小麦旗叶衰老过程不同数学模型拟合比较及衰老特征分析

吕国锋,范金平,张伯桥,高德荣,王慧,刘业宇,吴素兰,程凯,王秀娥

Comparison of different mathematical models describing flag leaf senescence process of wheat and characteristics of leaf senescence process

Guo-Feng LYU,Jin-Ping FAN,Bo-Qiao ZHANG,De-Rong GAO,Hui WANG,Ye-Yu LIU,Su-Lan WU,Kai CHENG,Xiu-E WANG

表1 Gompertz、Logistic和Richards模型拟合方程的特征参数

Table 1 Characteristic parameters of equations fitted by Gompertz, Logistic, and Richards models

模型 Model 数学式 Equation 最大衰老速度时间 TMRS 最大衰老速度时的% GLA ymax 最大衰老速度 MRS 绿色叶面积持续期 GLAD 平均衰老速度 ARS Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ $c$ $\frac{a}{\text{e}}$ $\frac{ab}{e}$ $c-\frac{\ln (-\ln 0.01)}{b}$ $\frac{-99a}{\text{GLAD}}$ Logistic $y=\frac{a}{1+{{\text{e}}^{-b(x-c)}}}$ $c$ $\frac{a}{2}$ $\frac{ab}{4}$ $c-\frac{\ln 99}{b}$ $\frac{-99a}{\text{GLAD}}$ Richards $y=\frac{a}{{{[1+{{\text{e}}^{-}}^{b(x-c)}]}^{\frac{1}{d}}}}$ $c-\frac{\lg d}{b}$ $\frac{a}{{{(d+1)}^{\frac{1}{d}}}}$ $\frac{ab}{{{(d+1)}^{(\frac{1}{d}+1)}}}$ $c-\frac{\ln ({{100}^{d}}-1)}{b}$ $\frac{-99a}{\text{GLAD}}$