Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing?
Abstract
:1. Introduction
2. Material and Methods
2.1. Population Dynamics
2.2. Optimization Model
2.3. Input Estimation
2.3.1. Transition Probabilities
Quality I | Quality II | Quality III | |
---|---|---|---|
(0,6) → (6,12) | p1 = 0.7697 | p1 = 0.5951 | p1 = 0.4564 |
(6,12) → (12,18) | p2 = 0.8602 | p2 = 0.6824 | p2 = 0.5326 |
(12,18) → (18,24) | p3 = 0.7913 | p3 = 0.6200 | p3 = 0.4697 |
(18,24) → (24,30) | p4 = 0.6828 | p4 = 0.5190 | p4 = 0.3692 |
(24,30) → (30,36) | p5 = 0.5533 | p5 = 0.3971 | p5 = 0.2475 |
(30,36) → (36,42) | p6 = 0.4106 | p6 = 0.2618 | p6 = 0.1119 |
(36,42) → (42,48) | p7 = 0.2587 | p7 = 0.1171 | - |
(42,48) → (48,→) | p8 = 0.1000 | - | - |
2.3.2. Recruitment and Basal Area
2.3.3. Natural Mortalities
2.3.4. Sustainable/Stable Harvesting Strategy: Stable Diameter Distribution
R = 200 stem/ha | R = 520 stem/ha | R = 840 stem/ha | |||
---|---|---|---|---|---|
Q I | G = 22 | λ0 | 1.305091 | 1.477671 | 1.594240 |
s | 0.233770 | 0.323259 | 0.372742 | ||
Gmin | 16.857068 | 14.888296 | 13.799677 | ||
Est. Dis. | [186.1, 122.9, 96.4, 77.2, 61.4, 47.5, 34.6, 22.1, 7.2] | [416.9, 239.8, 162.6, 110.9, 73.4, 45.7, 25.5, 11.4, 2.4] | [615.9, 325.9, 202.3, 125.4, 74.6, 41.1, 19.8, 7.4, 1.2] | ||
NPV0 | 5,347.36 | 6,118.03 | 6,383.55 | ||
G = 24 | λ0 | 1.292499 | 1.458959 | 1.571264 | |
s | 0.226305 | 0.314580 | 0.363570 | ||
Gmin | 18.568685 | 16.450081 | 15.274322 | ||
Est. Dis. | [188.3, 125.7, 99.8, 81.0, 65.4, 51.4, 38.3, 25.3, 8.6] | [423.2, 246.9, 169.9, 117.8, 79.4, 50.5, 28.9, 13.4, 2.9] | [626.4, 336.8, 212.6, 134.2, 81.5, 45.9, 22.7, 8.8, 1.5] | ||
NPV0 | 5,743.33 | 6,611.13 | 6,918.95 | ||
G = 26 | λ0 | 1.281305 | 1.442342 | 1.550881 | |
s | 0.219546 | 0.306683 | 0.355205 | ||
Gmin | 20.291808 | 18.026241 | 16.764668 | ||
Est. Dis. | [190.3, 128.3, 102.9, 84.5, 69.1, 55.3, 42.0, 28.5, 10.1] | [429.0, 253.5, 176.8, 124.3, 85.3, 55.3, 32.4, 15.5, 3.5] | [636.1, 347.0, 222.4, 142.6, 88.2, 50.8, 25.7, 10.2, 1.9] | ||
NPV0 | 6,130.45 | 7,096.29 | 7,447.43 | ||
Q II | G = 22 | λ0 | 1.262093 | 1.412527 | 1.514472 |
s | 0.207665 | 0.292049 | 0.339704 | ||
Gmin | 17.431369 | 15.574919 | 14.526515 | ||
Est. Dis. | [233.3, 147.0, 113.7, 90.3, 71.1, 53.9, 37.2, 16.6] | [516.1, 280.5, 185.4, 123.4, 79.1, 46.6, 23.0, 6.5] | [757.0, 376.4, 226.4, 135.8, 77.3, 39.6, 16.4, 3.7] | ||
NPV0 | 4,239.22 | 4,986.61 | 5,284.13 | ||
G = 24 | λ0 | 1.251140 | 1.396188 | 1.494358 | |
s | 0.200729 | 0.283764 | 0.330816 | ||
Gmin | 19.182509 | 17.189656 | 16.060414 | ||
Est. Dis. | [236.3, 150.7, 118.0, 95.0, 76.1, 58.9, 41.9, 19.5] | [524.6, 289.4, 194.4, 131.7, 86.1, 52.0, 26.5, 7.8] | [771.0, 389.9, 238.8, 146.1, 85.0, 44.7, 19.1, 4.5] | ||
NPV0 | 4,542.73 | 5,373.95 | 5,710.91 | ||
G = 26 | λ0 | 1.241406 | 1.381684 | 1.476521 | |
s | 0.194462 | 0.276245 | 0.322732 | ||
Gmin | 20.943989 | 18.817621 | 17.608961 | ||
Est. Dis. | [239.1, 154.0, 122.0, 99.5, 80.9, 63.8, 46.6, 22.6] | [532.4, 297.7, 202.8, 139.6, 93.0, 57.4, 30.1, 9.2] | [783.9, 402.5, 250.5, 156.0, 92.7, 49.8, 22.0, 5.4] | ||
NPV0 | 4,838.92 | 5,754.14 | 6,131.06 | ||
Q III | G = 22 | λ0 | 1.220604 | 1.350816 | 1.439536 |
s | 0.180733 | 0.259707 | 0.305332 | ||
Gmin | 18.023866 | 16.286454 | 15.282699 | ||
Est. Dis. | [295.4, 179.0, 138.1, 110.0, 86.7, 64.6, 32.8] | [644.2, 332.8, 216.0, 140.9, 87.0, 46.5, 14.8] | [937.6, 440.2, 257.8, 149.7, 80.5, 36.1, 9.2] | ||
