Scientia Silvae Sinicae ›› 2019, Vol. 55 ›› Issue (11): 126-136.doi: 10.11707/j.1001-7488.20191114
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Guijuan Yang1,Haifan Hu2,Honggang Sun2,*,Jianguo Zhang1,Aiguo Duan1
Received:2019-03-25
Online:2019-11-25
Published:2019-12-21
Contact:
Honggang Sun
Supported by:CLC Number:
Guijuan Yang,Haifan Hu,Honggang Sun,Jianguo Zhang,Aiguo Duan. The Influences of Stand Age, Planting Density and Self-Thinning on Relationship between Size Inequality and Periodic Annual Increment in Chinese Fir (Cunninghamia lanceolata)Plantations[J]. Scientia Silvae Sinicae, 2019, 55(11): 126-136.
Table 1
Descriptive statistics of the experimental plots"
| 样地编号 Plot No. | 造林密度 Planting density/(tree·hm-2) | 2006年活立木株数Survival trees in 2006/(tree·hm-2) | 林分平均胸径 Mean DBH/cm | 胸径范围 DBHmin~DBHmax/cm |
| A1 | 1 667 | 1 364 | 19.07(±2.95) | 3.80~23.70 |
| A2 | 1 667 | 1 484 | 17.41(±2.06) | 10.20~24.10 |
| A3 | 1 667 | 1 439 | 19.28(±2.14) | 9.70~31.50 |
| B1 | 3 333 | 2 653 | 15.31(±2.58) | 7.90~25.70 |
| B2 | 3 333 | 2 938 | 10.65(±2.42) | 6.49~13.80 |
| B3 | 3 333 | 1 754 | 12.29(±2.71) | 7.58~16.23 |
| C1 | 5 000 | 3 868 | 12.82(±2.54) | 3.80~23.74 |
| C2 | 5 000 | 3 598 | 9.57(±2.44) | 5.51~13.16 |
| C3 | 5 000 | 2 743 | 10.21(±2.74) | 6.04~14.04 |
| D1 | 6 667 | 4 647 | 8.76(±2.02) | 5.53~11.90 |
| D2 | 6 667 | 4 212 | 8.85(±2.67) | 4.95~13.14 |
| D3 | 6 667 | 2 983 | 9.13(±2.62) | 5.33~13.26 |
| E1 | 10 000 | 4 152 | 8.39(±2.01) | 5.55~11.70 |
| E2 | 10 000 | 3 328 | 8.42(±2.50) | 4.80~13.08 |
| E3 | 10 000 | 1 484 | 8.75(±2.71) | 5.10~13.11 |
Fig.1
Calculation principle of Gini coefficient"
Fig.2
Relationship between stand age and Gini coefficient at the five planting densities in Chinese fir plantations Solid lines indicate linear relationship between stand age and Gini coefficient before self-thinning happened and dished lines represent relationship between stand age and Gini coefficient after self-thinning happened. "
Table 2
Parameter estimates for the Gini coefficient using the generalized linear mixed effect models based on the effect on stand age, planting density and self-thinning"
| 固定效应项 Fixed components | 模型Models | ||
| Gini(Age) | Gini(Den) | Gini(Mort) | |
| 截距项Intercept | 0.370 4(< 0.000 1) | 0.293 6(< 0.000 1) | 0.355 9(< 0.000 1) |
| A | 0.251 4(0.002 84) | NA | 0.127 5(< 0.000 1) |
| Mort | -0.079 2(0.001 68) | -0.016 8(0.003 66) | -0.183 2(0.000 73) |
| Den2.0 m×1.5 m | 0.063 3(0.000 50) | 0.193 7(0.004 74) | NA |
| Den2.0 m×1.0 m | 0.071 6(< 0.000 1) | 0.256 4(0.002 65) | NA |
| Den1.0 m×1.5 m | 0.086 3(< 0.000 1) | 0.390 8(0.001 63) | NA |
| Den1.0 m×1.0 m | 0.094 5(< 0.000 1) | 0.446 3(0.003 20) | NA |
| A ×Mort | 0.015 5(0.004 62) | NA | 0.058 3(0.001 82) |
| A × Den2.0 m×1.5 m | 0.033 2(0.004 39) | NA | NA |
| A × Den2.0 m×1.0 m | 0.039 4(0.003 23) | NA | NA |
| A × Den1.0 m×1.5 m | 0.041 7(0.001 85) | NA | NA |
| A × Den1.0 m×1.0 m | 0.048 6(0.004 73) | NA | NA |
| Mort × Den2.0 m×1.5 m | 0.024 6(0.004 72) | -0.064 4(< 0.000 1) | NA |
| Mort × Den2.0 m×1.0 m | 0.037 9(0.003 20) | -0.057 0(< 0.000 1) | NA |
| Mort × Den1.0 m×1.5 m | 0.039 5(0.002 56) | -0.038 2(< 0.000 1) | NA |
| Mort × Den1.0 m×1.0 m | 0.042 8(0.003 41) | -0.031 9(< 0.000 1) | NA |
| R2 | 0.986 | 0.972 | 0.953 |
| RMSE | 0.141 | 0.161 | 0.117 |
| r | 0.872 | 0.853 | 0.944 |
Fig.3
Dynamics of the surviving stems in Chinese fir plantations"
Fig.4
Change in the ratio of the mean individual tree basal area of dead trees to that of all trees at the start of the given period (BAdead/BAtotal)in Chinese fir plantations"
Table 3
Parameter estimates for PAI using the generalized linear mixed effect models"
| 固定效应项 Fixed components | 模型Models | ||
| PAI(Age) | PAI(Den) | PAI(Mort) | |
| 截距项Intercept | 7.247 2(0.004 9) | 3.845 5(< 0.000 1) | 2.682 1(0.041 6) |
