The bubble your living in needs a water change.
LOL
I used to breed and supply shops with rainbowfish and other types of fish, and aquatic plants too. I don't know how many fry he rears in each tank, if he only has small numbers and lots of plants, then filtration is less of an issue. I am unsure how fast his fry grow, but there is lots of evidence to suggest that doing big regular water changes help fish grow faster.
I use to rear between 20-100 fry in tanks that were 2 foot long x 10 inches wide x 12 inches high. They had an air operated sponge filter, an airstone, a thin layer of gravel and a heater. I did big water changes each day and fed the fry heaps. Most of my rainbowfish were sold when 2-3 months of age and about 2 inches long.
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Many years ago aquariums did not have filters, heaters or decent lights. People had iron framed tanks and relied on plants to help keep the water clean. Their lights were yellow incandescent globes and they had a few fish in big tanks with lots of plants. They used candles, gas burners or wood fires to heat the tank or room.
People kept fish like this for many years, and a few even bred them. The fish that did best were usually from soft acid water, and marine fish and fish from hard alkaline water didn't do as well.
Some people did water changes on these tanks and some didn't. Most of the fish kept in these tanks only lived for a few years.
Fast forward to today and people regularly keep fish alive for years. Most people use filters and do water changes to keep the tank clean. Some people do natural systems that rely on plants to help keep the water clean.
If you have healthy disease free fish, and they aren't fed a lot of food, and there are lots of healthy actively growing plants in the aquarium, then yes you can keep fish without filters. However, water changes should be done regularly, regardless of filtration. Just to reduce the number of disease organisms in the water.
I'm not saying his fish look unhealthy, (his tanks looked milky cloudy and had a lot of algae), but keeping rainbows or any fish in over crowded tanks, and not doing big regular water changes, will eventually cause problems with disease outbreaks.