Why do these methods work in contravention of what seems to be found in nature?
Using simple aquarium test kits, I have measured PO4 and NO3 levels in healthy lakes which support an abundance of aquatic plant life. The PO4 and NO3 levels were too small to be measurable - nothing like as high as the levels commonly encouraged in the planted tank hobby. In these locales the lake water was very healthy, clear, not eutrophic. Algae types were neither dominant nor obvious.
While it is difficult to compare a natural environment such as a lake with an aquarium - lakes have thermal zones, areas of run-off, large dilution factors, large surface areas for gas exchange, relatively cool temperatures, and other features that aquariums do not have - the main difference I notice is that lake water is ALIVE. In aquariums, it has a tendency to become DEAD quickly, particularly as a result of chemical manipulation by the inexperienced aquarist.
IME / IMO it is all about water quality rather than nutrients - at least that is the way I tend to analyze and understand the problem or avoiding algae.
Algae prevail in DEAD water. Water changes rejuvenate the system. EI-style, which evolved in times before many people had spreadsheets etc, uses targeted dosing levels and water changes to ensure water quality is optimum. Water changes allow for unknowns to be addressed and buildups to be avoided. PPS is an analytic approach which hinges on providing enough but not too much, so as to ensure optimum water quality while having minimum water changes. When a PPS proponent fails in his/her dosing regime, they do a water change.
Nutrient dosing is just a part of the water quality story.
(Now if only that SAVE AS DRAFT button was down there I could have saved you from reading this embarrassing Plocher-like plonk).
Andrew Cribb