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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. Profession ...
by
Carl Sprengel Karl or Philipp Carl Sprengel (March 29, 1787 – April 19, 1859) was a German botanist from Schillerslage (now part of Burgdorf, Hanover). Sprengel worked under Albrecht Thaer (1752–1828) in Celle. He then worked from 1804 to 1808 wit ...
(1840) and later popularized by
Justus von Liebig Justus Freiherr von Liebig (12 May 1803 – 20 April 1873) was a German scientist who made major contributions to agricultural and biological chemistry, and is considered one of the principal founders of organic chemistry. As a professor at t ...
. It states that
growth Growth may refer to: Biology * Auxology, the study of all aspects of human physical growth * Bacterial growth * Cell growth * Growth hormone, a peptide hormone that stimulates growth * Human development (biology) * Plant growth * Secondary growth ...
is dictated not by total
resources Resource refers to all the materials available in our environment which are technologically accessible, economically feasible and culturally sustainable and help us to satisfy our needs and wants. Resources can broadly be classified upon their a ...
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 typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
s and
ecosystem model An ecosystem model is an abstract, usually mathematical, representation of an ecological system (ranging in scale from an individual population, to an ecological community, or even an entire biome), which is studied to better understand the re ...
s for factors such as
sunlight Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...
or
mineral nutrients In the context of nutrition, a mineral is a chemical element required as an essential nutrient by organisms to perform functions necessary for life. However, the four major structural elements in the human body by weight (oxygen, hydrogen, carbon, ...
.


Applications

This was originally applied to
plant Plants are predominantly photosynthetic eukaryotes of the kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all current definitions of Plantae exclud ...
or
crop A crop is a plant that can be grown and harvested extensively for profit or subsistence. When the plants of the same kind are cultivated at one place on a large scale, it is called a crop. Most crops are cultivated in agriculture or hydroponic ...
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, to put it more plainly, "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 typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
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 a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...
or
mineral nutrients In the context of nutrition, a mineral is a chemical element required as an essential nutrient by organisms to perform functions necessary for life. However, the four major structural elements in the human body by weight (oxygen, hydrogen, carbon, ...
(e.g.,
nitrate Nitrate is a polyatomic ion A polyatomic ion, also known as a molecular ion, is a covalent bonded set of two or more atoms, or of a metal complex, that can be considered to behave as a single unit and that has a net charge that is not zer ...
or
phosphate 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 orthophosphoric acid . The phosphate or orthophosphate ion is derived from phospho ...
). 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) The use of the equation is limited to a situation where there are steady state
ceteris paribus ' (also spelled '; () 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". A statement ...
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 nutritiona ...
, the law of the minimum was used by
William Cumming Rose William Cumming Rose (April 4, 1887 – September 25, 1985) was an American biochemist and nutritionist. He discovered the amino acid threonine, and his research determined the necessity for essential amino acids in diet and the minimum daily re ...
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 form ...
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 consumption of meat (red meat, poultry, seafood, insects, and the flesh of any other animal). It may also include abstaining from eating all by-products of animal slaughter. Vegetarianism m ...
s to enhance their
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
nutrition by
protein combining Protein combining or protein complementing is a dietary theory for protein nutrition that purports to optimize the biological value of protein intake. According to the theory, vegetarian and vegan diets may provide an insufficient amount of some ...
from various vegetable sources. One practitioner was
Nevin S. Scrimshaw Nevin Stewart Scrimshaw (January 20, 1918 – February 8, 2013) was an American food scientist and Institute Professor emeritus at the Massachusetts Institute of Technology. Scrimshaw was born in Milwaukee, Wisconsin. During the course of hi ...
fighting protein deficiency in India and Guatemala.
Frances Moore Lappé Frances Moore Lappé (born February 10, 1944) is an American researcher and author in the area of food and democracy policy. She is the author of 19 books including the three-million-copy selling 1971 book ''Diet for a Small Planet'', which the ...
published ''
Diet for a Small Planet ''Diet for a Small Planet'' is a 1971 bestselling book by Frances Moore Lappé, the first major book to note the environmental impact of meat production as wasteful and a contributor to global food scarcity. She argued for environmental vegetaria ...
'' 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 C ...
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 Robert Bruce Merrifield (July 15, 1921 – May 14, 2006) was an American biochemist who won the Nobel Prize in Chemistry in 1984 for the invention of solid phase peptide synthesis. Early life He was born in Fort Worth, Texas, on 15 July 1921, ...
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, water, soil, plants and animals, with a particular focus on how management affects the quality of life for both present and future generations ( stewardship) ...
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. O ...
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 is the opposite of infinite. It may refer to: * Finite number (disambiguation) * 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 marke ...
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 gas co ...
. 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 t ...
. 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". These failures may be addressed with
Pigovian tax A Pigouvian tax (also spelled Pigovian tax) is a tax on any market activity that generates negative externalities (i.e., external costs incurred by the producer that are not included in the market price). The tax is normally set by the government ...
es and subsidies, such as a
carbon tax A carbon tax is a tax levied on the carbon emissions required to produce goods and services. Carbon taxes are intended to make visible the "hidden" social costs of carbon emissions, which are otherwise felt only in indirect ways like more sev ...
. 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 yi, יצחק אזימאװ , birth_date = , birth_place = Petrovichi, Russian SFSR , spouse = , relatives = , children = 2 , death_date = , death_place = Manhattan, New York City, U.S. , nationality = Russian (1920–1922)Soviet (192 ...
noted, "We may be able to substitute nuclear power for coal power, and plastics for wood ... but for
phosphorus Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ear ...
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—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.A.N. Gorban, L.I. Pokidysheva, E.V. Smirnova, T.A. Tyukina
Law of the Minimum Paradoxes
Bull Math Biol 73(9) (2011), 2013–2044
Adaptation systems act as the
cooper Cooper, Cooper's, Coopers and similar may refer to: * Cooper (profession), a maker of wooden casks and other staved vessels Arts and entertainment * Cooper (producers), alias of Dutch producers Klubbheads * Cooper (video game character), in ...
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 change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
of what came before.


Biotechnology

One example of technological innovation is in
plant genetics Plant genetics is the study of genes, genetic variation, and heredity specifically in plants.Hartl D, Jones E (2005) It is generally considered a field of biology and botany, but intersects frequently with many other life sciences and is strongly ...
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 t ...
to alter biological dependence on the most limiting resource.
Biotechnological Biotechnology is the integration of natural sciences and engineering sciences in order to achieve the application of organisms, cells, parts thereof and molecular analogues for products and services. The term ''biotechnology'' was first used ...
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 *
Iron fertilization Iron fertilization is the intentional introduction of iron to iron-poor areas of the ocean surface to stimulate phytoplankton production. This is intended to enhance biological productivity and/or accelerate carbon dioxide () sequestration fr ...
*
Keystone species A keystone species is a species which has a disproportionately large effect on its natural environment relative to its abundance, a concept introduced in 1969 by the zoologist Robert T. Paine. Keystone species play a critical role in maintaini ...
*
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 is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
*
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 Specific definitions of sustainability are difficult to agree on and have varied in the literature and over time. The concept of sustainability can be used to guide decisions at the global, national, and individual levels (e.g. sustainable livi ...
* Theory of Constraints


References

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