Von Bertalanffy function
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:
- [math]\displaystyle{ L(a)= L_\infty(1-\exp(-k(a-t_0))) }[/math]
where [math]\displaystyle{ a }[/math] is age, [math]\displaystyle{ k }[/math] is the growth coefficient, [math]\displaystyle{ t_0 }[/math] is the theoretical age when size is zero, and [math]\displaystyle{ L_\infty }[/math] is asymptotic size.[4] It is the solution of the following linear differential equation:
- [math]\displaystyle{ \frac{dL}{da} = k (L_{\infty} - L ) }[/math]
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.[5]
See also
References
- ↑ Daniel Pauly; G. R. Morgan (1987). Length-based Methods in Fisheries Research. WorldFish. pp. 299. ISBN 978-971-10-2228-0. https://books.google.com/books?id=R4DC-ALyducC&pg=PA299.
- ↑ Food and Agriculture Organization of the United Nations (2005). Management Techniques for Elasmobranch Fisheries. Food & Agriculture Org.. pp. 93. ISBN 978-92-5-105403-1. https://books.google.com/books?id=KT0jXz2AyIsC&pg=PA93.
- ↑ 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.
- ↑ 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. https://books.google.com/books?id=ESUyc2dMrnEC&pg=PA301.
- ↑ Somers, I.F. (1988). "On a seasonally oscillating growth function". Fishbyte 6 (1): 8–11. https://econpapers.repec.org/RePEc:wfi:wfbyte:39518.
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