Malthusian growth model

The Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on a constant rate of compound interest. The model is named after the Reverend Thomas Malthus, who authored An Essay on the Principle of Population, one of the earliest and most influential books on population.
Contents
Formula
 P(t) = P_{0}e^{rt}
where P_{0} = Initial Population, r = growth rate, sometimes also called Malthusian Parameter, t = time.
Exponential law
As noted by Peter Turchin (Does population ecology have general laws?, 2001 and Complex Population Dynamics, 2003), this model is often referred to as The Exponential Law and is widely regarded in the field of population ecology as the first principle of population dynamics,^{[citation needed]} with Malthus as the founder.
At best, it can be described as an approximate physical law as it is generally acknowledged that nothing can grow at a constant rate 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 very shortterm predictions and of not much use for predictions beyond 10 or 20 years (How Many People Can The Earth Support, 1995). Antony Flew  in his introduction to the Penguin Books publication of Malthus' essay (1st edition)  argued a "certain limited resemblance" between Malthus' law of population to laws of Newtonian mechanics.
Malthusian law
The exponential law is also sometimes referred to as The Malthusian Law (refer "Laws Of Population Ecology" by Dr. Paul Haemig, 2005).
Rule of 70
The rule of 70 is a useful rule of thumb that roughly explains the time periods involved in exponential growth at a constant rate. For example, if growth is measured annually then a 1% growth rate results in a doubling every 70 years. At 2% doubling occurs every 35 years.
The number 70 comes from the observation that the natural log of 2 is approximately 0.7, by multiplying this by 100 we obtain 70. To find the doubling time we divide the natural log of 2 by the growth rate. To find the time it takes to increase by a factor of 3 we would use the natural log of 3, approximately 1.1.
Logistic growth model
The Malthusian growth model is the direct ancestor of the logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' An Essay on the Principle of Population. Benjamin Gompertz also published work developing the Malthusian growth model further.
See also
 Albert 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
 Irruptive growth  an extension of the Malthusian model accounting for population explosions and crashes
 Population
 Mathematical models
 Neomalthusianism
 Logistic function
 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
 Malthusian catastrophe
External links
 Malthusian Growth Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
 Logistic Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
 Laws Of Population Ecology Dr. Paul D. Haemig
 On principles, laws and theory of population ecology Professor of Entomology, Alan Berryman, Washington State University
 Mathematical Growth Models
 e the EXPONENTIAL  the Magic Number of GROWTH  Keith Tognetti, University of Wollongong, NSW, Australia
 Introduction to Social Macrodynamics Professor Andrey Korotayev
 Interesting Facts about Population Growth Mathematical Models from Jacobo Bulaevsky, Arcytech.
Topics on human population Major articles World population · Family planning · Green revolution · Overpopulation · Overconsumption (water crisis) · Reproductive rights · Sustainable developmentBiological topics Population biology · Population control (onechild policy · Immigration reduction) · Population decline · Population density (physiological density) · Population growth · Population pyramidPopulation ecology Carrying capacity · Ecological footprint · I = P • A • T · Malthusian growth model · World3 model · Food security · World energy consumption · World energy resources · Habitat destruction · Optimum populationLiterary works Lists Most highly populated countries · Metropolitan areas by populationEvents and
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