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''I = (PAT)'' is the mathematical notation of a formula put forward to describe the impact of human activity on the environment. :''I = P × A × T'' The expression equates
human impact on the environment Human impact on the environment (or anthropogenic impact) refers to changes to biophysical environments and to ecosystems, biodiversity, and natural resources caused directly or indirectly by humans. Modifying the environment to fit the need ...
to a function of three factors:
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction usi ...
(P), affluence (A) and
technology Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, scien ...
(T). It is similar in form to the Kaya identity which applies specifically to emissions of the
greenhouse gas A greenhouse gas (GHG or GhG) is a gas that absorbs and emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse gases in Earth's atmosphere are water vapor (), carbon dioxide (), methane ...
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
. The validity of expressing environmental impact as a simple product of independent factors, and the factors that should be included and their comparative importance, have been the subject of debate among
environmentalists An environmentalist is a person who is concerned with and/or advocates for the protection of the environment. An environmentalist can be considered a supporter of the goals of the environmental movement, "a political and ethical movement that se ...
. In particular, some have drawn attention to potential inter-relationships among the three factors; and others have wished to stress other factors not included in the formula, such as political and social structures, and the scope for beneficial, as well as harmful, environmental actions.


History

The equation was developed in 1970 during the course of a debate between
Barry Commoner Barry Commoner (May 28, 1917 – September 30, 2012) was an American cellular biologist, college professor, and politician. He was a leading ecologist and among the founders of the modern environmental movement. He was the director of the ...
, Paul R. Ehrlich and
John Holdren John Paul Holdren (born in Sewickley, Pennsylvania, March 1, 1944) is an American scientist who served as the senior advisor to President Barack Obama on science and technology issues through his roles as Assistant to the President for Science and ...
. Commoner argued that
environmental impact Environmental issues are effects of human activity on the biophysical environment, most often of which are harmful effects that cause environmental degradation. Environmental protection is the practice of protecting the natural environment on t ...
s in the United States were caused primarily by changes in its production technology following
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
and focused on present-day deteriorating environmental conditions in the United States. Ehrlich and Holdren argued that all three factors were important but emphasized the role of human
population growth Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to ...
, focusing on a broader scale, being less specific in space and time. —— The equation can aid in understanding some of the factors affecting human impacts on the environment, but it has also been cited as a basis for many of the dire environmental predictions of the 1970s by
Paul Ehrlich Paul Ehrlich (; 14 March 1854 – 20 August 1915) was a Nobel Prize-winning German physician and scientist who worked in the fields of hematology, immunology, and antimicrobial chemotherapy. Among his foremost achievements were finding a cure ...
,
George Wald George Wald (November 18, 1906 – April 12, 1997) was an American scientist who studied pigments in the retina. He won a share of the 1967 Nobel Prize in Physiology or Medicine with Haldan Keffer Hartline and Ragnar Granit. In 1970, Wald pr ...
,
Denis Hayes Denis Allen Hayes (born August 29, 1944) is an environmental advocate and an advocate for solar power. He rose to prominence in 1970 as the coordinator for the first Earth Day. Hayes founded the Earth Day Network and expanded it to more than 18 ...
,
Lester Brown Lester Russel Brown (born March 28, 1934) is an American environmental analyst, founder of the Worldwatch Institute, and founder and former president of the Earth Policy Institute, a nonprofit research organization based in Washington, D.C. B ...
, René Dubos, and Sidney Ripley that did not come to pass. R Bailey (2000) ''Earth day then and now'',
Reason Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, lang ...
32(1), 18-28
Neal Koblitz classified equations of this type as "mathematical
propaganda Propaganda is communication that is primarily used to influence or persuade an audience to further an agenda, which may not be objective and may be selectively presenting facts to encourage a particular synthesis or perception, or using loaded ...
" and criticized Ehrlich's use of them in the media (e.g. on ''
The Tonight Show ''The Tonight Show'' is an American late-night talk show that has aired on NBC since 1954. The show has been hosted by six comedians: Steve Allen (1954–1957), Jack Paar (1957–1962), Johnny Carson (1962–1992), Jay Leno (1992–2009 and 201 ...
'') to sway the general public. N Koblitz (1981) "Mathematics as Propaganda", in ''Mathematics Tomorrow'', ed. Lynn Steen, pp 111-120.


