Written by the Fiveable Content Team • Last updated August 2025
Written by the Fiveable Content Team • Last updated August 2025
Definition
The von Bertalanffy growth function is a model that describes the growth of an individual organism over time. It is often used in biological studies to characterize and predict the size of animals like fish.
The von Bertalanffy growth equation is given by $L(t) = L_{\infty}(1 - e^{-K(t-t_0)})$, where $L(t)$ is the length at time $t$, $L_{\infty}$ is the asymptotic maximum length, $K$ is the growth coefficient, and $t_0$ is the hypothetical age at zero length.
It can be used to model both linear and non-linear growth patterns depending on parameter values.
The von Bertalanffy equation can generate an infinite series when expanded as a Taylor series around a point.
The parameters $L_{\infty}$, $K$, and $t_0$ need to be estimated from data usually using methods such as nonlinear regression or maximum likelihood estimation.
In calculus, this model can illustrate concepts of limits and convergence related to infinite series.
An infinite sum of terms that are expressed as derivatives of a function evaluated at a single point.
Nonlinear Regression: A form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of model parameters.