What is law of minimum??
Answers
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 dictated not by total resources available, but by the scarcest resource (limiting factor). The law has also been applied to biological populations and ecosystem models for factors such as sunlight or mineral nutrients
Liebig's law has been extended to biological populations (and is commonly used in ecosystem modelling). 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 factor.[1]
For instance, in the equation below, the growth of population {\displaystyle O} O is a function of the minimum of three Michaelis-Menten terms representing limitation by factors {\displaystyle I} I, {\displaystyle N} N and {\displaystyle P} P.
{\displaystyle {\frac {dO}{dt}}=O\left(\min \left({\frac {\mu _{I}I}{k_{I}+I}},{\frac {\mu _{N}N}{k_{N}+N}},{\frac {\mu _{P}P}{k_{P}+P}}\right)-m\right)} {\displaystyle {\frac {dO}{dt}}=O\left(\min \left({\frac {\mu _{I}I}{k_{I}+I}},{\frac {\mu _{N}N}{k_{N}+N}},{\frac {\mu _{P}P}{k_{P}+P}}\right)-m\right)}
The use of the equation is limited to a situation where there are steady state ceteris paribus conditions, and factor interactions are tightly controlled. hopw this would help u
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