Saying it is OK to allow a fish to go 2 months without food is terrible information to be giving out for newbies to be reading. Google some information on them. My biggest question though is why would anyone want to do this? I’m curious, Colin, you of all people! Why would you allow your rainbow fish to go 2 months? If a fish is too sick to eat and hadn’t eaten in 2 weeks, it’s time to consider your options.
I'm not saying fish should go for 2 months without food, but they can go for a long periods without food.
Unlike mammals that eat to keep warm, most fish take their body temperature from the surrounding environment. This means any food they eat is used for growth and movement. If adult fish are in good condition and have fat reserves, they can go for a very long time without food. Obviously it's better if they don't go for months without food but they can do it and don't suffer from starvation like mammals do.
After a few days without food, most animals (including fish), develop a smaller stomach. The stomach shrinks and stops producing stomach acids that help digest food. The body then goes into survival mode where they use less energy and cellular changes start to occur. Recent research has found that fasting for periods of time actually increases lifespan in all animals including people.
There are fish in the southern half of Australia in the Galaxias Genus, and they regularly go for months without food. Their stomach shuts down and they basically just hang around in shallow pools of water waiting for food and rain. These fish are really interesting because they can start their stomach up and get it working at optimum efficiency, within minutes of eating something. They can also increase the size of their stomach so it uses almost the entire digestive tract. This is a survival adaptation that lets them gorge on food when it's available and go into a conservative state when no food is available.
Galaxias only grow to about 4-6 inches and are long narrow fish, shaped like a pencil. So they don't hold a lot of body mass.
There is another smaller fish from the south-west of Western Australia, called the salamanderfish (Lepidogalaxias salamandroides). These fish reach 3 inches maximum and are usually less. They go dormant during summer and have to survive for 6 months or more without food or water. They bury into the mud and produce a mucous coating over their body to retain moisture. Many of these fish are only 1-2 inches long and 2-3 mm in diameter when they do this. They have a very small body mass but do survive for long periods without food.
In the deepest parts of the ocean are numerous species of fish and crustacean that go for up to a year or more without food. They are so far down in the ocean that food rarely makes it down that far. When something big like a whale dies, its carcass might sink to the bottom and the deep water fish can then gorge themselves. They might spend a month or more feeding on the rotting body and once it's gone they starve until the next body sinks down there.
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As for my rainbowfish going without food for 2 months, I went up north to study and asked my sister to feed my fish every couple of days. The food was all set up, tanks on timers, everything was ready to go. Well she fed them the first time and then forgot. So the fish went for 2 months without any food. They ate the plants in the tanks and picked all the algae off the glass. I lost some baby fish and a few specialised feeders, but most of the fish where fine.
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I agree with you that if a fish is sick and hasn't eaten for a while, then perhaps look at euthanising it. But the choice is up to the owner. Generally tho, when animals (including fish) are no longer interested in food, then it's time to let them move on to a better place.