A Dynamic System of Growth and Yield Equations for Pinus patula
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Forest Inventory Data
2.3. Development of Compatible Models
2.4. Fitting Models and Statistical Analysis
3. Results
3.1. Growth Models
3.2. Using the Compatible System
4. Discussion
5. Conclusions
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Variable | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|
A1 | 18.22 | 16.93 | 5.00 | 74.25 |
A2 | 19.22 | 16.93 | 6.00 | 75.25 |
DH1 | 14.78 | 6.35 | 4.55 | 34.85 |
DH2 | 16.00 | 6.17 | 6.32 | 35.41 |
DBH1 | 13.37 | 6.63 | 5.75 | 39.21 |
DBH2 | 14.44 | 6.36 | 7.14 | 39.84 |
BA1 | 21.22 | 14.06 | 1.35 | 66.53 |
BA2 | 23.82 | 13.46 | 2.59 | 68.26 |
V1 | 160.76 | 159.59 | 3.62 | 618.24 |
V2 | 191.56 | 169.73 | 9.01 | 665.33 |
LT1 | 1525.38 | 1024.50 | 300.00 | 6050.00 |
LT2 | 1510.61 | 1006.83 | 300.00 | 6025.00 |
Indicator | Equations |
---|---|
Sum of squares of error (SSE) | |
Root of mean square error (RMSE) | |
Coefficient of determination adjusted by the number of parameters (R2adj) | |
Absolute average bias () | |
Akaike information criterion (AIC) |
Equation | SSE | RMSE | R2-adj | AIC | |
---|---|---|---|---|---|
Prediction | |||||
5 (DBH1) | 316.4 | 2.232 | 0.886 | 0.097 | 111.45 |
7 (DBH1) | 337.5 | 2.306 | 0.879 | 0.020 | 115.71 |
9 (BA1) | 2102.2 | 5.754 | 0.831 | 0.344 | 236.43 |
11 (BA1) | 2393.2 | 6.139 | 0.808 | 0.350 | 244.99 |
13 (V1) | 121,918.0 | 43.646 | 0.925 | 6.825 | 502.42 |
15 (V1) | 24,648.7 | 19.625 | 0.985 | 1.779 | 396.91 |
Projection | |||||
6 (DBH2) | 9.2 | 0.378 | 0.997 | 0.028 | −121.83 |
8 (DBH2) | 8.6 | 0.364 | 0.997 | 0.045 | −126.81 |
10 (BA2) | 117.8 | 1.351 | 0.990 | 0.041 | 46.24 |
12 (BA2) | 70.7 | 1.047 | 0.994 | 0.207 | 12.58 |
14 (V2) | 20,373.3 | 17.704 | 0.989 | 9.462 | 384.33 |
16 (V2) | 15,255.0 | 15.320 | 0.992 | 4.145 | 365.24 |
17 (LT2) | 103,635.0 | 39.930 | 0.998 | 3.901 | 487.69 |
18 (LT2) | 104,208.0 | 40.040 | 0.998 | 3.839 | 488.06 |
Equations | Parameter | Estimate | Standard Error | Pr > |t| | Equations | Parameter | Estimate | Standard Error | Pr > |t| |
---|---|---|---|---|---|---|---|---|---|
(5) and (6) | β0 | 2.478 | 0.354 | <0.0001 | (7) and (8) | β0 | −2.568 | 0.557 | <0.0001 |
β1 | −2.729 | 0.730 | <0.0004 | β1 | 0.705 | 0.053 | <0.0001 | ||
β2 | −0.204 | 0.033 | <0.0001 | β2 | 0.184 | 0.025 | <0.0001 | ||
β3 | 0.656 | 0.067 | <0.0001 | β3 | 2.329 | 0.194 | <0.0001 | ||
(9) and (10) | β0 | −3.613 | 0.599 | <0.0001 | (11) and (12) | β0 | −10.712 | 0.641 | <0.0001 |
β1 | −6.392 | 1.468 | <0.0001 | β1 | 0.095 | 0.021 | <0.0001 | ||
β2 | 0.566 | 0.053 | <0.0001 | β2 | 0.596 | 0.060 | <0.0001 | ||
β3 | 1.149 | 0.120 | <0.0001 | β3 | 3.722 | 0.250 | <0.0001 | ||
(13) and (14) | δ0 | 2.843 | 0.128 | <0.0001 | (15) and (16) | δ0 | 0.778 | 0.043 | <0.0001 |
δ1 | −1.725 | 0.120 | <0.0001 | δ1 | −13.580 | 0.627 | <0.0001 | ||
δ2 | 0.278 | 0.034 | <0.0001 | δ2 | 1.072 | 0.032 | <0.0001 | ||
(17) | α1 | −0.012 | 0.003 | <0.0001 | (18) | α1 | −0.00039 | 0.000 | <0.0001 |
