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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Carrying capacity | 1/5 | https://en.wikipedia.org/wiki/Carrying_capacity | reference | science, encyclopedia | 2026-05-05T07:17:32.393840+00:00 | kb-cron |
The carrying capacity of an ecosystem is the maximum population size of a biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available. 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. 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.
== 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
K
{\displaystyle K}
:
d
N
d
t
=
r
N
(
1
−
N
K
)
,
{\displaystyle {\mathrm {d} N \over \mathrm {d} t}=rN\left(1-{N \over K}\right),}
where
N is the population size, r is the intrinsic rate of natural increase K is the carrying capacity of the local environment, and dN/dt, the derivative of N with respect to time t, is the rate of change in population with time. Thus, the equation relates the growth rate of the population N to the current population size, incorporating the effect of the two constant parameters r and K. (Note that decrease is negative growth.) The choice of the letter K came from the German Kapazitätsgrenze (capacity limit).
The Verhulst equation is a first-order ordinary differential equation. Combined with an initial value
N
=
N
0
{\displaystyle N=N_{0}}
for the population at time
t
=
0
{\displaystyle t=0}
, the solution takes the form of the logistic growth curve:
N
(
t
)
=
K
1
+
A
e
−
r
t
,
{\displaystyle N(t)={K \over 1+Ae^{-rt}},}
where