Carrying capacity
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. 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 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 and Errington defining 'carrying capacity' as the number of animals above which predation would become 'heavy'. 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.
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. 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.
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. 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, steer or ox, and if it weaning, pregnant or 'wet'.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. New Zealand uses either LU, EE or SU. In the US and Canada the traditional system uses animal units. A French/Swiss unit is Unité de Gros Bétail.
File:Sömmerung von Milchkühen, Schweizer Alp im Wallis.jpg|thumb|Summering of milk cows in the Swiss Alps in Valais Canton
In some European countries such as Switzerland the pasture is traditionally measured in Stoß, with one Stoß equaling four Füße. A more modern European system is Großvieheinheit, 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.
This system can also be applied to natural areas. Grazing megaherbivores at roughly 1 GV/ha is considered sustainable in central European grasslands, although this varies widely depending on many factors. In ecology it is theoretically taken that a grazing pressure of 0.3 GV/ha by wildlife is enough to hinder afforestation in a natural area. Because different species have different ecological niches, with horses for example grazing short grass, cattle longer grass, and goats or deer preferring to browse shrubs, niche differentiation 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 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 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 has introduced three international units to measure carrying capacity: FAO Livestock Units for North America, FAO Livestock Units for sub-Saharan Africa, and 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. 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.