Liebig's Law Of The Minimum
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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 Agricultural science (or agriscience for short) is a broad multidisciplinary field of biology that encompasses the parts of exact, natural, economic and social sciences that are used in the practice and understanding of agriculture. Professio ...
by Carl Sprengel (1840) and later popularized by
Justus von Liebig Justus ''Freiherr'' von Liebig (12 May 1803 – 18 April 1873) was a Germans, German scientist who made major contributions to the theory, practice, and pedagogy of chemistry, as well as to agricultural and biology, biological chemistry; he is ...
. It states that growth is dictated not by total
resources ''Resource'' refers to all the materials available in our environment which are Technology, technologically accessible, Economics, economically feasible and Culture, culturally Sustainability, sustainable and help us to satisfy our needs and want ...
available, but by the scarcest resource (
limiting factor A limiting factor is a variable of a system that causes a noticeable change in output or another measure of a type of system. The limiting factor is in a pyramid shape of organisms going up from the producers to consumers and so on. A factor not l ...
). The law has also been applied to biological
population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...
s and ecosystem models for factors such as
sunlight Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible spectrum, visible light perceptible to the human eye as well as invisible infrare ...
or mineral nutrients.


Applications

This was originally applied to
plant Plants are the eukaryotes that form the Kingdom (biology), kingdom Plantae; they are predominantly Photosynthesis, photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with c ...
or
crop A crop is a plant that can be grown and harvested extensively for profit or subsistence. In other words, a crop is a plant or plant product that is grown for a specific purpose such as food, Fiber, fibre, or fuel. When plants of the same spe ...
growth, where it was found that increasing the amount of plentiful
nutrient A nutrient is a substance used by an organism to survive, grow and reproduce. The requirement for dietary nutrient intake applies to animals, plants, fungi and protists. Nutrients can be incorporated into cells for metabolic purposes or excret ...
s 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 the rough analog, "A chain is only as strong as its weakest link." Though diagnosis of limiting factors to crop yields is a common study, the approach has been criticized.


Scientific applications

Liebig's law has been extended to biological
population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...
s (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 Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible spectrum, visible light perceptible to the human eye as well as invisible infrare ...
or mineral nutrients (e.g.,
nitrate Nitrate is a polyatomic ion with the chemical formula . salt (chemistry), Salts containing this ion are called nitrates. Nitrates are common components of fertilizers and explosives. Almost all inorganic nitrates are solubility, soluble in wa ...
or
phosphate Phosphates are the naturally occurring form of the element phosphorus. In chemistry, a phosphate is an anion, salt, functional group or ester derived from a phosphoric acid. It most commonly means orthophosphate, a derivative of orthop ...
). 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. For instance, in the equation below, the growth of population O is a function of the minimum of three Michaelis-Menten terms representing limitation by factors I, N and P. : \frac = O\left(\min \left( \frac, \frac, \frac \right) -m\right) Where O is the biomass concentration or population density. μI,μN,μP are the specific growth rates in response to the concentrations of three different limiting nutrients, represented by I,N,P respectively. kI,kN,kP are the half-saturation constants for the three nutrients I,N,P respectively. These constants represent the concentration of the nutrient at which the growth rate is half of its maximum. I,N,P are the concentrations of the three nutrients /factors. m is the mortality rate or decay constant. The use of the equation is limited to a situation where there are steady state
ceteris paribus ' (also spelled ') (Classical ) is a Latin phrase, meaning "other things equal"; some other English translations of the phrase are "all other things being equal", "other things held constant", "all else unchanged", and "all else being equal". ...
conditions, and factor interactions are tightly controlled.


