An Inverse Growth Curve Representation of the Clutter-Jones Stand Survival Model

Abstract

Abstract The Clutter-Jones (CJ) stand survival model has been widely used for the projection of the reduction in trees per unit area in a forest stand over time. To better understand this well-recognized model, we introduced a varying-parameter formulation as an alternative to its original difference equation form, where plot-specific effects are presented explicitly. This new parameterization turns out to be a type of Richards (generalized logistic) equation with its independent variable age log-transformed, which might be termed “log-Richards” (LR) and falls into the category of the generalized algebraic difference approach (GADA) models. Under the LR GADA representation, a half-reduction age, at which half of the trees in a stand die, may be examined to improve stand survival simulation. The new reformulation provides an inverse growth curve modeling viewpoint of stand survival over time. It may motivate one to derive new survival models directly from existing growth equations that allow for generating inverse growth curves, complementary to the commonly used differential equation method in developing stand mortality models. Study Implications: The Clutter-Jones stand survival model plays an important role in southern pine plantation management as a component of whole-stand modeling systems. This study introduces a varying-parameter formulation as an alternative to its original difference equation form, providing an inverse growth curve modeling viewpoint of stand survival over time.