Everything about Malthusian Growth Model totally explained
-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.==Formula==
»
where P
0 = Initial Population,
r = growth rate,
t = time.
Exponential law
As noted by doctor
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, with
Malthus as the founder.
At best, it can be described as an approximate
physical law as it's generally acknowledged that nothing can grow at a constant rate indefinitely (
Cassell's Laws Of Nature, Professor
James Trefil, 2002 - Refer 'exponential growth law'). Professor of Populations Joel E. Cohen has stated that the simplicity of the model makes it useful for very short-term predictions and of not much use for predictions beyond 10 or 20 years (
How Many People Can The Earth Support, 1995).
Philosopher
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. This view has been echoed by many other philosophers since.
Also, "e: The Story Of A Number" by Eli Maor (1994), "What Evolution Is" by
Ernst Mayr, (2001),"The Complete Idiot's Guide To Calculus" by W. Michael Kelly (2002) and "The Galilean turn in population ecology" Mark Colyvan and Lev R. Ginzburg (2003).
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 take the natural log of 2 by the growth rate. To find the time it takes to increase by a factor of 3 we'd 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'd read Malthus'
An Essay on the Principle of Population.
Benjamin Gompertz also published work developing the Malthusian growth model further.
Further Information
Get more info on 'Malthusian Growth Model'.
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