TheInfoList

The carrying capacity of an
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...

is the maximum population size of a biological
species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individu ...

that can be sustained by that specific environment, given the food,
habitat In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers at the ...

,
water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known li ...

, and other
resource Resource refers to all the materials available in our environment which help us to satisfy our needs and wants. Resources can broadly be classified upon their availability — they are classified into renewable A renewable resource, also know ...

s available. The carrying capacity is defined as the
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
population ecology Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment (biophysical), environment, such as birth rate, birth and death rates, and by immigration and ...
corresponds to the population equilibrium, when the number of deaths in a population equals the number of births (as well as immigration and emigration). The effect of carrying capacity on
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. ...
is modelled with a
logistic function A logistic function or logistic curve is a common S-shaped curve (sigmoid curve A sigmoid function is a function (mathematics), mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid f ...
. Carrying capacity is applied to the maximum population an environment can support in
ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms In biol ...
,
agriculture Agriculture is the science, art and practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary Image:Family watching television 1958.jpg, Exercise trends, Increases in sedentary behaviors su ...

and
fisheries Fishery can mean either the enterprise of raising or harvesting fish Fish are aquatic Aquatic means relating to water Water (chemical formula H2O) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical ...

. The term carrying capacity has been applied to a few different processes in the past before finally being applied to population limits in the 1950s.

# Origins

In terms of
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. ...
, the term 'carrying capacity' was not explicitly used in 1838 by the
Belgian Belgians ( nl, Belgen, french: Belges, german: Belgier) are people identified with the Belgium, Kingdom of Belgium, a federation, federal state in Western Europe. As Belgium is a multinational state, this connection may be residential, legal, ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ...

Pierre François Verhulst 250px, Pierre François Verhulst Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logist ...
when he first published his equations based on research on modelling population growth. The origins of the term "carrying capacity" are uncertain, with sources variously stating that it was originally used "in the context of international
shipping Freight transport is the physical process of transport Transport (in British English), or transportation (in American English), is the Motion, movement of humans, animals, and cargo, goods from one location to another. In other words, ...

" in the 1840s, or that it was first used during 19th-century laboratory experiments with micro-organisms. A 2008 review finds the first use of the term in English was an 1845 report by the
US Secretary of State The United States secretary of state implements foreign policy ''Foreign Policy'' is an American news publication, founded in 1970 and focused on global affairs, current events, and domestic and international policy. It produces content dail ...
to the
US Senate The United States Senate is the upper chamber of the United States Congress The United States Congress is the legislature of the federal government of the United States. It is Bicameralism, bicameral, comprising a lower body, the ...
. It then became a term used generally in biology in the 1870s, being most developed in wildlife and
livestock Livestock are the domesticated Domestication is a sustained multi-generational relationship in which one group of organisms assumes a significant degree of influence over the reproduction and care of another group to secure a more predictabl ...
management in the early 1900s. It had become a staple term in ecology used to define the biological limits of a natural system related to population size in the 1950s. Neo-Malthusians and
eugenicist Eugenics ( ; from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ...
s popularised the use of the words to describe the number of people the Earth can support in the 1950s, although American
biostatisticians Biostatistics (also known as biometry) are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiment ...
Raymond Pearl Raymond Pearl (June 3, 1879 – November 17, 1940) was an American biologist Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a professional who has specialized knowledge in ...
and
Lowell Reed Lowell Jacob Reed (January 8, 1886 – April 29, 1966) was 7th president of the Johns Hopkins University The Johns Hopkins University is a private university, private research university in Baltimore, Baltimore, Maryland. Founded in 1876, the ...
had already applied it in these terms to human populations in the 1920s. Hadwen and Palmer (1922) defined carrying capacity as the density of stock that could be for a definite period without damage to the range. It was first used in the context of
wildlife management Wildlife management is the management process influencing interactions among and between wildlife Wildlife traditionally refers to undomesticated animal Animals (also called Metazoa) are multicellular A multicellular organism ...
by the American
Aldo Leopold Aldo Leopold (January 11, 1887 – April 21, 1948) was an American author, philosopher, naturalist, scientist, ecologist, forester, conservationist, and environmentalist. He was a professor at the University of Wisconsin A university () is an ed ...
in 1933, and a year later by the also American
Paul Lester Errington Paul may refer to: *Paul (name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity *Paul the Apostle (AD 5–67), also known as Saul of Tarsus or Saint Paul, early Christian missionar ...
, a
wetlands A wetland is a distinct ecosystem that is flooded by water, either permanently (for years or decades) or seasonally (for weeks or months). Flooding results in oxygen-free (Anoxic waters, anoxic) processes prevailing, especially in the soils. ...
specialist. Both used the term in different ways, Leopold largely in the sense of grazing animals (differentiating between a 'saturation level', an intrinsic level of density a species would live in, and carrying capacity, the most animals which could be in the field) and Errington defining 'carrying capacity' as the number of animals above which
predation Predation is a biological interaction In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical en ...

