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A Malthusian growth model, sometimes called a simple exponential growth model, is essentially
exponential growth Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a ...
based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote ''
An Essay on the Principle of Population An, AN, aN, or an may refer to: Businesses and organizations * Airlinair (IATA airline code AN) * Alleanza Nazionale, a former political party in Italy * AnimeNEXT, an annual anime convention located in New Jersey * Anime North, a Canadian ...
'' (1798), one of the earliest and most influential books on
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction usi ...
."Malthus, An Essay on the Principle of Population: Library of Economics" Malthusian models have the following form: : P(t) = P_0e^ where * ''P''0 = ''P''(0) is the initial population size, * ''r'' = the population growth rate, which
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who ...
called the ''Malthusian parameter of population growth'' in
The Genetical Theory of Natural Selection ''The Genetical Theory of Natural Selection'' is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and ...
, and
Alfred J. Lotka Alfred James Lotka (March 2, 1880 – December 5, 1949) was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist, Lotka is best known for his proposa ...
called the ''intrinsic rate of increase'', * ''t'' = time. The model can also been written in the form of a differential equation: : \frac = rP with initial condition: P(0)= P0 This model is often referred to as the ''exponential law''. It is widely regarded in the field of
population ecology Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment, such as birth and death rates, and by immigration and emigration. The discipline is import ...
as the
first principle In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nua ...
of
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a ...
, with
Malthus Thomas Robert Malthus (; 13/14 February 1766 – 29 December 1834) was an English cleric, scholar and influential economist in the fields of political economy and demography. In his 1798 book ''An Essay on the Principle of Population'', Mal ...
as the founder. The exponential law is therefore also sometimes referred to as the ''Malthusian Law''. By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources: A model of population growth bounded by resource limitations was developed by
Pierre Francois Verhulst Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation ...
in 1838, after he had read Malthus' essay. Verhulst named the model a
logistic function A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the ...
.


See also

*
Albert Allen Bartlett Albert Allen Bartlett (March 21, 1923 – September 7, 2013) was an emeritus professor of physics at the University of Colorado at Boulder, US. Professor Bartlett had lectured over 1,742 times since September, 1969 on ''Arithmetic, Population, ...
– a leading proponent of the Malthusian Growth Model * Exogenous growth model – related growth model from
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...
*
Growth theory Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of ...
– related ideas from
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...
*
Human overpopulation Humans (''Homo sapiens'') are the most abundant and widespread species of primate, characterized by bipedalism and exceptional cognitive skills due to a large and complex brain. This has enabled the development of advanced tools, cultu ...
*
Irruptive growth Irruptive growth is a growth pattern over time, defined by a sudden rapid growth in the population of an organism. Irruptive growth is studied in population ecology. Population cycles often display irruptive growth, but with a predictable pattern s ...
– an extension of the Malthusian model accounting for population explosions and crashes *
Malthusian catastrophe Malthusianism is the idea that population growth is potentially exponential while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population die off. This event, c ...
*
Neo-malthusianism Malthusianism is the idea that population growth is potentially exponential while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population die off. This event, c ...
*
The Genetical Theory of Natural Selection ''The Genetical Theory of Natural Selection'' is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and ...


References


External links


Malthusian Growth Model
from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota

from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota

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 Andrey Vitalievich Korotayev (russian: link=yes, Андре́й Вита́льевич Корота́ев; born 17 February 1961) is a Russian anthropologist, economic historian, comparative political scientist, demographer and sociologist, ...

Ecological Orbits
Lev Ginzburg, Mark Colyvan {{modelling ecosystems, expanded=none Empirical laws Mathematical modeling Population Population ecology 1798 in economics