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A Malthusian Growth Model, sometimes called a simple exponential growth model, is essentially exponential growth based on a constant rate. The model is named after Thomas Robert Malthus, who wrote ''An Essay on the Principle of Population'' (1798), one of the earliest and most influential books on population.〔"Malthus, An Essay on the Principle of Population: Library of Economics" (description), Liberty Fund, Inc., 2000, ''EconLib.org'' webpage: (EconLib-MalPop ).〕 Malthusian models have the following form: : where * ''P''0 = ''P''(0) is the initial population size, * ''r'' = the population growth rate, sometimes called Malthusian parameter, * ''t'' = time. This model is often referred to as the ''exponential law''.〔Peter Turchin, "Complex population dynamics: a theoretical/empirical synthesis" Princeton (online )〕 It is widely regarded in the field of population ecology as the first principle of population dynamics,〔Turchin, P. "Does Population Ecology Have General Laws?" Oikos 94:17–26. 2000〕 with Malthus as the founder. The exponential law is therefore also sometimes referred to as the ''Malthusian Law''.〔Paul Haemig, "Laws of Population Ecology", 2005〕 It is generally acknowledged that populations can not grow indefinitely. 〔''Cassell's Laws Of Nature'', James Trefil, 2002 – Refer 'exponential growth law'.〕 Joel E. Cohen has stated that the simplicity of the model makes it useful for short-term predictions, but not of much use for predictions beyond 10 or 20 years.〔Cohen, J. E. ''How Many People Can The Earth Support'', 1995.〕 The simplest way to limit Malthusian growth model is by extending it to a logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' essay. ==See also== *Albert Allen Bartlett – a leading proponent of the Malthusian Growth Model *Exogenous growth model – related growth model from economics *Exponential growth *Growth theory – related ideas from economics *Human overpopulation *Irruptive growth – an extension of the Malthusian model accounting for population explosions and crashes *Logistic function *Malthusian catastrophe *Mathematical models *Neo-malthusianism *Population *Population ecology *Scientific laws named after people – strictly speaking, no scientific law has been named after Malthus *Scientific phenomena named after people – being mathematical, and relating to population dynamics, the Malthusian growth model qualifies 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Malthusian growth model」の詳細全文を読む スポンサード リンク
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