Algae does need nutrients to grow but if you have seen how plants can grow on bare rock, you realize that once established it needs very little nutrients to stay (in fact hair algae needs less nutrients then your corals do to thrive). GHA are very efficient nutrient uptakers and even a little fish poop in the water will be grabbed before the skimmer can remove it.
You are going to have to physically remove it, yourself or some kind of grazer (keep in mind if you get something to graze on it the resulting poop will fuel the algae)
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