Protein nutrition

In
human nutrition Human nutrition deals with the provision of essential nutrients in food that are necessary to support human life and good health. Poor nutrition is a chronic problem often linked to poverty, food security, or a poor understanding of nutrition ...
, the law of the minimum was used by William Cumming Rose to determine the
essential amino acid An essential amino acid, or indispensable amino acid, is an amino acid that cannot be synthesized from scratch by the organism fast enough to supply its demand, and must therefore come from the diet. Of the 21 amino acids common to all life forms ...
s. In 1931 he published his study "Feeding experiments with mixtures of highly refined amino acids". Knowledge of the essential amino acids has enabled
vegetarian Vegetarianism is the practice of abstaining from the Eating, consumption of meat (red meat, poultry, seafood, insects as food, insects, and the flesh of any other animal). It may also include abstaining from eating all by-products of animal slau ...
s to enhance their
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metab ...
nutrition by protein combining from various vegetable sources. One practitioner was Nevin S. Scrimshaw fighting protein deficiency in India and Guatemala. Frances Moore Lappé published '' Diet for a Small Planet'' in 1971 which popularized protein combining using grains, legumes, and dairy products. The law of the minimum was tested at
University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...
in 1947. "The formation of protein molecules is a coordinated tissue function and can be accomplished only when all amino acids which take part in the formation are present at the same time." It was further concluded, that "'incomplete' amino acid mixtures are not stored in the body, but are irreversibly further metabolized." Robert Bruce Merrifield was a laboratory assistant for the experiments. When he wrote his autobiography he recounted in 1993 the finding: :We showed that no net growth occurred when one essential amino acid was omitted from the diet, nor did it occur if that amino acid was fed several hours after the main feeding with the deficient diet.


Other applications

More recently Liebig's law is starting to find an application in
natural resource management Natural resource management (NRM) is the management of natural resources such as Land (economics), land, water, soil, plants and animals, with a particular focus on how management affects the quality of life for both present and future generati ...
where it surmises that growth in markets dependent upon
natural resource Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest, and cultural value. ...
inputs is restricted by the most limited input. As the
natural capital Natural capital is the world's stock of natural resources, which includes geology, soils, air, water and all living organisms. Some natural capital assets provide people with free goods and services, often called ecosystem services. All of t ...
upon which growth depends is limited in supply due to the
finite Finite may refer to: * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Gr ...
nature of the planet, Liebig's law encourages scientists and natural resource managers to calculate the scarcity of essential resources in order to allow for a multi-generational approach to
resource consumption Resource consumption is about the consumption of non-renewable, or less often, renewable resources. Specifically, it may refer to: * water consumption * energy consumption ** electric energy consumption ** world energy consumption * natural ...
. Neoclassical economic theory has sought to refute the issue of resource scarcity by application of the law of substitutability and
technological innovation Technological innovation is an extended concept of innovation. While innovation is a rather well-defined concept, it has a broad meaning to many people, and especially numerous understanding in the academic and business world. Innovation refers to ...
. The substitutability "law" states that as one resource is exhausted—and prices rise due to a lack of surplus—new markets based on alternative resources appear at certain prices in order to satisfy demand. Technological innovation implies that humans are able to use technology to fill the gaps in situations where resources are imperfectly substitutable. A market-based theory depends on proper pricing. Where resources such as clean air and water are not accounted for, there will be a "
market failure In neoclassical economics, market failure is a situation in which the allocation of goods and services by a free market is not Pareto efficient, often leading to a net loss of economic value.Paul Krugman and Robin Wells Krugman, Robin Wells (2006 ...
". These failures may be addressed with Pigovian taxes and subsidies, such as a
carbon tax A carbon tax is a tax levied on the carbon emissions from producing goods and services. Carbon taxes are intended to make visible the hidden Social cost of carbon, social costs of carbon emissions. They are designed to reduce greenhouse gas emis ...
. While the theory of the law of substitutability is a useful rule of thumb, some resources may be so fundamental that there exist no substitutes. For example,
Isaac Asimov Isaac Asimov ( ;  – April 6, 1992) was an Russian-born American writer and professor of biochemistry at Boston University. During his lifetime, Asimov was considered one of the "Big Three" science fiction writers, along with Robert A. H ...
noted, "We may be able to substitute nuclear power for coal power, and plastics for wood ... but for
phosphorus Phosphorus is a chemical element; it has Chemical symbol, symbol P and atomic number 15. All elemental forms of phosphorus are highly Reactivity (chemistry), reactive and are therefore never found in nature. They can nevertheless be prepared ar ...
there is neither substitute nor replacement." Where no substitutes exist, such as phosphorus, recycling will be necessary. This may require careful long-term planning and governmental intervention, in part to create Pigovian taxes to allow efficient market allocation of resources, in part to address other market failures such as excessive time discounting.


