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[APD] definition of "limiting"

When I say growth or growth rate I mean the scientific definition which
is the rate of tissue increase as defined by carbon content on a mass
basis. It has units of one over time. We can say that under specific
conditions a plant has a growth rate of 200%/week, it means that it has
added 2 times its original mass in a week and then weighs 3 times its
original mass. Therefore if the growth rate is 0% it means the (carbon)
mass is unchanged at the end of a week.

Growth rate is determined by a complex set of factors including the
concentration of all major & minor nutrients, including CO2, light,
light spectra and also by the concentration or presence of other toxic
elements which interfere with uptake or metabolism of the primary
nutrients. Metals are an example of toxins which can poison growth.
Complex toxins such as allelopathogens or decomposition by-products of
plastics are known examples of confounds which can affect growth

When I say "limited" I'm talking about Liebig's Law where the dominant
rate governing factor in the complex formula for a given test scenario.
In other words, if nitrate nitrogen were held at a constant low value of
say 0.5 ppm by continuous water change and all other mineral nutrients
and CO2 were held at appropriate levels, then the growth rate would
largely be determined by the concentration of nitrate nitrogen. Double
the nitrate nitrogen to 1 ppm and you should see twice the growth rate.
This is the governing factor for growth and therefore it is said to be
"limiting" in the sense of Liebig's Law. That doesn't mean that limiting
is preventing the plant or algae from growing at all, it means that if
you change the concentration of that nutrient in short supply it has the
dominant effect upon growth. Changes in other nutrient concentrations
will have only very minor effects upon the growth.

Its very important that we clearly understand the meaning of "limiting"
if we're going to communicate effectively on this topic.

See also <http://www.wordiq.com/definition/Liebig's_Law_of_the_Minimum>
and <http://www.avocadosource.com/tools/FertCalc_files/liebigs_law.htm>

Note that there is an hypothetical morphological limit to growth for
every species. At some point when all the governing factors are
carefully tuned, no further increase of growth rate can be gained. Its
very difficult to attain this experimentally. This is where the model
proposed by Justus von Liebig breaks down because the plant's own
morphology becomes the "limiting" factor. The size of the plant and the
rate at which it can conduct nutrients inside itself becomes the most
important factor. This is a difficult concept so I'm not surprised if
some folks may be having problems grokking it. I suggest you read up
using Internet references on biology rather than try to make sense of a
lot of the folderol you find on the APD. It's a case of "too much

In aquaria, we never attain the morphological limit often because we
can't keep up with the demands of the plants unless we had a system with
a huge pool of nutrients at a fixed concentration that were being
supplied continuously. You need a LOT of circulation in the tank to
ensure maximum CO2 uptake at the plant leaves. For CO2, at the
morphological limit, Dr Huebert has determined that beyond 50 ppm you
(probably) can't get any additional benefits from higher CO2
concentration. Tom has suggested that around 30 ppm CO2 is going to mean
CO2 would unlikely be the limiting or dominant growth regulating factor.
At that point, either nitrogen or phosphorus can be limiting but so can
any other major or minor nutrient. And if you have toxins in the tank
from plastic degradation (breakdown) or heavy metals, you may NOT be
getting nice growth at all.

Note: I'm not suggesting that you "cure" algae by making something
"limiting" for the growth of that algae. Algae, just like macrophytes
always has SOMETHING as the dominant factor governing growth rate. Algae
can attain a much higher growth rate than a macrophyte simply because
its morphology is efficient because it is small. For green water we get
doubling times of what days? Hours?

I suppose we can think that we have algae under "control" when the
growth rate of algae is lower than the growth rate of our fastest
growing macrophytes. You can't ever get stuff like Anubias to have a
faster growth rate than algae. That's why an aquarium with only Anubias
is probably going to have a tough time keeping ahead of algae, if algae
is present in the aquarium. If you bleach the Anubias, and sterilize the
tank, you can certainly prevent the introduction of filament algae. You
definitely need a good population of algae consumers like snails to keep
ahead of the growth of scum and bacteria in the tank. For tanks with
slow growing plants and with low light demands (Anubias, Crypts), I have
been suggesting that 1 wpg or LESS is more appropriate.

>From a practical standpoint, you often do NOT want truly high growth
rates in aquaria. Imagine that the mass of Hygrophila were doubling or
tripling each week! Practically, I think we're seeing doubling times for
Hygrophila around 4-8 weeks and most people would consider this high
growth. Its not high in the sense that its not even close to the
morphological growth limit for this species.


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