he warned was wishful thinking, US peak production would come no later than 1970. Likewise for the world, he projected a peak somewhere between 1985 (one trillion barrels ultimate recoverable) and 2000 (two trillion barrels recoverable). Ayers made his projections without a mathematical model. He wrote: "But if the curve is made to look reasonable, it is quite possible to adapt mathematical expressions to it and to determine, in this way, the peak dates corresponding to various ultimate recoverable reserve numbers" By observing past discoveries and production levels, and predicting future discovery trends, the geoscientist M. King Hubbert used statistical modelling in 1956 to predict that United States oil production would peak between 1965 and 1971. This prediction appeared accurate for a time however during 2018 daily production of oil in the United States was exceeding daily production in 1970, the year that was previously the peak. Hubbert used a semi-logistical curved model (sometimes incorrectly compared to a normal distribution). He assumed the production rate of a limited resource would follow a roughly symmetrical distribution. Depending on the limits of exploitability and market pressures, the rise or decline of resource production over time might be sharper or more stable, appear more linear or curved. That model and its variants are now called Hubbert peak theory; they have been used to describe and predict the peak and decline of production from regions, countries, and multinational areas. The same theory has also been applied to other limited-resource production. More recently, the term "peak oil" was popularized by Colin Campbell and Kjell Aleklett in 2002 when they helped form the Association for the Study of Peak Oil and Gas (ASPO). In his publications, Hubbert used the term "peak production rate" and "peak in the rate of discoveries". In a 2006 analysis of Hubbert theory, it was noted that uncertainty in real world oil production amounts and confusion in definitions increases the uncertainty in general of production predictions. By comparing the fit of various other models, it was found that Hubbert's methods yielded the closest fit overall but none of the models were very accurate. In 1956 Hubbert himself recommended using "a family of possible production curves" when predicting a production peak and decline curve. A comprehensive 2009 study of oil depletion by the UK Energy Research Centre noted: The report noted that Hubbert had used the logistic curve because it was mathematically convenient,