The dependent variable: Impact

The variable "I" in the "I=PAT" equation represents environmental impact. The environment may be viewed as a self-regenerating system that can endure a certain level of impact. The maximum endurable impact is called the
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 ...
. As long as "I" is less than the carrying capacity the associated population, affluence, and technology that make up "I" can be perpetually endured. If "I" exceeds the carrying capacity, then the system is said to be in overshoot, which may only be a temporary state. Overshoot may degrade the ability of the environment to endure impact, therefore reducing the carrying capacity. Impact may be measured using
ecological footprint The ecological footprint is a method promoted by the Global Footprint Network to measure human demand on natural capital, i.e. the quantity of nature it takes to support people or an economy. It tracks this demand through an ecological accounti ...
analysis in units of global hectares (gha). Ecological footprint per capita is a measure of the quantity of Earth's biologically productive surface that is needed to regenerate the resources consumed per capita. Impact is modeled as the product of three terms, giving gha as a result. Population is expressed in human numbers; therefore affluence is measured in units of gha per capita. Technology is a unitless efficiency factor.


The three factors


Population

In the I=PAT equation, the variable P represents the population of an area, such as the world. Since the rise of industrial societies, human population has been increasing exponentially. This has caused
Thomas Malthus Thomas Robert Malthus (; 13/14 February 1766 – 29 December 1834) was an English cleric, scholar and influential economist in the fields of political economy and demography. In his 1798 book ''An Essay on the Principle of Population'', Mal ...
,
Paul Ehrlich Paul Ehrlich (; 14 March 1854 – 20 August 1915) was a Nobel Prize-winning German physician and scientist who worked in the fields of hematology, immunology, and antimicrobial chemotherapy. Among his foremost achievements were finding a cure ...
and many others to postulate that this growth would continue until checked by widespread hunger and famine (see Malthusian growth model). The United Nations project that world population will increase from 7.7 billion today (2019) to 9.8 billion in 2050 and about 11.2 billion in 2100. These projections take into consideration that population growth has slowed in recent years as women are having fewer children. This phenomenon is the result of
demographic transition In demography, demographic transition is a phenomenon and theory which refers to the historical shift from high birth rates and high death rates in societies with minimal technology, education (especially of women) and economic development, to l ...
all over the world. Although the UN projects that human population may stabilize at around 11.2 billion in 2100, the I=PAT equation will continue to be relevant for the increasing
human impact on the environment Human impact on the environment (or anthropogenic impact) refers to changes to biophysical environments and to ecosystems, biodiversity, and natural resources caused directly or indirectly by humans. Modifying the environment to fit the need ...
in the short to mid-term future.


Environmental impacts of population

Increased population increases humans' environmental impact in many ways, which include but are not limited to: * Increased
land use Land use involves the management and modification of natural environment or wilderness into built environment such as settlements and semi-natural habitats such as arable fields, pastures, and managed woods. Land use by humans has a long ...
- Results in habitat loss for other species * Increased
resource use Resource consumption is about the consumption of non-renewable, or less often, renewable resources. Specifically, it may refer to: * water consumption * energy consumption ** electric energy consumption ** world energy consumption * natural gas ...
- Results in changes in land cover * Increased
pollution Pollution is the introduction of contaminants into the natural environment that cause adverse change. Pollution can take the form of any substance (solid, liquid, or gas) or energy (such as radioactivity, heat, sound, or light). Pollutants, th ...
- Can cause sickness and damages
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
s *Increased
climate change In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to ...
*Increased
biodiversity loss Biodiversity loss includes the worldwide extinction of different species, as well as the local reduction or loss of species in a certain habitat, resulting in a loss of biological diversity. The latter phenomenon can be temporary or permanent, de ...


