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
• 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

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.

Modelling ecosystems – trophic components General Abiotic component Abiotic stress Behaviour Biogeochemical cycle Biomass Biotic component Biotic stress Carrying capacity Competition Ecosystem Ecosystem ecology Ecosystem model Keystone species List of feeding behaviours Metabolic theory of ecology Productivity Resource Producers Autotrophs Chemosynthesis Chemotrophs Foundation species Mixotrophs Myco-heterotrophy Mycotroph Organotrophs Photoheterotrophs Photosynthesis Photosynthetic efficiency Phototrophs Primary nutritional groups Primary production Consumers Apex predator Bacterivore Carnivores Chemoorganotroph Foraging Generalist and specialist species Intraguild predation Herbivores Heterotroph Heterotrophic nutrition Insectivore Mesopredator release hypothesis Omnivores Optimal foraging theory Predation Prey switching Decomposers Chemoorganoheterotrophy Decomposition Detritivores Detritus Microorganisms Archaea Bacteriophage Environmental microbiology Lithoautotroph Lithotrophy Microbial cooperation Microbial ecology Microbial food web Microbial intelligence Microbial loop Microbial mat Microbial metabolism Phage ecology Food webs Biomagnification Ecological efficiency Ecological pyramid Energy flow Food chain Trophic level Example webs Cold seeps Hydrothermal vents Intertidal Kelp forests Lakes North Pacific Subtropical Gyre Rivers San Francisco Estuary Soil Tide pool Processes Ascendency Bioaccumulation Cascade effect Climax community Competitive exclusion principle Consumer-resource systems Copiotrophs Dominance Ecological network Ecological succession Energy quality Energy Systems Language f-ratio Feed conversion ratio Feeding frenzy Mesotrophic soil Nutrient cycle Oligotroph Paradox of the plankton Trophic cascade Trophic mutualism Trophic state index Defense/counter Animal coloration Antipredator adaptations Camouflage Deimatic behaviour Herbivore adaptations to plant defense Mimicry Plant defense against herbivory Predator avoidance in schooling fish

Modelling ecosystems – other components Population ecology Abundance Allee effect Depensation Ecological yield Effective population size Intraspecific competition Logistic function Malthusian growth model Maximum sustainable yield Overpopulation in wild animals Overexploitation Population cycle Population dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Resilience Small population size Stability Species Biodiversity Density-dependent inhibition Ecological effects of biodiversity Ecological extinction Endemic species Flagship species Gradient analysis Indicator species Introduced species Invasive species Latitudinal gradients in species diversity Minimum viable population Neutral theory Occupancy-abundance relationship Population viability analysis Priority effect Rapoport's rule Relative abundance distribution Relative species abundance Species diversity Species homogeneity Species richness Species distribution Species-area curve Umbrella species Species interaction Antibiosis Biological interaction Commensalism Community ecology Ecological facilitation Interspecific competition Mutualism Storage effect Spatial ecology Biogeography Cross-boundary subsidy Ecocline Ecotone Ecotype Disturbance Edge effects Foster's rule Habitat fragmentation Ideal free distribution Intermediate Disturbance Hypothesis Island biogeography Landscape ecology Landscape epidemiology Landscape limnology Metapopulation Patch dynamics r/K selection theory Source–sink dynamics Niche Ecological niche Ecological trap Ecosystem engineer Environmental niche modelling Guild Habitat Marine habitats Limiting similarity Niche apportionment models Niche construction Niche differentiation Other networks Assembly rules Bateman's principle Bioluminescence Ecological collapse Ecological debt Ecological deficit Ecological energetics Ecological indicator Ecological threshold Ecosystem diversity Emergence Extinction debt Kleiber's law Liebig's law of the minimum Marginal value theorem Thorson's rule Xerosere Other Allometry Alternative stable state Balance of nature Biological data visualization Constructal theory Ecocline Ecological economics Ecological footprint Ecological forecasting Ecological humanities Ecological stoichiometry Ecopath Ecosystem based fisheries Endolith Evolutionary ecology Functional ecology Industrial ecology Macroecology Microecosystem Natural environment Regime shift Systems ecology Theoretical ecology List of ecology topics