would become 'heavy' (this definition has largely been rejected, including by Errington himself). The important and popular 1953
textbook A textbook is a book A book is a medium for recording information Information is processed, organised and structured data. It provides context for data and enables decision making process. For example, a single customer’s sale at ...
on ecology by
Eugene Odum Eugene Pleasants Odum (September 17, 1913 – August 10, 2002) was an American biologist A biologist is a professional who has specialized knowledge in the field of biology, understanding the underlying mechanisms that govern the functioning ...
, ''Fundamentals of Ecology'', popularised the term in its modern meaning as the equilibrium value of the logistic model of population growth.

# Mathematics

The specific reason why a population stops growing is known as a
limiting In electronics, a limiter is a circuit that allows signals below a specified input power or level to pass unaffected while Attenuator (electronics), attenuating (lowering) the peaks of stronger signals that exceed this threshold. Limiting is a t ...
or regulating factor. The difference between the
birth rate The crude birth rate (CBR) in a period is the total number of live births per 1,000 population divided by the length of the period in years. The number of live births is normally taken from a universal registration system for births; population ...
and the
death rate Mortality rate, or death rate, is a measure of the number of death Death is the permanent, irreversible cessation of all biological functions that sustain a living Living or The Living may refer to: Common meanings *Life, a conditi ...
is the natural increase. If the population of a given organism is below the carrying capacity of a given environment, this environment could support a positive natural increase; should it find itself above that threshold the population typically decreases. Thus, the carrying capacity is the maximum number of individuals of a species that an environment can support. Population size decreases above carrying capacity due to a range of factors depending on the
species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individu ...

concerned, but can include insufficient
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gre ...

,
food supply Food security is a measure of the availability of food and individuals' Economic inequality, ability to access it. According the Committee on World Food Security, United Nations’ Committee on World Food Security, food security is defined as the ...
, or
sunlight Sunlight is a portion of the given off by the , in particular , , and light. On , sunlight is and through , and is obvious as when the Sun is above the . When direct is not blocked by s, it is experienced as sunshine, a combination of b ...

. The carrying capacity of an
environment Environment most often refers to: __NOTOC__ * Natural environment, all living and non-living things occurring naturally * Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
may vary for different species. In the standard ecological
algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ...

as illustrated in the simplified Verhulst model of
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. ...
, carrying capacity is represented by the constant K: : $\frac = rN \left\left(1 - \frac\right\right)$ where is the
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...

size, is the intrinsic growth rate is the carrying capacity of the local environment, and , the
derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

of with respect to time , is the rate of change in population with time. Thus, the equation relates the growth rate of the population to the current population size, incorporating the effect of the two constant parameters and . (Note that decrease is negative growth.) The choice of the letter came from the
German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citizens of Germany, see also German nationality law * German language The German la ...

