There is a lot of work out there on what limits algae growth and the truth is that the identity of the limiting nutrient shifts from circumstance to circumstance. In high N conditions, P is the primary limiting factor but non-existent K (and Na) will also limit growth. High P and N is limiting... I'm ignoring the affect of Fe, Mg, Mn etc... In the aquarium scene the idea is that plant can out compete algae for NP & K if their other needs are met (generally we have plant packed aquarium with a NPK so up and ample CO2). If we skimp on the CO2 or let some nutrient level get too low then the algae explodes (and it seems to be pot-luck which algae gets out of hand). Given the ample access to water and CO2 and the high levels of micronutrients it possible that the plants are simply able to use the N and P faster than the algae can, rather than that they are limited in any particular way.
One other thing about algae, and why they do well in saline polluted rivers, is that they use Na and K ions to import bicarbonate and then use it as a C source. They can do this day and night. K-light is also Na-light so the algae have lost there most powerful weapon in their struggle against plants for nutrients.
tt4n