Editing Ludwig von Bertalanffy (section)

=== Individual growth model ===
The [[cell growth|individual growth]] [[model (abstract)|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''):

<math>L'(t) = r_B \left( L_\infty - L(t) \right)</math>

when <math>r_B</math> is the Bertalanffy growth rate and <math>L_\infty</math> the ultimate length of the individual. This model was proposed earlier by August Friedrich Robert Pūtter (1879-1929), writing in 1920.<ref>August Friedrich Robert Pūtter (6 April 1879 - 11 March 1929) wrote a textbook on comparative physiology entitled ''Vergleichende Physiologie'' (Jena: G. Fischer, 1911) and many other notable works. For a translation of his "Studien ūber physiologische Ähnlichkeit. VI. Wachstumsähnlichkeiten" ("Studies on Physiological Similarity. VI. Analogies of Growth") in ''Pflūgers Archiv fūr die gesamte Physiologie des Menschen und der Tiere'', '''180''': 298-340, see http://www.dfo-mpo.gc.ca/Library/147555.pdf</ref>

The [[dynamic energy budget theory]] provides a mechanistic explanation of this model in the case of [[isomorph]]s 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.<ref name=ber1934>Bertalanffy, L. von, (1934). ''Untersuchungen über die Gesetzlichkeit des Wachstums''. I. Allgemeine Grundlagen der Theorie; mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Arch. Entwicklungsmech., 131:613-652.</ref>

[[Image:PassiveAnalog.jpg|thumb|right|Passive electrical schematic of the Bertalanffy module together with equivalent expression in the [[Energy Systems Language]]]]