Malthusian growth model
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.^{[1]}
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.^{[2]} It is widely regarded in the field of population ecology as the first principle of population dynamics,^{[3]} with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law.^{[4]}
It is generally acknowledged that populations can not grow indefinitely. ^{[5]} 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.^{[6]}
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
References
- ↑ "Malthus, An Essay on the Principle of Population: Library of Economics" (description), Liberty Fund, Inc., 2000, EconLib.org webpage: EconLib-MalPop.
- ↑ Peter Turchin, "Complex population dynamics: a theoretical/empirical synthesis" Princeton online
- ↑ Turchin, P. "Does Population Ecology Have General Laws?" Oikos 94:17–26. 2000
- ↑ Paul Haemig, "Laws of Population Ecology", 2005
- ↑ Cassell's Laws Of Nature, James Trefil, 2002 – Refer 'exponential growth law'.
- ↑ Cohen, J. E. How Many People Can The Earth Support, 1995.
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.
- A Trap At The Escape From The Trap? Demographic-Structural Factors of Political Instability in Modern Africa and West Asia.
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