I = PAT

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

The expression equates human impact (I) on the environment to a function of three factors: population (P), affluence (A) and technology (T). It is similar in form to the Kaya identity, which applies specifically to emissions of the greenhouse gas carbon dioxide.

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. 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.

The equation was developed in 1970 during the course of a debate between Barry Commoner, Paul R. Ehrlich and John Holdren. Commoner argued that environmental impacts in the United States were caused primarily by changes in its production technology following World War II 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, 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 a number 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. 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 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. 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 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.