From what I have seen detritus naturally gets trapped in hair algae and byropsis. I would think that the detritus would then be a natural source of nutrition for the algae. I would think this means that once you have your nutrient problem under control you could still have algae issues just because of the natural trapping of detritus within the patches of the algae. So if this is true you could have a relatively nutrient free tank, but still have algae issues. I'm not saying this is fact but I have always wondered about it.
Not necessarily... detritus gets a bad rap a lot of time. Its a generic term for particulate organic matter (POM) and can include calcium bound with phosphates (like from Kalkwasser) or even vitamins bound to other molecules. Detritus is not fish poop. It could potentially be a source of organic phosphates (which may fuel inorganic phosphate levels as well), but the nitrogen cycle is different than the phosphate cycle: there is no pathway, biologically, from organic nitrogen to inorganic nitrogen. So given a system with higher than NSW levels of NO3, the organic phosphate can fuel hair algae. But this is done via bacterial pathways first, algae does not uptake particulate matter (I know this is what you are not saying). Then algae can leverage this source of bacteria.
