page_title: Ludwig von Bertalanffy
section_title: Individual growth model
hierarchical_section_title: Ludwig von Bertalanffy / Work / Individual growth model
caption_attribution_description: English: Passive analog model
context_page_description: Karl Ludwig von Bertalanffy was an Austrian biologist known as one of the founders of general systems theory. This is an interdisciplinary practice that describes systems with interacting components, applicable to biology, cybernetics and other fields. Bertalanffy proposed that the classical laws of thermodynamics might be applied to closed systems, but not necessarily to "open systems" such as living things. His mathematical model of an organism's growth over time, published in 1934, is still in use today.
  Bertalanffy grew up in Austria and subsequently worked in Vienna, London, Canada, and the United States.
context_section_description: The individual growth model published by Ludwig von Bertalanffy in 1934 is widely used in biological models and exists in a number of permutations.
  In its simplest version the so-called Bertalanffy growth equation is expressed as a differential equation of length (L) over time (t):
  when  is the Bertalanffy growth rate and  the ultimate length of the individual. This model was proposed earlier by August Friedrich Robert Pūtter (1879-1929), writing in 1920.
  The dynamic energy budget theory provides a mechanistic explanation of this model in the case of isomorphs that experience a constant food availability. The inverse of the Bertalanffy growth rate appears to depend linearly on the ultimate length, when different food levels are compared. The intercept relates to the maintenance costs, the slope to the rate at which reserve is mobilized for use by metabolism. The ultimate length equals the maximum length at high food availabilities.
caption: Passive electrical schematic of the Bertalanffy module together with equivalent expression in the Energy Systems Language
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