This article has few large issues when applying it to the hobbyist tank: temperature is a huge factor and they acknowledge it.
Light is also massive difference.
Flow and replacement water is also very different.
But..what is the real smoking gun here in the research that is different from our aquaria???
Plants!!
You need to find tropical or subtropical temps and then add lots of plants to such systems.
Here's one such article and it shows no correlation between P and N and algae vs submersed plant growth:
http://lakewatch.ifas.ufl.edu/LWTEAMFOLDER/CanfieldPubs/macrophyte.pdf
This addresses the plant absence/presence and temp factors. It also has a very high no# of lake samples!!
you can grow plants without CO2, the question is, at what rate, well, about 10-20X slower and species will compete for CO2 since it is very limiting. If you add a lot of PO4, then the plants will take up the CO2 at MAXIMUM rates since they are not limited as strongly by PO4. This is predicted by Liebig's Law of the Minimum. CO2 Limitations, strong ones anyway, will induce algae since plant growth is very much linked to ample CO2.
A non CO2 tank might have say 3 ppm when the lights 1st come on, then after about 1-2 hours, it'll be almost all gone.
Plants stop growing. a little more CO2 comes in, they get what little is there.
They adapt well to low levels if there's ample time to do so.
This is done at the enzymatic level.
CO2 enriched planted tanks, the plant has much "lazier" and fewer CO2 fixing enzymes. There is ample support in research for this also.
If the non CO2 is limited strong to moderately by PO4, plants still do okay, but they are not growing that fast, but...............they still grow. That is a key point.
If you suddenly remove the PO4 limitation, then what was once a well adapted system enzymatically, now is feast or famine. The plants do poorly in the transition period and you end up with algae.
Bridging ther gap between non CO2 and CO2 is an issue for hobbyists. a good hobby article on this is the Tropica one which the matrix shows how all types of planted tanks still have some growth, even at low light and non CO2 levels, what changes is the rate.
http://www.tropica.com/en/tropica-abc/basic-knowledge/co2-and-light.aspx
I can promise you, I can grow far more species together, in a CO2 enriched system, than anyone might in a non CO2 system.
Non CO2 enrichment has dependency on well, obviously.............CO2, so anything that drives more growth, gets more and more choked by this constraint. One way to think about this is by considering what moderately limiting CO2 is vs strongly limiting CO2 is and their affects on plants and growth.
If you say cut the rates of growth back by 40% via limiting CO2, this is not too bad, the plant can still use many of the same enzymes and does not need to rework the photosynthetic "factory". If you limiting the growth vai CO2 by say 90%, then the factory and enzymes need to be entirely reworked and the system crashes= algae.
Algae grows when plants do not. Since this hobby is based on growing nice planted tanks, I focus there, then algae is not much of an issue.
Examples of PO4 rich non CO2:
you can guess why there's no/little algae in this tank:
But how about this one?