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:

$P(t) = P_0e^{rt} \,$

where

• P₀ = 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
• Growth theory – related ideas from economics
• Human overpopulation
• Irruptive growth – an extension of the Malthusian model accounting for population explosions and crashes
• Malthusian catastrophe
• Neo-malthusianism

References

1. "Malthus, An Essay on the Principle of Population: Library of Economics" (description), Liberty Fund, Inc., 2000, EconLib.org webpage: EconLib-MalPop.
2. Turchin, P. "Complex population dynamics: a theoretical/empirical synthesis" Princeton online
3. Turchin, P. "Does Population Ecology Have General Laws?" Oikos 94:17–26. 2000
4. Paul Haemig, "Laws of Population Ecology", 2005
5. Cassell's Laws Of Nature, James Trefil, 2002 – Refer 'exponential growth law'.
6. 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
• Introduction to Social Macrodynamics Professor Andrey Korotayev
• Interesting Facts about Population Growth Mathematical Models from Jacobo Bulaevsky, Arcytech.