Well, it started back around the 1960's and 1970's in Limnology sicences, then got transferred over to this hobby.
The problem was that Phillips et al 1978 suggested that plants will slowly be replaced by algae when there is a high PO4.
This was a suggestion/based on correlation, not a causual relationship.
But.........Phillips did not do a fair comparison in the correlation with lakes with plants vs algae etc.
They measured the algae in their water smaples, but not the macrophtyes/plants.
Algae have high concentrations of PO4 in them, more than the water.
So do plants.
But they did not add the plant fraction when they made the comparison.
so it skewed the data to suggest that algae likes and does better at higher PO4 in lakes.
when the plant PO4 fraction was later added to the data, there was no relationship in their study
310 citations by subsequent researchers later...........the myht has be engrained into science. Whittling myths out of science is tough, as tough as the hobby.
Well another question is....what type of lakes?
Warm shallow well plants lakes or the type that feeeze yearly and are deep in the middle and cold?
I've shown numerous good research papers that show that if you have lots of weeds ina lake, and add more nutrients, NO3/PO4 etc, you'll get what?
Most aquatic plants are weeds and limited by a few things: nutrients/light/being blasted washed out flooded so deep no light makes it/desiccation/water levels changes/CO2.
So we have stable water levels in our tank, CO2, light, nutrients, so they grow well and no algae.
When you louse up say CO2...then you get algae, when you neglect the plant nutrients: you get algae and so on.........
Those folks in the hobby from the past where just going off the best info they had at the time back then.
I figured this out before I found any research for support and why and who started it.
I knew adding PO4 did not cause algae.
I added it and had only intense plant growth.
So why would adding progressively more and more fish cause algae though?
We do not dose that(well, very very very few might consider it), because even low levels are bad for fish and it's very good to induce algae, whereas NO3 from KNO3, does not.
Most miss the NH4 and by the time they measure the NH4, it's already converted into NO3.
With active fast growing pklants and high O2 from their growth, there's no NH4 detected in a well run plant tank, why? They remove the NH4 directly as do the well fed bacteria who have lots of O2 to respire the oxidize the NH4 into NO3, which leaves none of that NH4 for the algae spores to bloom.
CO2 variation causes lots of variation for NH4 uptake, O2 levels and plant growth algae, so it's the more critical parameter in our tanks.
Many blamed PO4/NO3 rather than their CO2 levels for issues with alage.