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. The function is commonly applied in ecology to model fish growth and in paleontology to model sclerochronological parameters of shell growth.

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. It is the solution of the following linear differential equation:

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