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通过对Chapman-Richards函数中的参数h, k 和 m取任意值,文中导出了广义的Chapman-Richards模型。基于通解的结构和生物学解释,该模型可以划分为8种类型(3大类),其中4种类型代表着树木和林分生长的4种典型生长模式,适合于在林业中应用。文中详细讨论了这4个模型的性质和参数的生物学意义。广义的Chapman-Richards模型能够很好地描述有渐进线或无渐进线,存在拐点或不存在拐点的各种生长曲线。为了说明模型的普适性,将该模型应用于4种不同初植密度的柳杉人工林林分平均胸径生长和红松天然林树木胸径和树高生长模拟中。通过比较广义的Chapman-Richards模型和Schnute模型,发现两个模型的参数和方程表达式是可以在理论上互相导出,从实际应用结果来看两者拟合结果也完全一致。图3表5参19。
By taking arbitrary values of parameters h, k and m in Chapman-Richards function, the generalized Chapman-Richards model is derived. Based on the structural and biological interpretation of the general solution, the model can be divided into eight types (three categories), of which four types represent four typical growth patterns of trees and stand growth and are suitable for application in forestry. The biological properties of these four models and their parameters are discussed in detail in this paper. The generalized Chapman-Richards model can well describe various growth curves with or without asymptotic lines, inflection points or inflection points. In order to illustrate the universality of the model, the model was applied to the mean DBH growth of Cryptomeria fortunei plantations and the DBH growth and tree height growth simulation of natural forests of Cryptomeria. By comparing the generalized Chapman-Richards model with the Schnute model, it is found that the parameters and the equation expressions of the two models can be derived from each other theoretically, and the fitting results are completely consistent from the practical application. Figure 3 Table 5 参 19.