''Kapazitätsgrenze'' (capacity limit). This equation is a modification of the original Verhulst model: : $\frac = rN - \alpha N^2$ In this equation, the carrying capacity , $N^*$, is : $N^* = \frac.$ When the Verhulst model is plotted into a graph, the population change over time takes the form of a
sigmoid curve A sigmoid function is a function (mathematics), mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formul ...
, reaching its highest level at . This is the logistic growth curve and it is calculated with: : $f\left(x\right) = \frac,$ where : is the
natural logarithm The natural logarithm of a number is its logarithm In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...
base (also known as
Euler's number The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways. It is the base of a logarithm, base of the natural logarithm. It is the Limit of a sequence, limit of ...
), : is the value of the sigmoid's midpoint, : is the curve's maximum value, : is the logistic growth rate or steepness of the curve and : $f\left(x_0\right) = L/2.$ The logistic growth curve depicts how population growth rate and the carrying capacity are inter-connected. As illustrated in the logistic growth curve model, when the population size is small, the population increases exponentially. However, as population size nears the carrying capacity, the growth decreases and reaches zero at . What determines a specific system's carrying capacity involves a
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 lim ...
which may be something such as available supplies of
food Food is any substance consumed to provide Nutrient, nutritional support for an organism. Food is usually of plant, animal or Fungus, fungal origin, and contains essential nutrients, such as carbohydrates, fats, protein (nutrient), proteins, vi ...
,
water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known li ...
, nesting areas, space or amount of
waste Waste (or wastes) are unwanted or unusable materials. Waste is any substance which is discarded after primary use, or is worthless, defective and of no use. A by-product A by-product or byproduct is a secondary product derived from a produ ...

that can be absorbed. Where resources are finite, such as for a population of ''
Osedax ''Osedax'' is a genus of deep-sea siboglinid polychaetes, commonly called boneworms, zombie worms, or bone-eating worms. ''Osedax'' is Latin for "bone-eater". The name alludes to how the worms bore into the bones of whale carcasses to reach enc ...
'' on a
whale fall A whale fall occurs when the carcass Carcass or Carcase (both pronounced ) may refer to: *Dressed carcass, the body of a livestock animal ready for butchery, after removal of skin, visceral organs, head, feet etc. *Carrion, the dead body of an ...

or bacteria in a petridish, the population will curve back down to zero after the resources have been exhausted, with the curve reaching its apogee at . In systems in which resources are constantly replenished, the population will reach its equilibrium at . Software is available to help calculate the carrying capacity of a given natural environment.

# Population ecology

Carrying capacity is a commonly used method for
biologist A biologist is a professional who has specialized knowledge in the field of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Mol ...
s when trying to better understand biological populations and the factors which affect them. When addressing biological populations, carrying capacity can be used as a stable dynamic equilibrium, taking into account extinction and colonization rates. In
population biology The term population biology has been used with different meanings. In 1971 Edward O. Wilson ''et al''. used the term in the sense of applying mathematical models to population genetics Population genetics is a subfield of that deals with gene ...
, logistic growth assumes that population size fluctuates above and below an equilibrium value. Numerous authors have questioned the usefulness of the term when applied to actual wild populations. Although useful in theory and in laboratory experiments, the use of carrying capacity as a method of measuring population limits in the environment is less useful as it assumes no interactions between species.

# Agriculture

Calculating the carrying capacity of a
paddock A paddock is a small enclosure for horses. In the United Kingdom, this term also applies to a field for a general automobile racing competition, particularly Formula 1 Formula One (also known as Formula 1 or F1) is the highest class of int ...

in Australia is done in
Dry Sheep EquivalentDry Sheep Equivalent (DSE) is a standard unit frequently used in Australia to compare the feed requirements of different classes of stock or to assess the carrying capacity and potential productivity of a given farm or area of grazing land. The uni ...
s (DSEs). A single DSE is 50 kg
Merino The Merino is a breed A breed is a specific group of domestic animals having homogeneous appearance (phenotype), homogeneous behavior, and/or other characteristics that distinguish it from other organisms of the same species. In literature, ...

wether Wether may refer to: *A castrated male goat *A castrated male Domestic sheep, sheep *A misspelling of weather *A misspelling of wikt:whether, whether *Wether Down, a hill in Hampshire *Wether Hill (Lake District), a hill in Cumbria *Wether Holm (di ...