| A | 0.782 4(0.018 7) | NA | 0.591 2(0.002 3) |
| A2 | -0.026 9(0.036 2) | NA | -1.548 0(1.244 5) |
| Gini | -1.834 0(0.000 4) | -2.908 5(0.023 7) | -0.691 5(0.048 1) |
| Mort | NA | 5.240 7(0.026 1) | 3.028 4 (0.029 3) |
| Den2.0 m×1.5 m | 1.832 3(0.002 3) | 1.258 6(0.000 5) | NA |
| Den2.0 m×1.0 m | 2.377 5(0.023 7) | 3.642 5(0.008 7) | NA |
| Den1.0 m×1.5 m | 4.860 3(0.034 4) | 4.981 2(0.004 4) | NA |
| Den1.0 m×1.0 m | 5.494 2(0.002 7) | 5.739 4(0.025 9) | NA |
| A×Gini | NA | NA | -4.961 7(0.006 1) |
| A× Mort | -0.234 9(0.016 3) | NA | -0.741 6(< 0.000 1) |
| A× Den2.0 m×1.5 m | NA | NA | 1.684 2(0.561 8) |
| A× Den2.0 m×1.0 m | NA | NA | 2.183 3(0.337 1) |
| A× Den1.0 m×1.5 m | NA | NA | 2.835 4(1.546 2) |
| A× Den1.0 m×1.0 m | NA | NA | 3.665 9(1.721 8) |
| A2× Gini | -0.025 1(0.384 5) | NA | NA |
| A2× Mort | NA | NA | 0.384 6(< 0.000 1) |
| Gini× Mort | NA | -2.452 8(0.010 9) | -0.174 3(0.167 1) |
| Mort× Den2.0 m×1.5 m | NA | 2.617 3(0.002 2) | NA |
| Mort× Den2.0 m×1.0 m | NA | 5.781 8(0.039 1) | NA |
| Mort× Den1.0 m×1.5 m | NA | 8.653 9(0.037 4) | NA |
| Mort× Den1.0 m×1.0 m | NA | 11.274 4(0.002 5) | NA |
| Gini × Den2.0 m×1.5 m | NA | -3.738 2(0.043 8) | -0.378 1(0.008 1) |
| Gini × Den2.0 m×1.0 m | NA | -5.698 0(0.003 1) | -1.559 7(0.001 6) |
| Gini × Den1.0 m×1.5 m | NA | -9.403 8(0.042 6) | -2.670 4(0.002 5) |
| Gini × Den1.0 m×1.0 m | NA | -12.817 3(0.020 7) | -3.418 3(0.005 9) |
| R2 | 0.938 1 | 0.891 7 | 0.912 5 |
| RMSE | 0.164 3 | 0.276 1 | 0.175 0 |
| r | 0.891 7 | 0.858 6 | 0.914 3 |
Fig.5
The effect of size inequality on PAI at stand age, planting density and self-thinning of Chinese fir plantations The trend lines in the Fig. 5a-c were deduced as the following steps. Firstly, the fixed components of the model(5), (6) and(7)were deleted based on the NA in the Tab. 3. Secondly, the first derivative models of the PAI versus Gini were computed and the estimated parameters were added in the first derivative model. Finally, the trend lines of PAI with stand age, planting density and self-thinning were drawn in the different stand age, planting density and before and after self-thinning conditions. "
Fig.6
The dynamic of PAI of the Chinese fir plantations before and after self-thinning trajectory The trend line of PAI(Mort) versus age(A)before self-thinning trajectory was deduced as the following steps. Firstly, the values with Mort=0, the upper Gini limit 0.4 and the estimated parameters of the PAI(Mort)in the Tab. 3 were added the model(7), and then the trend line between PAI(Mort)and A was drawn before self-thinning began between 4 and 24 stand age. The trend line of PAI(Mort) versus age(A) after self-thinning trajectory was deduced as the following steps.Firstly, the values with Mort=1, the upper Gini limit 0.8 and the estimated parameters of the PAI(Mort) in the Tab. 3 were added the model (7).and then the trend line between PAI(Mort) and A was drawn after self-thinning began between 6 and 26 stand age. "
Fig.7
The dynamic of PAI of Chinese fir plantations at the different planting densities The PAI versus planting density was deduced as the following steps. Firstly, the values with Mort=0, the upper Gini limit 0.4 and the estimated parameters of the PAI(Den)in the Tab. 3 were added the model (6) and then the PAI was computed before self-thinning happened at the different planting density. Thirdly, the values with Mort=1, the upper Gini limit 0.8 and the estimated parameters of the PAI(Den)in the Tab. 3 were added the model(6) and then the PAI was computed after self-thinning happened at the different planting density. Finally, the total PAI was summed PAI before and after self-thinning happened at the different planting density. "
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