The amount of nitrate being absorbed by algae is insignificant. The best way to remove nitrate is to do partial water change. We typically do 30~50% partial water change once a week to remove nitrate build up, as well as to restore water buffer, and minerals.
Everyone who had kept an aquarium for more than a few months would encounter algae more or less, whether they like it or not.
Algae feeds on mainly ammonia and nitrate, as well as phosphate, and some minerals too.
Excessive light is also another major reason, more so than the reasons above. It can be easily controlled by using an automatic timer to turn the lights on for only 8~12 hours.
In some natural environment, most places do not have overgrown algae as the water contain very little nitrogen based nutrients. You will not find any natural water with over 5ppm nitrate. Unless with human interferences such as leaking fertilizer into the water system, which can cause algae boom. In typical aquariums, nitrate concentration is usually between 20~40+ even with weekly partial water change, this number can be a whole lot higher in some less well maintained fish tanks. We usually aim for no more than 40 for the health of fish, because it is said that high nitrate can lower the immune system of fish.
In some natural places, you might find overgrown algae, but you should avoid it in a closed system like an aquarium. Although it is not that you can avoid it just because you want to.
Algae come in many forms. Some will grow on the surface areas only, some will make your water green, some will become hair like, some will create hard to remove green spots. I say avoid them at all cost.
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