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:

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