The smallest concentration?
Sounds like a simple question.
It's not and the answer is hardly "any".
That assumes a few things though.
1#, the nutrient is replentished rapidly and continuously.
Some tanks can have this via fish waste or tap etc as well as dosing, some have sediment sources as well.
2. Rate of growth is very very very important, some want faster growth for pruning and scaping, some want slower growth for lazier approaches, plants can grow very very very very slow if you want......I've seen Anubias plants 8 years old that grew a leave once every 1-2 years and they were fine and nice looking plants.
Rate of growth also implies
nutrient demand for that rate of growth.
3. Light and CO2 also play huge roles in the rate of growth and the rate of nutrient demand.
4. How do we assess " nutrient demand"?
Luxury uptake is more than the plant really needs, but like us and a fat reserve, they use the excess for leaner times etc, how lean should a pklant get and how close to limitation do you want to be?
It's clearly not needed nor provides a more stable environment for the plant on a biochemical, enzymatic, molecular, ecological or physiological level.
But some seem to want to argue that they do
Even in face of the overwhelming evidence to the contrary, and of course I'm the bad guy for pointing that out with the tidal wave of evidence from a wide range fields.
Self imposed barriers, assumptions and limitations.
I'm not sure why some folks put those upon themselves when it's clearly not required nor needed.
If you look at enzyme uptake, plants can and do adapt to various concentrations, especially K+. So at 1ppm, they have one type of enzyme transportor, at 10 ppm, they have another, at 0.1ppm, they have yet another.
It takes time for these enzymes to adapt and be "built". It takes less energy for the plant to take up the higher K+ concentration than the lower one.
We also know that higher does not influence algae.
Here's an example of graph used to show this for K+ in molecular plant science:
Regards,
Tom Barr