Since you are posting in The Deep End you will want a more detailed answer than this but I can help from the aquatic plant perspective.
Plant growth is limited by N (nitrogen), P (phosphorus), and (K) potassium - a deficit of any one of these will hinder growth. These are the major elements, there are also minor elements like iron and a few others that can be limiting. Then each plant has a range of other things that limit or encourage growth like sunlight, salinity, oxygen, water movement, etc. There are hundreds of species of algae, and we really do not know what would limit each as most within a category look pretty much the same to us though some are different colors (green, pink, yellowish, blue) or forms (free-floating, attached, rope-like, matted, sheet, slimy).
Increasing phosphates alone will not increase organic activity unless that is the only thing that was limited, for the plants can still be limited by other things; sunlight, nitrogen, potassium, chlorine, salt, etc. But, if there were sufficient other nutrients and conditions were right (light, salinity, flow, etc) and algae spores were present, then adding Phosphates could trigger an algae bloom. Any one thing that is missing or restricted that is important to that species of algae will limit that type of algae. The concern is how many other types of algae there might be that are not limited by that low or missing value.
When I was participating in an online planted tank forum there was a brilliant young man from California working with the state on natural ponds and aquatic life (nice guy, kind and funny, so very smart -- I met him once and he is totally gorgeous too -- yes, Tom I still have a secret crush on you) and his take on algae seemed to be that if you tried to limit something in the pond/aquarium to choke out one particular algae, another algae would come along that was not limited by that so it was a losing proposition. Plus, they were a bear to really identify, too many are too similar and no one has really bothered to work out the precise needs of one vs the other. So, in the fish tank, we added fertilizers to get the plants to out grow the algae and stocked algae eating critters like shrimp to keep the rest at bay.
Probably not the answer you wanted, but I thought I'd put in these two cents just for fun.