Affluence

The variable A in the I=PAT equation stands for affluence. It represents the average consumption of each person in the population. As the consumption of each person increases, the total environmental impact increases as well. A common proxy for measuring consumption is through
GDP per capita Lists of countries by GDP per capita list the countries in the world by their gross domestic product (GDP) per capita. The lists may be based on nominal or purchasing power parity GDP. Gross national income (GNI) per capita accounts for inflo ...
. While GDP per capita measures production, it is often assumed that consumption increases when production increases. GDP per capita has been rising steadily over the last few centuries and is driving up human impact in the I=PAT equation.


Environmental impacts of affluence

Increased consumption significantly increases human environmental impact. This is because each product consumed has wide-ranging effects on the environment. For example, the construction of a car has the following environmental impacts: * 605,664 gallons of water for parts and tires; * 682 lbs. of pollution at a mine for the lead battery; * 2178 lbs. of discharge into water supply for the 22 lbs. of copper contained in the car. The more cars per capita, the greater the impact. Ecological impacts of each product are far-reaching; increases in consumption quickly result in large impacts on the environment through direct and indirect sources.


Technology

The T variable in the I=PAT equation represents how resource intensive the production of affluence is; how much environmental impact is involved in creating, transporting and disposing of the goods, services and amenities used. Improvements in efficiency can reduce resource intensiveness, reducing the T multiplier. Since technology can affect environmental impact in many different ways, the unit for T is often tailored for the situation to which I=PAT is being applied. For example, for a situation where the human impact on climate change is being measured, an appropriate unit for T might be greenhouse gas emissions per unit of GDP.


Environmental impacts of technology

Increases in efficiency from technologies can reduce specific environmental impacts, but due to increasing prosperity these technologies yield for the people and businesses that adopt them, technologies actually end up generating greater overall growth into the resources that sustain us.


Criticism

Criticisms of the I=PAT formula: * Too simplistic for complex problem * Interdependencies between variables * General sweeping assumptions of variables’ effect toward environmental impact * Cultural differences cause wide variation in impact * Technology cannot properly be expressed in a unit. Varying the unit will prove to be inaccurate, as the result of the calculation depends on one’s view of the situation.


Interdependencies

The I=PAT equation has been criticized for being too simplistic by assuming that P, A, and T are independent of each other. In reality, at least seven interdependencies between P, A, and T could exist, indicating that it is more correct to rewrite the equation as I = f(P,A,T). For example, a doubling of technological efficiency, or equivalently a reduction of the T-factor by 50%, does not necessarily reduce the environmental impact (I) by 50% if efficiency induced price reductions stimulate additional consumption of the resource that was supposed to be conserved, a phenomenon called the rebound effect (conservation) or
Jevons Paradox In economics, the Jevons paradox (; sometimes Jevons effect) occurs when technological progress or government policy increases the efficiency with which a resource is used (reducing the amount necessary for any one use), but the falling cost of ...
. As was shown by Alcott, despite significant improvements in the carbon intensity of GDP (i.e., the efficiency in carbon use) since 1980, world fossil energy consumption has increased in line with economic and population growth. Similarly, an extensive historical analysis of technological efficiency improvements has conclusively shown that improvements in the efficiency of energy and material use were almost always outpaced by economic growth, resulting in a net increase in resource use and associated pollution.


Neglect of beneficial human impacts

There have also been comments that this model depicts people as being purely detrimental to the environment, ignoring any
conservation Conservation is the preservation or efficient use of resources, or the conservation of various quantities under physical laws. Conservation may also refer to: Environment and natural resources * Nature conservation, the protection and manageme ...
or restoration efforts that societies have made.


