The carrying capacity of an ecosystem is the maximum population size of a living biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available, over a fixed amount of time. The carrying capacity is defined as the environment's maximal load, which in population ecology corresponds to the population equilibrium, when the number of deaths in a population equals the number of births (as well as immigration and emigration). Carrying capacity of the environment implies that the resources extraction is not above the rate of regeneration of the resources and the wastes generated are within the assimilating capacity of the environment. The effect of carrying capacity on population dynamics is modelled with a logistic function. Carrying capacity is applied to the maximum population an environment can support in ecology, agriculture and fisheries. The term carrying capacity had been applied to a few different processes in the past before finally being applied to human population limits in the 1950s. The notion of carrying capacity for humans is covered by the notion of sustainable population.
An early detailed examination of global limits on human population was published in the 1972 book Limits to Growth, which has prompted follow-up commentary and analysis, including much criticism.Turner, Graham (2008) "A comparison of The Limits to Growth with thirty years of reality" Commonwealth Scientific and Industrial Research Organisation (CSIRO) Sustainable Ecosystems. A 2012 review in the journal Nature by 22 international researchers expressed concerns that the Earth may be "approaching a state shift" in which the biosphere may become less hospitable to human life, and in which the human carrying capacity may diminish. This concern that humanity may be passing beyond "tipping points" for safe use of the biosphere has increased in subsequent years. Although the global population has now passed 8 billion, recent estimates of Earth's carrying capacity run from two to four billion people, depending on how optimistic researchers are about the prospects for international cooperation to solve problems requiring collective action.Examples include Lianos, T. P., & Pseiridis, A. (2016). Sustainable welfare and optimum population size. Environment, Development and Sustainability, 18(6), 1679-1699; Tucker, C. K. (2019). A Planet of 3 Billion: Mapping Humanity's Long History of Ecological Destruction and Finding Our Way to a Resilient Future: a Global Citizen's Guide to Saving the Planet. Atlas Observatory Press; Dasgupta, P. (2019). Time and the generations: population ethics for a diminishing planet. Columbia University Press; Tamburino, L., & Bravo, G. (2021). Reconciling a positive ecological balance with human development: A quantitative assessment. Ecological Indicators, 129, 107973.
Origins In terms of population dynamics, the term 'carrying capacity' was not explicitly used in 1838 by the Belgian mathematician Pierre François Verhulst 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" 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 to the US Senate. It then became a term used generally in biology in the 1870s, being most developed in wildlife and livestock 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 eugenicists popularised the use of the words to describe the number of people the Earth can support in the 1950s, although American biostatisticians Raymond Pearl and Lowell Reed had already applied it in these terms to human populations in the 1920s.
Hadwen and Palmer (1923) defined carrying capacity as the density of stock that could be grazed for a definite period without damage to the range.
It was first used in the context of wildlife management by the American Aldo Leopold in 1933, and a year later by the American Paul Lester Errington, a wetlands specialist. They 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 would become 'heavy' (this definition has largely been rejected, including by Errington himself). The important and popular 1953 textbook on ecology by Eugene Odum, 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 or regulating factor.
The difference between the birth rate and the death rate 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 in long run.
Population size decreases above carrying capacity due to a range of factors depending on the species concerned, but can include insufficient space, food supply, or sunlight. The carrying capacity of an environment varies for different species.
In the standard ecological algebra as illustrated in the simplified Verhulst model of population dynamics, carrying capacity is represented by the constant :
where
is the population size, is the intrinsic rate of natural increase is the carrying capacity of the local environment, and , the derivative 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 Kapazitätsgrenze (capacity limit).
The Verhulst equation is a first-order ordinary differential equation. Combined with an initial value for the population at time , the solution takes the form of the logistic growth curve:
where
is Euler's number, is a constant determined by the initial population via .Murray, James D. "Mathematical biology: I. An introduction. Vol. 17." Springer Science & Business Media, 2007. When the initial population is below the carrying capacity, is positive; when it is above, is negative. is the initial exponential growth rate, and is the carrying capacity.
The logistic growth curve depicts how population growth rate and 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 carrying capacity, the growth decreases and reaches zero at .Swafford, Angela Lynn. "Logistic Population Growth: Equation, Definition & Graph." Study.com. N.p., 30 May 2015. Web. 21 May 2016. "Logistic Population Growth - Boundless Open Textbook." Boundless. N.p., n.d. Web. 21 May 2016.
What determines a specific system's carrying capacity involves a limiting factor; this may be available supplies of food or water, nesting areas, space, or the amount of waste that can be absorbed without degrading the environment and decreasing carrying capacity.
Population ecology
Carrying capacity is a commonly used concept for biologists when trying to better understand biological populations and the factors which affect them. When addressing biological populations, carrying capacity can be seen as a stable dynamic equilibrium, taking into account extinction and colonization rates. In population biology, 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, carrying capacity as a method of measuring population limits in the environment is less useful as it sometimes oversimplifies the interactions between species.
Agriculture It is important for farmers to calculate the carrying capacity of their land so they can establish a sustainable stocking rate. For example, calculating the carrying capacity of a paddock in Australia is done in Dry Sheep Equivalents (DSEs). A single DSE is 50 kg Merino wether, dry ewe 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 measured 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 ox ('bullock' in Australia), and if it weaning, pregnant or 'wet' (i.e. lactating).
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 Nix, J. 2009. Farm Management Pocketbook. 39th Ed. Corby: The Andersons Centre. New Zealand uses either LU,New Zealand Livestock Units on Ruralfind EE (ewe equivalents) or SU (stock units).Cornforth, I S and Sinclair, A G, Fertiliser Recommendations for Pastures and Crops in New Zealand, 2nd Ed (New Zealand Ministry of Agriculture, Wellington, New Zealand, 1984), quoted in A History of the Stock Unit System, New Zealand Ministry of Agriculture In the US and Canada the traditional system uses animal units (AU).Jasper Womach, Report for Congress: Agriculture: A Glossary of Terms, Programs, and Laws, 2005 Edition A French/Swiss unit is Unité de Gros Bétail (UGB).Coefficients de conversion des animaux en unités de gros bétail (French): Conversion factors for livestock units.La Commission Européen: Agriculture et Environnement (French) European Commission, Agriculture and Environment (English version).
In some European countries such as Switzerland the pasture (alm or alp) is traditionally measured in Stoß, with one Stoß equaling four Füße (feet). A more modern European system is Großvieheinheit (GV or GVE), corresponding to 500 kg in liveweight of cattle. In extensive agriculture 2 GV/ha is a common stocking rate, in intensive agriculture, when grazing is supplemented with extra fodder, 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 high 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.top agrar 11/2001, o.n.A.