I = PAT

I = (PAT) is the mathematical notation of a formula put forward to describe the impact of human activity on the environment.

[1] It is similar in form to the Kaya identity, which applies specifically to emissions of the greenhouse gas carbon dioxide.

Ehrlich and Holdren argued that all three factors were important but emphasized the role of human population growth, focusing on a broader scale, being less specific in space and time.

[2][3][4][5] The equation can aid in understanding some of the factors affecting human impacts on the environment,[6] but it has also been cited as a basis for many of the dire environmental predictions of the 1970s by Paul Ehrlich, George Wald, Denis Hayes, Lester Brown, René Dubos, and Sidney Ripley that did not come to pass.

[7] Neal Koblitz classified equations of this type as "mathematical propaganda" and criticized Ehrlich's use of them in the media (e.g. on The Tonight Show) to sway the general public.

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.

[11] 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 or Jevons paradox.

For instance, economic activity in one area can lead to resource extraction in another or cause pollution that spreads to different locations.

[14] There have also been comments that this model depicts people as being purely detrimental to the environment, ignoring any conservation or restoration efforts that societies have made.

This means the equation does not account for varying degrees of power, influence, and responsibility of individuals over environmental impact.

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.

[18][19][20] 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,[5] where they examine the pre-industrial (and indeed prehistoric) impact of human beings on the environment.

[21] 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 and material sufficiency and degrowth 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.