, dry or non-pregnant ewe, which is maintained in a stable condition. Not only sheep are calculated in DSEs, the carrying capacity for other livestock is also calculated using this measure. A 200 kg weaned calf of a British style breed gaining 0.25 kg/day is 5.5DSE, but if the same weight of the same type of calf were gaining 0.75 kg/day, it would be measure at 8DSE. Cattle are not all the same, their DSEs can vary depending on breed, growth rates, weights, if it is a cow ('dam'), steer or ('bullock' in Australia), and if it
weaning Weaning is the process of gradually introducing an infant An infant (from the Latin word ''infans'', meaning 'unable to speak' or 'speechless') is the more formal or specialised synonym for the common term ''baby'', meaning the very y ...
, pregnant or 'wet' (i.e. ). It is important for farmers to calculate the carrying capacity of their land so they can establish a sustainable stocking rate. In other parts of the world different units are used for calculating carrying capacities. In the United Kingdom the paddock is measured in LU, livestock units, although different schemes exist for this.Chesterton, Chris, ''Revised Calculation of Livestock Units for Higher Level Stewardship Agreements, Technical Advice Note 33'' (Second edition), Rural Development Service, 2006
New Zealand uses either LU, EE (ewe equivalents) or SU (stock units). In the USA and Canada the traditional system uses
animal unitThe concept of an animal unit (AU) has traditionally been used in North America to facilitate planning, analysis and administration of forage use by grazing livestock, but the term has also had other applications (in relation to odor control regulati ...
s (AU). A French/Swiss unit is ''Unité de Gros Bétail'' (UGB). In some European countries such as Switzerland the pasture ( ''alm'' or ''alp'') is traditionally measured in ''Stoß'', with one ''Stoß'' equalling four ''Füße'' (feet). A more modern European system is ''Großvieheinheit'' (GV or GVE), corresponding to 500 kg in liveweight of cattle. In
extensive agriculture Extensive farming or extensive agriculture (as opposed to intensive farming) is an agricultural Agriculture is the science, art and practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary ...
2 GV/ha is a common stocking rate, in
intensive agriculture Intensive agriculture, also known as intensive farming (as opposed to extensive farming Extensive farming or extensive agriculture (as opposed to intensive farming) is an agricultural Agriculture is the science, art and practice of cultiv ...
, when
grazing In agriculture Agriculture is the science, art and practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary Image:Family watching television 1958.jpg, Exercise trends, Increases in sede ...

is supplemented with extra
fodder Fodder (), also called provender (), is any agricultural Agriculture is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary Image:Family watching television 1958.jpg, Exercise ...

, rates can be 5 to 10 GV/ha. In Europe average stocking rates vary depending on the country, in 2000 the Netherlands and Belgium had a very rate of 3.82 GV/ha and 3.19 GV/ha respectively, surrounding countries have rates of around 1 to 1.5 GV/ha, and more southern European countries have lower rates, with Spain having the lowest rate of 0.44 GV/ha. This system can also be applied to natural areas. Grazing
megaherbivore In terrestrial zoology, the megafauna (from Ancient Greek, Greek μέγας ''megas'' "large" and New Latin ''fauna'' "animal life") comprises the large or giant animals of an area, habitat, or geological period, extinct and/or extant. The most c ...
s at roughly 1 GV/ha is considered sustainable in central European grasslands, although this varies widely depending on many factors. In
ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms In biol ...
it is theoretically (i.e. cyclic succession,
patch dynamics Patch dynamics is an ecological perspective that the structure, function, and dynamics of ecological systems can be understood through studying their interactive patches. Patch dynamics, as a term, may also refer to the spatiotemporal changes wi ...
, ''Megaherbivorenhypothese'') taken that a grazing pressure of 0.3 GV/ha by wildlife is enough to hinder
afforestation Afforestation is the establishment of a forest or stand of trees (forestation Forestation is either growing existing forests (proforestation) or establishing forest growth on areas that either had forest or lacked it naturally. In the first ...
in a natural area. Because different species have different
ecological niche In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms ...

