Richards Growth Curve

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Richards growth curve is often applied to fit empirical data on forest growth. However, the parameters of the Richards growth function are not easy to interpret in forest management terms. This graph allows interpretation of a Richards curve (red) in terms of site productivity and "rejuvenation bias"—a parameter of a 4/5 law model characterizing the effects of intensive thinning or delayed development at a early stage of growth.

Contributed by: Georgii Alexandrov (March 2011)
Open content licensed under CC BY-NC-SA



Input your data (or simulation results) by moving the points on the plot, or adding or removing points. Next, use the sliders to adjust parameters of the Chapman-Richards model as desired. Site productivity and rejuvenation bias are recalculated and displayed at the bottom of the plot. To add or remove a point, Alt-Click (Cmd-Click on Mac) somewhere in the plot area.

The Richards growth function is a solution of a special case of the Bernoulli differential equation,


This function is approximated by a 4/5 law model of forest growth in the neighborhood of the inflection point in order to provide an interpretation of its parameters in forest management terms.

Further details can be found in: G. A. Alexandrov, "Forest Growth in the Light of Thermodynamic Theory of Ecological Systems," Ecological Modelling, in press, doi:10.1016/j.ecolmodel.2007.11.022.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.