The generalized Chapman-Richards function and applications to tree and stand growth

Abstract

The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters η,k andm were unconstrained. Based on the structure of solutions and biological interpretations, the model could be classified into eight cases (three categories) at all and among them only 4 kinds of cases are suitable in forestry that represent four typical growth patterns of trees and stands. For each of 4 equations, the model properties and biological interpretations for parameters were discussed in detail. The generalized Chapman-Richards model was capable of describing a wide range of growth curves that was asymptotic or nonasymptotic, with or without inflection point. In order to illustrate the versatility, of the model, it was fitted to a group of data sets concerning the DBH growth of cryptomeria plantations with 4 initial densities and the DBH and height growth of natural Korean pinetree. Comparing the generalized Chapman-Richards function and the Schnute model, it was found that the parameters and expressions of the two models were interchangeable in theory, and the fitting results were explicitly identical in empirical applications.