Thursday, March 05, 2009

Liebig's law of the minimum

Growth is controlled not by the total of resources available, but by the scarcest resource (limiting factor). - WIKI

NVDL: In our case the limiting factor is energy from fossil fuels.
clipped from en.wikipedia.org

Liebig's Law of the Minimum, often simply called Liebig's Law or the Law of the Minimum, is a principle developed in agricultural science by Carl Sprengel (1828) and later popularized by Justus von Liebig. It states that growth is controlled not by the total of resources available, but by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth, where it was found that increasing the amount of plentiful nutrients did not increase plant growth. Only by increasing the amount of the limiting nutrient (the one most scarce in relation to "need") was the growth of a plant or crop improved.

Liebig's Law has been extended to biological populations (and is commonly used in ecosystem models). For example, the growth of an organism such as a plant may be dependent on a number of different factors, such as sunlight or mineral nutrients (e.g. nitrate or phosphate).
 \frac{dO}{dt} = min \left( \frac{I}{k_{I} + I}, \frac{N}{k_{N} + N}, \frac{P}{k_{P} + P} \right)
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