s, with horses for example grazing short grass, cattle longer grass, and goats or deer preferring to
browse Browsing is a kind of orienting strategy. It is supposed to identify something of relevance for the browsing organism. When used about human beings it is a metaphor taken from the animal kingdom. It is used, for example, about people browsing ope ...
shrubs,
niche differentiation In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms ...
allows a terrain to have slightly higher carrying capacity for a mixed group of species, than it would if there were only one species involved. Some
niche market A niche market is the subset of the market on which a specific product is focused. The market niche defines the product features aimed at satisfying specific market needs, as well as the price A price is the (usually not negative) quantit ...
schemes mandate lower stocking rates than can maximally be grazed on a pasture. In order to market ones' meat products as 'biodynamic', a lower ''Großvieheinheit'' of 1 to 1.5 (2.0) GV/ha is mandated, with some farms having an operating structure using only 0.5 to 0.8 GV/ha. The
Food and Agriculture Organization The Food and Agriculture Organization of the United Nations (FAO)french: Organisation des Nations unies pour l'alimentation et l'agriculture; it, Organizzazione delle Nazioni Unite per l'Alimentazione e l'Agricoltura is a specialized agency ...
has introduced three international units: FAO Livestock Units for North America,P Chilonda and J Otte, Indicators to monitor trends in livestock production at national, regional and international levels, ''Livestock Research for Rural Development'', 18 (8), 2006, Article #117
/ref>[ftp://ftp.fao.org/docrep/fao/007/j0945e/j0945e00.pdf ''Compendium of Agricultural-Environmental Indicators'', Annexe 2: Definitions, Food and Agriculture Organization of the United Nations (includes different values for various regions)] FAO Livestock Units for sub-Saharan Africa, and Tropical Livestock Units.FAO paper about Tropical Livestock Units
Another rougher and less precise method of determining the carrying capacity of a paddock is simply by looking objectively at the condition of the herd. In Australia, the national standardized system for rating livestock conditions is done by body condition scoring (BCS). An animal in a very poor condition is scored with a BCS of 0, and an animal which is extremely healthy is scored at 5: animals may be scored between these two numbers in increments of 0.25. At least 25 animals of the same type must be scored to provide a statistically representative number, and scoring must take place monthly -if the average falls, this may be due to a stocking rate above the paddock's carrying capacity or too little fodder. This method is less direct for determining stocking rates than looking at the pasture itself, because the changes in the condition of the stock may lag behind changes in the condition of the pasture.

# Fisheries

In
fisheries Fishery can mean either the enterprise of raising or harvesting fish Fish are aquatic Aquatic means relating to water Water (chemical formula H2O) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical ...
, the carrying capacity is used in the formulae to calculate sustainable yields for
fisheries management The goal of Fisheries management is to produce sustainable biological, social, and economic benefits from renewable aquatic resources. Fisheries are classified as renewable because the organisms of interest (e.g., fish, shellfish, reptiles, amphi ...
. The
maximum sustainable yield In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield (or catch) that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of ...
(MSY) is defined as "the highest average catch that can be continuously taken from an exploited population (=stock) under average environmental conditions". It was originally calculated as half of the carrying capacity, but has been refined over the years, now being seen as roughly 30% of the population, depending on the species or population. Because the population of a species which is brought below its carrying capacity due to fishing will find itself in the exponential phase of growth, as seen in the Verhulst model, the harvesting of an amount of fish at or below MSY is a surplus yield which can be sustainably harvested without reducing population size at equilibrium, keeping the population at its maximum
recruitment Recruitment refers to the overall process of identifying, sourcing, screening, shortlisting, and interviewing candidates for job Employment is the relationship between two parties Image:'Hip, Hip, Hurrah! Artist Festival at Skagen', by ...
(however, annual fishing can be seen as a modification of ''r'' in the equation -i.e. the environment has been modified, which means that the population size at equilibrium with annual fishing is slightly below what ''K'' would be without it). Note that mathematically and in practical terms, MSY is problematic. If mistakes are made and even a tiny amount of fish are harvested each year above the MSY, populations dynamics imply that the total population will eventually decrease to zero. The actual carrying capacity of the environment may fluctuate in the real world, which means that practically, MSY may actually vary slightly from year to yearMilner-Gulland, E.J., Mace, R. (1998)
''Conservation of biological resources''
Wiley-Blackwell.
(annual sustainable yields and maximum average yield attempt to take this into account). Other similar concepts are
optimum sustainable yield In population ecology Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment (biophysical), environment, such as birth rate, birth and death rates ...
and
maximum economic yield In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function (mathematics), function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, ei ...
, these are both harvest rates below MSY. These calculations are used to determine fishing quotas.

