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:

${\displaystyle L(a)=L_{\infty }(1-\exp(-k(a-t_{0})))}$

where ${\displaystyle a}$ is age, ${\displaystyle k}$ is the growth coefficient, ${\displaystyle t_{0}}$ is the theoretical age when size is zero, and ${\displaystyle L_{\infty }}$ is asymptotic size.[4] It is the solution of the following linear differential equation:

${\displaystyle {\frac {dL}{da}}=k(L_{\infty }-L)}$

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

• Gompertz function
• Monod equation
• Michaelis–Menten kinetics

References

1. Daniel Pauly; G. R. Morgan (1987). Length-based Methods in Fisheries Research. WorldFish. p. 299. ISBN 978-971-10-2228-0.
2. 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.
3. 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.
4. 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.
5. Somers, I.F. (1988). "On a seasonally oscillating growth function". Fishbyte. 6 (1): 8–11.