium or pond size can have an impact on some of the above but in itself does not affect growth.
Nitrates and their effect on fish have been well studied and high nitrates are known to affect the growth of fish. Nitrates should be kept low at all times and should not exceed 25mg/l in an aquarium or pond. Nitrates are best controlled by regular water changes.
Pheromones are hormones which act externally, hormones are contained within the body and affect the body from within. Pheromones can affect the body when in the local environment rather than in the body itself.
Fish release growth inhibiting pheromones which limit their growth and the growth of other fish in the same environment. If these pheromones are allowed to build up in a closed system then they will have an impact on growth.
In a small body of water they are likely to be present at higher concentrations because there is less water to dilute them. Water changes are the best way to control the level of these pheromones.
A good balanced diet is essential for all living things. The diet must contain all the nutrients that an animal needs. Some animals are specialist feeders and won't thrive on the wrong diet even if they accept it cleaner wrasse, moorish idols and marine butterfly fish are all examples of this. Diets which lack certain important elements or are of the wrong balance will impact on the growth of fish.
When we make a regular partial water change we are actually making several changes:
All these things have an impact of fish growth so making water changes of sufficient volume and making them often enough has a huge impact not only on the growth of fish but on the well being of the fish.
Like water quality keeping the fish in water of the right chemistry has an impact on growth. Most captive bred fish now accept and do best in water which avoids extremes.
But others which still regularly come from the wild such as Rift Valley Cichlids and others need water which replicates their wild environment in order to thrive. If a fish is kept in the wrong type of environment it will become stressed and fish which are stressed don't grow as well as they should.
Some people grow to 6 ft 6 ins (almost 2m). While others stop growing at 5ft (1.5 m). The same things affect fish, some fish despite their care simply won't grow as well as another fish of the same species kept in the same aquarium. There is nothing that can be done to alter this. Fish which have been line bred for many generation in captivity often end up smaller than their wild cousins due to this.
The effects of many of the things mentioned in this article are made worse when the volume of water is small. But they are not directly caused by the volume of water being small. It is true that because of the care captive fish receive they are more likely to end up being smaller when kept in a small aquarium, but this is entirely due to not being given good care. If a fish kept in a small tank is given excellent care and all these problems are overcome then the growth of that fish will not be impacted on.
It is often said that a fish's growth is restricted by the size of the tank that it is kept in. This statement on it's own is wrong, fish don't limit their growth based on tank size. But other factors which affect the growth of fish can be more effective in a small aquarium.
It is poor care which limits fish growth, not aquarium size, although it has to be said that a small aquarium size does contribute to other factors which do limit growth.
It is more difficult to maintain a small aquarium at its optimum than it is a larger aquarium simply because small volumes of water are more easily subject to change.