Neglect of political and social contexts

Another major criticism of the I=PAT model is that it ignores the political context and decision-making structures of countries and groups. This means the equation does not account for varying degrees of power, influence, and responsibility of individuals over environmental impact. Also, the P factor does not account for the complexity of social structures or behaviors, resulting in blame being placed on the global poor. I=PAT does not account for sustainable resource use among some poor and indigenous populations, unfairly characterizing these populations whose cultures support low-impact practices. However, it has been argued that the latter criticism not only assumes low impacts for indigenous populations, but also misunderstands the I=PAT equation itself. Environmental impact is a function of human numbers, affluence (i.e., resources consumed per capita) and technology. It is assumed that small-scale societies have low environmental impacts due to their practices and orientations alone but there is little evidence to support this. In fact, the generally low impact of small-scale societies compared to state societies is due to a combination of their small numbers and low-level technology. Thus, the environmental sustainability of these societies is largely an epiphenomenon due their ''inability'' to significantly affect their environment. That all types of societies are subject to I=PAT was actually made clear in Ehrlich and Holdren's 1972 dialogue with Commoner in ''The Bulletin of the Atomic Scientists'', where they examine the pre-industrial (and indeed prehistoric) impact of human beings on the environment. Their position is further clarified by Holdren's 1993 paper, ''A Brief History of "IPAT"''.


Policy implications

As a result of the interdependencies between P, A, and T and potential rebound effects, policies aimed at decreasing environmental impacts through reductions in P, A, and T may not only be very difficult to implement (e.g.,
population control Population control is the practice of artificially maintaining the size of any population. It simply refers to the act of limiting the size of an animal population so that it remains manageable, as opposed to the act of protecting a species from ...
and material sufficiency and
degrowth Degrowth (french: décroissance) is a term used for both a political, economic, and social movement as well as a set of theories that critique the paradigm of economic growth. It can be described as an extensive framework that is based on crit ...
movements have been controversial) but also are likely to be rather ineffective compared to rationing (i.e., quotas) or Pigouvian taxation of resource use or pollution.


See also

* Affluence *
Carbon footprint A carbon footprint is the total greenhouse gas (GHG) emissions caused by an individual, event, organization, service, place or product, expressed as carbon dioxide equivalent (CO2e). Greenhouse gases, including the carbon-containing gases carbo ...
*
Eco-economic decoupling In economic and environmental fields, decoupling refers to an economy that would be able to grow without corresponding increases in environmental pressure. In many economies, increasing production ( GDP) currently raises pressure on the environ ...
*
Ecological footprint The ecological footprint is a method promoted by the Global Footprint Network to measure human demand on natural capital, i.e. the quantity of nature it takes to support people or an economy. It tracks this demand through an ecological accounti ...
*
Ecological indicator Ecological indicators are used to communicate information about ecosystems and the impact human activity has on ecosystems to groups such as the public or government policy makers. Ecosystems are complex and ecological indicators can help describe ...
*
Embodied energy Embodied energy is the sum of all the energy required to produce any goods or services, considered as if that energy was incorporated or 'embodied' in the product itself. The concept can be useful in determining the effectiveness of energy-produ ...
* Kaya identity *
Life cycle assessment Life cycle assessment or LCA (also known as life cycle analysis) is a methodology for assessing environmental impacts associated with all the stages of the life cycle of a commercial product, process, or service. For instance, in the case o ...
*
Population growth Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to ...
*
Sustainability measurement Sustainability measurement are tools and methods that attempt to measure the degree of sustainability of processes, products, services, businesses and so forth. Sustainability is difficult to quantify, perhaps even immeasurable. The metrics used to ...
*
Sustainability metrics and indices Sustainability metrics and indices are measures of sustainability, and attempt to quantify beyond the generic concept. Though there are disagreements among those from different disciplines (and influenced by different political beliefs about the ...
*
Technology Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, scien ...
*
Water footprint A water footprint shows the extent of water use in relation to consumption by people. The water footprint of an individual, community, or business is defined as the total volume of fresh water used to produce the goods and services consumed by t ...


References

{{DEFAULTSORT:I equals PAT Human impact on the environment Environmental social science concepts Equations Human geography Technology assessment Population ecology