Carrying capacity
The carrying capacity of an environment 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). 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 has been applied to a few different processes in the past before finally being applied to population limits in the 1950s.[1] The notion of carrying capacity for humans is covered by the notion of sustainable population.
Not to be confused with Biocapacity.
At the global scale, scientific data indicates that humans are living beyond the carrying capacity of planet Earth and that this cannot continue indefinitely. This scientific evidence comes from many sources worldwide. It was presented in detail in the Millennium Ecosystem Assessment of 2005, a collaborative effort involving more than 1,360 experts worldwide.[2] More recent, detailed accounts are provided by ecological footprint accounting,[3] and interdisciplinary research on planetary boundaries to safe human use of the biosphere.[4] The Sixth Assessment Report on Climate Change from the IPCC[5] and the First Assessment Report on Biodiversity and Ecosystem Services by the IPBES,[6] large international summaries of the state of scientific knowledge regarding climate disruption and biodiversity loss, also support this view.
An early detailed examination of global limits was published in the 1972 book Limits to Growth, which has prompted follow-up commentary and analysis.[7] A 2012 review in 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 human carrying capacity may diminish.[8] This concern that humanity may be passing beyond "tipping points" for safe use of the biosphere has increased in subsequent years.[9][10] Recent estimates of Earth's carrying capacity run between two billion and four billion people, depending on how optimistic researchers are about international cooperation to solve collective action problems.[11] These estimates affirm that the more people we seek to sustain, the more modest their average standard of living needs to be.
Origins[edit]
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.[12]
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,[13][14] or that it was first used during 19th-century laboratory experiments with micro-organisms.[15] 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.[14] 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.[13][14]
Neo-Malthusians and eugenicists popularised the use of the words to describe the number of people the Earth can support in the 1950s,[14] 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.[16][17]
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).[16][18] 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.[16][19]
The specific reason why a population stops growing is known as a limiting or regulating factor.[20]
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.[21] Thus, the carrying capacity is the maximum number of individuals of a species that an environment can support.[22]
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:
where
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).
This equation is a modification of the original Verhulst model:
In this equation, the carrying capacity K, , is
When the Verhulst model is plotted into a graph, the population change over time takes the form of a sigmoid curve, reaching its highest level at K. This is the logistic growth curve and it is calculated with:
where
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 K.[25]
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. Where resources are finite, such as for a population of Osedax on a whale fall 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 K. In systems in which resources are constantly replenished, the population will reach its equilibrium at K.
Software is available to help calculate the carrying capacity of a given natural environment.[26]
Humans[edit]
Human carrying capacity is a function of how people live and the technology at their disposal. The two great economic revolutions that marked human history up to 1900—the agricultural and industrial revolutions—greatly increased the Earth's human carrying capacity, allowing human population to grow from 5 to 10 million people in 10,000 BCE to 1.5 billion in 1900.[50] The immense technological improvements of the past 100 years—in applied chemistry, physics, computing, genetic engineering, and more—have further increased Earth's human carrying capacity, at least in the short term. Without the Haber-Bosch process for fixing nitrogen, modern agriculture could not support 8 billion people.[51] Without the Green Revolution of the 1950s and 60s, famine might have culled large numbers of people in poorer countries during the last three decades of the twentieth century.[52]
Recent technological successes, however, have come at grave environmental costs. Climate change, ocean acidification, and the huge dead zones at the mouths of many of world's great rivers, are a function of the scale of contemporary agriculture[53] and the many other demands 8 billion people make on the planet.[54] Scientists now speak of humanity exceeding or threatening to exceed 9 planetary boundaries for safe use of the biosphere.[55] Humanity's unprecedented ecological impacts threaten to degrade the ecosystem services that people and the rest of life depend on—potentially decreasing Earth's human carrying capacity.[56] The signs that we have crossed this threshold are increasing.[57][6]
The fact that degrading Earth's essential services is obviously possible, and happening in some cases, suggests that 8 billion people may be above Earth's human carrying capacity. But human carrying capacity is always a function of a certain number of people living a certain way.[58][59] This was encapsulated by Paul Ehrlich and James Holdren's (1972) IPAT equation: environmental impact (I) = population (P) x affluence (A) x the technologies used to accommodate human demands (T).[60] IPAT has found spectacular confirmation in recent decades within climate science, where the Kaya identity for explaining changes in CO2 emissions is essentially IPAT with two technology factors broken out for ease of use.[61]
This suggests to technological optimists that new technological discoveries (or the deployment of existing ones) could continue to increase Earth's human carrying capacity, as it has in the past.[62] Yet technology has unexpected side effects, as we have seen with stratospheric ozone depletion, excessive nitrogen deposition in the world's rivers and bays, and global climate change.[56][10] This suggests that 8 billion people may be sustainable for a few generations, but not over the long term, and the term ‘carrying capacity’ implies a population that is sustainable indefinitely. It is possible, too, that efforts to anticipate and manage the impacts of powerful new technologies, or to divide up the efforts needed to keep global ecological impacts within sustainable bounds among more than 200 nations all pursuing their own self-interest, may prove too complicated to achieve over the long haul.[63]
Two things can be confidently asserted regarding Earth's carrying capacity, based on the Great Acceleration of energy and materials use, waste generation, and ecological degradation post-WW II.[64] First, expansions in human carrying capacity have come at the expense of many other species occupying Earth today.[6][65] Between 1970 and today, populations of wild vertebrates have declined 60%;[66] similarly sharp declines may have occurred among insects and vascular plants,[67] although the evidence is sketchier. So our successful efforts to increase human carrying capacity have come at the expense of Earth's capacity to sustain other species.[53] As we have converted habitat and resources to our own use, other species have sharply declined—to the extent that conservation biologists speak of an incipient mass species extinction.[68]
Second, expansions in per capita wealth and the concomitant increases in per capita consumption, resource use and waste generation, tend to decrease the total number of people that can be sustained, long term.[58][69] All else being equal, a richer population, living more luxuriously, has a lower carrying capacity than a poorer, more abstemious population.[59] As affluence goes up, population must come down to remain within any theoretical carrying capacity, and vice versa.[70]
As aforementioned, one issue with applying carrying capacity to any species is that ecosystems are not constant and change over time, therefore changing the resources available. Research has shown that sometimes the presence of human populations can increase local biodiversity, demonstrating that human habitation does not always lead to deforestation and decreased biodiversity. Another issue to consider when applying carrying capacity, especially to humans, is that measuring food resources is arbitrary. This is due to choosing what to consider (e.g., whether or not to include plants that are not available every year), how to classify what is considered (e.g., classifying edible plants that are not usually eaten as food resources or not), and determining if caloric values or nutritional values are privileged. Additional layers to this for humans are their cultural differences in taste (e.g., some consume flying termites) and individual choices on what to invest their labor into (e.g., fishing vs. farming), both of which vary over time. This leads to the need to determine whether or not to include all food resources or only those the population considered will consume. Carrying capacity measurements over large areas also assumes homogeneity in the resources available but this does not account for how resources and access to them can greatly vary within regions and populations. They also assume that the populations in the region only rely on that region’s resources even though humans exchange resources with others from other regions and there are few, if any, isolated populations. Variations in standards of living which directly impact resource consumption are also not taken into account. These issues show that while there are limits to resources, a more complex model of how humans interact with their ecosystem needs to be used to understand them.[71]