摘要
生物的整个生长过程大都呈慢-快-慢的“S”形节律,对此可用logistic模型加以刻画。根据Lagrange中值定理,本文提出了logistic曲线上两个重要特征点——速生期始、终点的定量分析方法,根据这两点,可将其整个连续性生长过程划分为前慢期、速生期和后慢期3个阶段。最后,以小叶杨胸径和树高生长过程为例进行了验证。
The growth course of living things takes a slow-fast-slow('S' shape) pattern which can be described by Logistic model. Based on the Law of Lagrangian mean value,the quantitative analysis method for the two important characteristic points on Logistic curve, the starting and the stopping points of fast growing, is presented in this paper. The values on abscissa axis can be calculated with the following equations:
where s = [ (a + 1) + eα(α-1)] (eα-1)-1, a and b are two parameters of Logistic model.By these two points, the whole successive growth course of living things can be divided into three phases, pre-slow growing period, fast growing period and post-slow growing period. Finally in the paper, a real case of height and DBH increment courses of Populus simonii Carr. is tested and verified.
关键词
生长阶段
速生期
logistic曲线
Logistic curve
growth phase
fast growing peroid
Populus simonii Carr.
