The geophysicist M. King Hubbert (1903-1989) made use of the Hubbert curve, which is the derivative of the logistic curve, to formulate a model of the rate of petroleum extraction. According to this model, the rate of production of oil is determined by the rate of new oil well discovery; a "Hubbert peak" in the oil extraction rate will be followed by a gradual decline of oil production to nothing.

An example of a Hubbert curve is:

The Hubbert curve closely resembles the shape of, but is different from, the probability density function of the normal distribution.

Based on his model, Hubbert predicted (accurately) that, following from the peak of well discovery in 1948, oil production in the contiguous United States would peak in the late 1960s. According to this model, complete exhaustion of the U.S. oil reserves would then follow by the end of the 21st century.

Recently geologists have used Hubbert's model to predict the peak in world oil production. Due to difficulty in obtaining accurate data the predictions vary somewhat. Some of the geologists known as the pessimists are predicting in the range of the present to 2010, while those known as the optimists are predicting in the range of 2010 to 2020.

Some people believe that if the Hubbert model is accurate, there are drastic implications for human culture and technological society, which is currently heavily dependent on oil as a fuel and chemical feedstock. Some of them envisage a Malthusian catastrophe occurring as the oil finally runs out.

However, the validity of this model is disputed by many geophysicists, and most predictive economic models show that oil running out will lead to its replacement by other fuel sources and chemical feedstocks.

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