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3 Logistic、Gompertz和Richards模型对不同延绿类型品种拟合结果

Table 3 Curve fitting of Logistic, Gompertz, and Richards models for the flag leaf senescence process of varieties tested

类型 Type 品种数 No. of varieties 模型 Model 方程 Equation 方程系数Coefficients 模型适合性 Fitness of model a b c d R2 RMSE 2011 延绿 Stay green 10 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 98.40 -3.67 1.35 0.9536 4.149 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 98.53 -3.15 1.48 0.9577 3.961 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 99.20 -1.97 6.30 1.57×10-4 0.9426 4.662 中等延绿 Moderately stay green 21 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 95.59 -4.93 0.93 0.9646 6.436 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 96.71 -2.95 1.09 0.9710 5.798 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 97.05 -2.62 7.40 6.85×10-8 0.9713 5.858 中等早衰 Moderately non-stay green 28 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 95.43 -5.39 0.72 0.9846 4.760 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 96.91 -3.12 0.86 0.9893 3.976 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 97.10 -3.07 5.76 2.98×10-7 0.9887 4.098 早衰 Non-stay green 32 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 97.39 -7.58 0.33 0.9948 3.167 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 97.47 -5.07 0.50 0.9949 3.124 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 97.36 -3.86 3.54 8.40×10-6 0.9880 4.832 2012 延绿 Stay green 22 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 94.31 -2.84 0.78 0.9516 7.150 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 96.29 -1.95 0.98 0.9609 6.424 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 96.29 -2.04 6.01 3.62×10-5 0.9596 6.564 中等延绿 Moderately stay green 32 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 94.81 -2.79 0.52 0.9735 5.808 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 98.08 -1.78 0.73 0.9797 5.075 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 98.07 -1.78 3.52 7.01×10-3 0.9795 5.118 类型 Type 品种数 No. of varieties 模型 Model 方程 Equation 方程系数Coefficients 模型适合性 Fitness of model a b c d R2 RMSE 中等早衰 Moderately non-stay green 40 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 93.31 -3.42 0.20 0.9809 5.367 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 96.30 -2.12 0.39 0.9840 4.917 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 95.96 -2.16 4.57 1.17×10-4 0.9836 4.992 早衰 Non-stay green 11 Logistic $y=a/1+{{\text{e}}^{-b(x-c)}}$ 93.46 -4.30 -0.23 0.9916 3.783 Gompertz $y=a{{\text{e}}^{-{{\text{e}}^{-b(x-c)}}}}$ 94.44 -3.17 -0.08 0.9917 3.768 Richards $y=a/{{[1+{{\text{e}}^{-b(x-c)}}]}^{\frac{1}{d}}}$ 94.03 -3.65 0.02 0.50 0.9898 4.216