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Von Bertalanffy function

Growth curve model From Wikipedia, the free encyclopedia

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The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals.[1] The function is commonly applied in ecology to model fish growth[2] and in paleontology to model sclerochronological parameters of shell growth.[3]

The model can be written as the following:

where is age, is the growth coefficient, is the theoretical age when size is zero, and is asymptotic size.[4] It is the solution of the following linear differential equation:

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History

In 1920, August Pütter proposed that growth was the result of a balance between anabolism and catabolism.[5] von Bertalanffy, citing Pütter, borrowed this concept and published its equation first in 1941,[6] and elaborated on it later on.[7] The original equation was under the following form: with the weight, and constants of anabolism and catabolism respectively, and , constant exponants. Von Bertalanffy gave himself the resulting equation for as a function of , assuming that and  :[7]

Prior to von Bertalanffy, in 1921, J. A. Murray wrote a similar differential equation,[8] with , according to the then-called "surface law", and , but Murray's article does not appear in van Bertalanffy sources.

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Seasonally-adjusted von Bertalanffy

The seasonally-adjusted von Bertalanffy is an extension of this function that accounts for organism growth that occurs seasonally. It was created by I. F. Somers in 1988.[9]

See also

References

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