NPV0 | 3,202.56 | 3,906.48 | 4,224.82 | ||
G = 24 | λ0 | 1.211164 | 1.336630 | 1.422004 | |
s | 0.174348 | 0.251850 | 0.296767 | ||
Gmin | 19.815651 | 17.955611 | 16.877591 | ||
Est. Dis. | [299.6, 183.8, 143.8, 116.4, 93.7, 71.8, 38.0] | [655.8, 344.3, 227.4, 151.3, 95.6, 52.8, 17.6] | [956.3, 457.2, 273.0, 162.1, 89.4, 41.4, 11.0] | ||
NPV0 | 3,421.69 | 4,194.95 | 4,548.76 | ||
G = 26 | λ0 | 1.202780 | 1.324044 | 1.406468 | |
s | 0.168593 | 0.244738 | 0.288999 | ||
Gmin | 21.616583 | 19.636810 | 18.486024 | ||
Est. Dis. | [303.4, 188.3, 149.1, 122.5, 100.4, 79.0, 43.6] | [666.3, 355.0, 238.2, 161.4, 104.2, 59.2, 20.4] | [973.6, 473.1, 287.6, 174.1, 98.3, 46.9, 12.9] | ||
NPV0 | 3635.05 | 4477.23 | 4866.59 |
2.3.5. Stumpage Value Model
Products | Diameter classes (cm) | ||
---|---|---|---|
<20 | 20–40 | >40 | |
Poles | 0 | 11.85 | 0 |
Sawlog | 0 | 9.8 | 11.76 |
High quality sawlog | 0 | 0 | 9.96 |
Total average price | 6 | 22.85 | 22.32 |
3. Results and Discussion
3.1. Results
R = 200 stem/ha | R = 520 stem/ha | R = 840 stem/ha | |||||
---|---|---|---|---|---|---|---|
NPV (€/ha) | NPV increase (%) | NPV (€/ha) | NPV increase (%) | NPV (€/ha) | NPV increase (%) | ||
Q I | G = 22 | 6205.07 | 16.04 | 7188.49 | 17.50 | 7468.18 | 17.00 |
G = 24 | 6636.65 | 15.55 | 7767.29 | 17.49 | 8095.43 | 17.00 | |
G = 26 | 7056.80 | 15.11 | 8316.44 | 17.19 | 8718.00 | 17.06 | |
Q II | G = 22 | 4788.21 | 12.95 | 5754.83 | 15.40 | 6139.05 | 16.18 |
G = 24 | 5124.07 | 12.80 | 6203.83 | 15.44 | 6623.80 | 15.99 | |
G = 26 | 5453.96 | 12.71 | 6647.77 | 15.53 | 7098.14 | 15.77 | |
Q III | G = 22 | 3,502.94 | 9.38 | 4,389.27 | 12.36 | 4,820.65 | 14.10 |
G = 24 | 3,724.85 | 8.86 | 4,701.48 | 12.07 | 5,185.97 | 14.00 | |
G = 26 | 3,941.58 | 8.43 | 5,007.24 | 11.84 | 5,529.35 | 13.62 |
R = 200 stem/ha | R = 520 stem/ha | R = 840 stem/ha | |||||
---|---|---|---|---|---|---|---|
Δ | λT | Δ | λT | Δ | λT | ||
Q I | G = 22 | 0.450415 | 0.056033 | 0.397311 | 0.002602 | 0.394624 | 0.000226 |
G = 24 | 0.434304 | 0.178754 | 0.392813 | 0.002866 | 0.390207 | 0.000284 | |
G = 26 | 0.425244 | 0.210573 | 0.437235 | 0.002866 | 0.387282 | 0.000559 | |
QII | G = 22 | 0.467745 | 0.310556 | 0.490225 | 0.006628 | 0.361989 | 0.004161 |
G = 24 | 0.467935 | 0.333705 | 0.487651 | 0.011089 | 0.351967 | 0.004161 | |
G = 26 | 0.468382 | 0.354182 | 0.478031 | 0.014921 | 0.346997 | 0.004161 | |
Q III | G = 22 | 0.348297 | 0.604092 | 0.392534 | 0.275817 | 0.335904 | 0.365103 |
G = 24 | 0.422880 | 0.551102 | 0.385367 | 0.303478 | 0.323309 | 0.336591 | |
G = 26 | 0.417756 | 0.562400 | 0.378934 | 0.337522 | 0.324559 | 0.312709 |
3.2. Discussion and Conclusions
Conflicts of Interest
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López-Torres, I.; Ortuño-Pérez, S.; García-Robredo, F.; Fullana-Belda, C. Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing? Forests 2013, 4, 830-848. https://doi.org/10.3390/f4040830
López-Torres I, Ortuño-Pérez S, García-Robredo F, Fullana-Belda C. Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing? Forests. 2013; 4(4):830-848. https://doi.org/10.3390/f4040830
Chicago/Turabian StyleLópez-Torres, Ignacio, Sigfredo Ortuño-Pérez, Fernando García-Robredo, and Carmen Fullana-Belda. 2013. "Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing?" Forests 4, no. 4: 830-848. https://doi.org/10.3390/f4040830