# Humans

Talk of economic and population growth leading to the limits of Earth's carrying capacity are popular in
environmentalism Environmentalism or environmental rights is a broad philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical real ...
. The potential limiting factor for the
human population Humans (''Homo sapiens'') are the most abundant and widespread species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A speci ...
might include water availability, energy availability,
renewable resource A renewable resource, also known as a flow resource, is a natural resource Natural resources are resource Resource refers to all the materials available in our environment which help us to satisfy our needs and wants. Resources can bro ...
s,
non-renewable resource A non-renewable resource (also called a finite resource) is a natural resource Natural resources are resource Resource refers to all the materials available in our environment which help us to satisfy our needs and wants. Resources can ...
s, heat removal,
photosynthetic capacity Photosynthetic capacity (Amax) is a measure of the maximum rate at which leaves are able to carbon fixation, fix carbon during photosynthesis. It is typically measured as the amount of carbon dioxide that is fixed per metre squared per second, for ...
, and land availability for
food production The food industry is a complex, global network of diverse businesses that supplies most of the food consumed by the World population, world's population. The term food industries covers a series of industrial activities directed at the product ...
. The applicability of carrying capacity as a measurement of the Earth's limits in terms of the human population has not been very useful, as the Verhulst equation does not allow an unequivocal calculation and prediction of the upper limits of population growth. Carrying capacity has been used as a tool in
Neo-Malthusian Malthusianism is the idea that Malthusian growth model, population growth is potentially exponential while the growth of the food supply or other resources is linear growth, linear, which eventually reduces living standards to the point of triggeri ...
arguments since the 1950s. The concept of carrying capacity has been applied to determining the population limits in
Shanghai Shanghai (, , Standard Chinese, Standard Mandarin pronunciation: ) is one of the four Direct-administered municipalities of China, direct-administered municipalities of the China, People's Republic of China. The city is located on the sou ...

, a city faced with rapid
urbanization Urbanization (or urbanisation) refers to the population shift from rural File:Rural landscape in Finland.jpg, A rural landscape in Lappeenranta, South Karelia, Finland. 15 July 2000. In general, a rural area or a countryside is a geographi ...
. Several estimates of the carrying capacity of the earth for humans have been made with a wide range of population numbers. A 2001 UN report said that two-thirds of the estimates fall in the range of 4 billion to 16 billion with unspecified standard errors, with a median of about 10 billion. The application of the concept of carrying capacity for the
human population Humans (''Homo sapiens'') are the most abundant and widespread species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A speci ...
, which exists in a
non-equilibrium Non-equilibrium thermodynamics is a branch of thermodynamics Thermodynamics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departme ...
, is criticized for not successfully being able to model the processes between humans and the environment. In popular discourse the concept has largely left the domain of academic consideration, and is simply used vaguely in the sense of a "balance between nature and human populations". In
human ecology #REDIRECT Human ecology 275px, Part of the '' built environment'' suburban tract housing">suburb.html" ;"title="built environment'' suburb">built environment'' suburban tract housing in Colorado Springs, Colorado Human ecology is an interdiscip ...
a popular definition from 1949 states "the maximum number of people that a given land area will maintain in perpetuity under a given system of usage without land degradation setting in". Sociologists have criticized this for numerous reasons. Aside from the fact that humans are able to adopt new customs and technology, some common critiques are 1.) an assumption an equilibrium population exists, 2.) difficulties in measuring resources, 3.) inability to account for human tastes and how much labour they will expend, 4.) assumption of full usage of resources, 5.) assumption of
landscape A landscape is the visible features of an area of land Land is the solid surface of Earth that is not permanently submerged in water. Most but not all land is situated at elevations above sea level (variable over geologic time frames) an ...

homogeneity, 6.) assumption that regions are isolated from each other, 7.) contradicted by history, and 8.) the standard of living is ignored.