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:
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.
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
- ^ Daniel Pauly; G. R. Morgan (1987). Length-based Methods in Fisheries Research. WorldFish. p. 299. ISBN 978-971-10-2228-0.
- ^ Food and Agriculture Organization of the United Nations (2005). Management Techniques for Elasmobranch Fisheries. Food & Agriculture Org. p. 93. ISBN 978-92-5-105403-1.
- ^ Moss, D.K.; Ivany, L.C.; Jones, D.S. (2021). "Fossil bivalves and the sclerochronological reawakening". Paleobiology. 47 (4): 551–573. doi:10.1017/pab.2021.16. S2CID 234844791.
- ^ John K. Carlson; Kenneth J. Goldman (5 April 2007). Special Issue: Age and Growth of Chondrichthyan Fishes: New Methods, Techniques and Analysis. Springer Science & Business Media. ISBN 978-1-4020-5570-6.
- ^ Pütter, August (1920). "Studien über physiologische Ähnlichkeit VI. Wachstumsähnlichkeiten". Pflüger's Archiv für die Gesamte Physiologie des Menschen und der Tiere. 180 (1): 298–340.
- ^ von Bertalanffy, Ludwig (1941). "Untersuchungen uber die Gesetzlichkeit des Wachstums. VII. Stoffwechseltypen und Wachstumstypen". Biologisches Zentralblatt. 61: 510–532.
- ^ a b von Bertalanffy, Ludwig (1957). "Quantitative laws in metabolism and growth". The Quarterly Review of Biology. 32 (3): 217–231.
- ^ Murray, J Alan (1921). "Normal growth in animals". The Journal of Agricultural Science. 11 (3): 258–274 – via Cambridge University Press.
- ^ Somers, I.F. (1988). "On a seasonally oscillating growth function". Fishbyte. 6 (1): 8–11.