A | LT | DH | DBH | BA | V | CAI | MAI |
---|---|---|---|---|---|---|---|
5 | 1500 | 2.41 | 2.76 | 0.27 | 0.23 | 0.05 | 0.05 |
6 | 1482 | 3.40 | 3.80 | 0.75 | 1.05 | 0.82 | 0.17 |
7 | 1463 | 4.47 | 4.86 | 1.59 | 3.24 | 2.19 | 0.46 |
8 | 1446 | 5.57 | 5.91 | 2.82 | 7.64 | 4.40 | 0.96 |
9 | 1428 | 6.69 | 6.94 | 4.43 | 14.97 | 7.33 | 1.66 |
10 | 1410 | 7.81 | 7.93 | 6.36 | 25.63 | 10.66 | 2.56 |
11 | 1393 | 8.91 | 8.89 | 8.53 | 39.70 | 14.07 | 3.61 |
12 | 1376 | 10.00 | 9.81 | 10.85 | 56.97 | 17.27 | 4.75 |
13 | 1359 | 11.06 | 10.70 | 13.26 | 77.04 | 20.06 | 5.93 |
14 | 1343 | 12.09 | 11.54 | 15.69 | 99.39 | 22.35 | 7.10 |
15 | 1326 | 13.08 | 12.34 | 18.08 | 123.49 | 24.10 | 8.23 |
16 | 1310 | 14.05 | 13.11 | 20.42 | 148.82 | 25.33 | 9.30 |
17 | 1294 | 14.98 | 13.85 | 22.66 | 174.91 | 26.09 | 10.29 |
18 | 1278 | 15.87 | 14.55 | 24.79 | 201.34 | 26.43 | 11.19 |
19 | 1262 | 16.73 | 15.22 | 26.80 | 227.78 | 26.43 | 11.99 |
20 | 1247 | 17.56 | 15.87 | 28.69 | 253.93 | 26.16 | 12.70 |
21 | 1232 | 18.36 | 16.49 | 30.45 | 279.60 | 25.66 | 13.31 |
22 | 1217 | 19.13 | 17.08 | 32.10 | 304.60 | 25.01 | 13.85 |
23 | 1202 | 19.86 | 17.65 | 33.62 | 328.83 | 24.23 | 14.30 |
24 | 1187 | 20.57 | 18.19 | 35.03 | 352.19 | 23.36 | 14.67 |
25 | 1172 | 21.26 | 18.72 | 36.33 | 374.64 | 22.44 | 14.99 |
26 | 1158 | 21.92 | 19.22 | 37.54 | 396.13 | 21.50 | 15.24 |
27 | 1144 | 22.55 | 19.71 | 38.64 | 416.67 | 20.54 | 15.43 |
28 | 1130 | 23.16 | 20.18 | 39.67 | 436.25 | 19.58 | 15.58 |
29 | 1116 | 23.75 | 20.64 | 40.61 | 454.89 | 18.64 | 15.69 |
30 | 1102 | 24.31 | 21.08 | 41.47 | 472.61 | 17.72 | 15.75 |
31 | 1089 | 24.86 | 21.50 | 42.27 | 489.44 | 16.83 | 15.79 |
32 | 1076 | 25.38 | 21.92 | 43.00 | 505.42 | 15.97 | 15.79 |
33 | 1062 | 25.89 | 22.32 | 43.68 | 520.57 | 15.15 | 15.77 |
34 | 1049 | 26.38 | 22.71 | 44.30 | 534.93 | 14.36 | 15.73 |
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Santiago-García, W.; Pérez-López, E.; Quiñonez-Barraza, G.; Rodríguez-Ortiz, G.; Santiago-García, E.; Ruiz-Aquino, F.; Tamarit-Urias, J.C. A Dynamic System of Growth and Yield Equations for Pinus patula. Forests 2017, 8, 465. https://doi.org/10.3390/f8120465
Santiago-García W, Pérez-López E, Quiñonez-Barraza G, Rodríguez-Ortiz G, Santiago-García E, Ruiz-Aquino F, Tamarit-Urias JC. A Dynamic System of Growth and Yield Equations for Pinus patula. Forests. 2017; 8(12):465. https://doi.org/10.3390/f8120465
Chicago/Turabian StyleSantiago-García, Wenceslao, Eloísa Pérez-López, Gerónimo Quiñonez-Barraza, Gerardo Rodríguez-Ortiz, Elías Santiago-García, Faustino Ruiz-Aquino, and Juan Carlos Tamarit-Urias. 2017. "A Dynamic System of Growth and Yield Equations for Pinus patula" Forests 8, no. 12: 465. https://doi.org/10.3390/f8120465
APA StyleSantiago-García, W., Pérez-López, E., Quiñonez-Barraza, G., Rodríguez-Ortiz, G., Santiago-García, E., Ruiz-Aquino, F., & Tamarit-Urias, J. C. (2017). A Dynamic System of Growth and Yield Equations for Pinus patula. Forests, 8(12), 465. https://doi.org/10.3390/f8120465