Liebig's Law

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 is controlled not by the total amount 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. This principle can be summed up in the aphorism, "The availability of the most abundant nutrient in the soil is only as good as the availability of the least abundant nutrient in the soil." Or, to put it more plainly, "A chain is only as strong as its weakest link."

Dobenecks used the image of a barrel—often called Liebig's barrel—to explain Liebig's law. Just as the capacity of a barrel with staves of unequal length is limited by the shortest stave, so a plant's growth is limited by the nutrient in shortest supply.

If a system satisfies the law of the minimum then adaptation will equalize the load of different factors because the adaptation resource will be allocated for compensation of limitation.

Adaptation system acts as a cooper of Liebig's barrel and repairs the shortest stave to improve the barrel capacity. Indeed, in well-adapted systems the limiting factor should be compensated as far as this is possible. This observation follows the concept of resource competition and fitness maximization.

Due to the law of the minimum paradoxes, if we observe the Law of the Minimum in artificial systems, then under natural conditions adaptation will equalize the load of different factors and we can expect a violation of the law of the minimum. Inversely, if artificial systems demonstrate significant violation of the law of the minimum, then we can expect that under natural conditions adaptation will compensate this violation.

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). The availability of these may vary, such that at any given time one is more limiting than the others. Liebig's Law states that growth only occurs at the rate permitted by the most limiting.

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