For examples of criticism see Environmental and Natural Resource Economics, by Tom Tietenburg, 7 th edition , p. 151. For EIA criticism, see http://www.api.org/aboutoilgas/security/upload/Caruso2005.pdf
It is like a scales. Although we will still be finding oil, still developing new fields if just slightly more of the world’s production capacity -- maybe just 51% -- is declining. Then production will have peaked. This is why it will be far earlier than most people expect.