This section also supports our observations in aquariums:
"Effects of living macrophytes differed with ambient nutrient conditions: under NH 4 + -surplus conditions, submersed macrophytes stimulated bacterioplankton through release of DOC or P, but in NH 4 + -depleted conditions, the influence of Vallisneria was negative or neutral."
What does this say?
They helped grow more bacteria when we add fertilizer such as NH4 -in our case as fish waste mostly (or very likely NO3 as well).
Under limiting N conditions, they have a neutral or negative effect.
So this would suggest a possible reason as to why BGA appears under N limiting conditions, the native bacteria may not be present, or competitive enough.
Most hobbyists seem to leave out such research or add the effects of plants in their theories, assumptions etc.
They are well linked to the bacteria, the algae and the inputs.
Taking out the plants really changes the system dramatically.
So think about this when folks make statements about how excess this or that causes harm, or is "bad". Maybe it is, but then again, maybe it's better and more stable.
Without a good study to answer the specific question, it's speculation.
However, such speculation is reasonable and supported vs saying whatever you want.
Not every test needs to answer the entire picture either, you might want to rule out one thing at a time, say allelopathy for causing algae.
So step wise, piece by piece, you are able to support such speculation more.
After a while, you see that it seems pretty likely after doing several small test.
That way you rule out possible confounding issues and alternatives.
Then the choices are much easier and narrowed down.
You get closer little by little to the truth.
But.........you never really will ever get 100% of that, so we often us estat's and confidence interval, say 95% of the time we get it right.
There is a lot of variables and variation in biology, so we deal with that variation by accepting a confidence level of 95%.
That's pretty high and pretty good, but we never get a 100% or absolute truth, pretty much like most things in life.
So do not fall for that trap.........clowns, Bozos, aqua schisters etc that claim "there is so much we do not know in biology, we cannot possibly hope to know everything about aquatic plants... and all the interactions and variables"yadyadayooo (Be wary of those type of folks that suggest this.).......these variables are accounted for and dealt with, of course we do not know everything, but that does mean the brains fall either.......
We can know 95% or more of something and be able to predict it with that accuracy.
Maybe we cannot get 95%, but some acceptable level, say 90%.
Those we chose. How much risk you are willing to accept etc.
Better than giving up or suggesting science cannot answer the question.
It can, it's just someone needs to do the work or look for the works that's been done on the topic.