Liebig's barrel

Dobenecks used the image of a
barrel A barrel or cask is a hollow cylindrical container with a bulging center, longer than it is wide. They are traditionally made of wooden stave (wood), staves and bound by wooden or metal hoops. The word vat is often used for large containers ...
— often called "Liebig's barrel" — to explain Liebig's law. Just as the maximum practical capacity of a barrel with staves of unequal length is limited by the length of the shortest stave. Similarly, a plant's growth is limited by the
nutrient A nutrient is a substance used by an organism to survive, grow and reproduce. The requirement for dietary nutrient intake applies to animals, plants, fungi and protists. Nutrients can be incorporated into cells for metabolic purposes or excret ...
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 systems act as the cooper of Liebig's barrel and lengthens the shortest stave to improve barrel capacity. Indeed, in well-adapted systems the limiting factor should be compensated as far as 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. In a limited system life will adjust as an
evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...
of what came before.


Biotechnology

One example of technological innovation is in plant genetics whereby the biological characteristics of species can be changed by employing
genetic modification Genetic engineering, also called genetic modification or genetic manipulation, is the modification and manipulation of an organism's genes using technology. It is a set of technologies used to change the genetic makeup of cells, including th ...
to alter biological dependence on the most limiting resource. Biotechnological innovations are thus able to extend the limits for growth in species by an increment until a new limiting factor is established, which can then be challenged through technological innovation. Theoretically there is no limit to the number of possible increments towards an unknown productivity limit. This would be either the point where the increment to be advanced is so small it cannot be justified economically or where technology meets an invulnerable natural barrier. It may be worth adding that biotechnology itself is totally dependent on external sources of
natural capital Natural capital is the world's stock of natural resources, which includes geology, soils, air, water and all living organisms. Some natural capital assets provide people with free goods and services, often called ecosystem services. All of t ...
.


See also

* Bottleneck (disambiguation) *
Critical chain Critical chain project management (CCPM) is a method of planning and managing projects that emphasizes the resources (people, equipment, physical space) required to execute project tasks. It was developed by Eliyahu M. Goldratt. It differs fro ...
*
Critical path method The critical path method (CPM), or critical path analysis (CPA), is an algorithm for schedule (project management), scheduling a set of project activities. A critical path is determined by identifying the longest stretch of dependent activiti ...
* Iron fertilization *
Keystone species A keystone species is a species that has a disproportionately large effect on its natural environment relative to its abundance. The concept was introduced in 1969 by the zoologist Robert T. Paine. Keystone species play a critical role in main ...
*
Limiting factor A limiting factor is a variable of a system that causes a noticeable change in output or another measure of a type of system. The limiting factor is in a pyramid shape of organisms going up from the producers to consumers and so on. A factor not l ...
*
Random walk In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a rand ...
*
Rate determining step In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step or r/d step) or rate-limiting step. For a given reaction mechanism, the prediction of the ...
*
Sustainability Sustainability is a social goal for people to co-exist on Earth over a long period of time. Definitions of this term are disputed and have varied with literature, context, and time. Sustainability usually has three dimensions (or pillars): env ...
*
Theory of Constraints The theory of constraints (TOC) is a management paradigm that views any manageable system as being limited in achieving more of its goals by a very small number of constraints. There is always at least one constraint, and TOC uses a focusing p ...


References

{{DEFAULTSORT:Liebig's Law Of The Minimum Agronomy Ecological theories Systems ecology Justus von Liebig