Balancing Large-Scale Wildlife Protection and Forest Management Goals with a Game-Theoretic Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. A Socially Optimal Habitat Protection Problem
2.2. A Bi-Level Habitat Protection Problem
2.3. The Follower’s Problem
2.4. The Leader’s Habitat Protection Problem
2.5. Equal Protected Area Proportion Problem
2.6. Equal Proportional Revenue Loss Problem
2.7. Maximum Harvest Revenue Problem
2.8. Case Study
2.9. Data
3. Results
3.1. Trade-Off between Maximizing Habitat Protection and Maximizing Harvest Revenue
3.2. General Habitat Protection Patterns
4. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | Parameter/Variable Name | Description |
---|---|---|
Sets: | ||
J | Patches j, k with suitable habitat—potential candidates for protection in a landscape J | j,k ∊ J |
Jd | Patches j, k with suitable habitat located in region d | Jd ∊ J |
Θj | Patches k which are connected to patch j and can transmit flow to j | kj ∊ Θj |
Θj+ | Patches k which are connected to patch j and can receive flow from j | kj ∊ Θj |
Θ jd | Patches k located in region d which can transmit flow to patch j located in region d | Θjd ∊ J |
N | Forest sites n—potential harvest blocks in landscape N | n ∊ N |
Nd | Forest sites n—potential harvest blocks located in region d | Nd ∊ N |
Ωj | Forest sites n—potential harvest blocks located in habitat patch j | Ωj ∊ N |
D | Forest management regions d where individual players (the followers) operate | d ∊ D |
C | Habitat protection levels c | c ∊ C |
T | Planning time periods, t | t ∊ T |
I | Harvest prescriptions, i | i ∊ I |
Decision variables: | ||
wkj | Binary indicator of the species flow via arc kj in the protected area over timespan T | wjk ∊ {0,1} |
vkj | Binary indicator of the connection between the adjacent unprotected patches k and j | vjk ∊ {0,1} |
ykj | Amount of flow between the adjacent protected patches k and j | yjk ≥ 0 |
zkj | Amount of flow between the adjacent unprotected patches k and j | zjk ≥ 0 |
xni | Binary selection of harvest prescription i in site n | xni ∊ {0,1} |
ωdc | Binary selection of the follower’s optima from a solution set for D regions × C protection levels | ωdc ∊ {0,1} |
The value of binary variable ωdc denoting the selection of the precomputed follower’s solution c with the protected area portion of FMU d equal to selected target S. | ∊{0,1} | |
P1 | The number of connections to node 0 above one in the network of protected patches | P1≥ 0 |
P2 | The number of connections to node 0 above θ in the network of unprotected patches | P2≥ 0 |
G | Proportional harvest revenue loss in region d over timespan T under protection level c | G ≥ 0 |
Qd | Maximum sustainable harvest volume in region d in period t | Qd ≥ 0 |
Parameters | ||
bnit | Habitat amount in site n in prescription i in period t | bnit ≥ 0 |
βnit | Habitat suitability in site n in prescription i in period t | βnit ≥ 0 |
Bj | Habitat amount in patch j under protection (assuming the no-harvest prescription i = 1) | Bj ≥ 0 |
αn | Habitat area in site n | αn ≥ 0 |
Aj | Habitat area in patch j | Aj ≥ 0 |
an | Harvestable forest area in site n | an ≥ 0 |
Vnit | Volume of timber available for the harvest at site n in period t in prescription i | Vnit ≥ 0 |
Rni | Net cash flow associated with harvesting site n according to prescription i | Rni ≥ 0 |
ETmin | Average target forest age in the managed area at the end of the planning horizon T | 80 |
Eni | Forest stand age in site n at the end of the planning horizon if prescription i is applied | 0–250 |
ρn | Net unit price of timber harvested from site n | ρn > 0 |
en | Postharvest regeneration costs | en > 0 |
Sd | Target proportion of the protected area in region (FMU) d | Sd ∊ [0;1] |
Sc | Target proportion of the protected area at protection level c | Sc ∊ [0;1] |
S | Target proportion of the protected range area | S ∊ [0;1] |
χjdc | Binary selection of patch j for protection in the follower’s solution for region d protection level c | χjdc ∊ {0,1} |
rmax d | Harvest revenue in the maximum sustainable harvest scenario without protection in region d | rmax d ≥ 0 |
rdc | Total harvest revenue over horizon T in region d at protection level c | rdc ≥ 0 |
gdc | Proportional loss in harvest revenue in region d at protection level c vs. no-protection scenario | gdc ∊ [0;1] |
ψj | Binary indicator of patches in northwestern and northeastern region’s corners which must remain unharvested to maintain the connectivity of habitat between regions | ψj ∊ {0,1} |
γjd | Binary parameter defining patches j located in region d | γjd ∊ {0,1} |
δnd | Binary parameter defining sites n located in region d | δnd ∊ {0,1} |
μj | Binary parameter defining sites where permanent roads enter the area | μj ∊ {0,1} |
θ | The number of major access points of entry to the range area (equal to the number of regions D) | 3 |
σ | Allowable decrease in harvest volume in consecutive planning periods t and t +1 | 0.02 |
ε | Small value | 0.05 |
f1, f2, f3 | Scaling factors | f1, f2, f3 > 0 |
U | Large positive value | U > 0 |
Problem Type and Objective | Equalization Constraints for FMUs d | ||
---|---|---|---|
None | Equal Protected Area Proportion | Equal Proportional Harvest Revenue Loss | |
Bi-level, max (protected habitat) | Bi-level habitat protection problem 2 | Bi-level equal protected area proportion problem 4 | Bi-level equal proportional revenue loss problem 6 |
Single-level, socially optimal max (protected habitat) | Socially optimal habitat protection problem 1 | Socially optimal habitat protection equal protected area proportion problem 3 | Socially optimal habitat protection equal proportional revenue loss problem 5 |
Single-level, max (harvest revenue) | Maximum harvest revenue problem 7 |
Land Cover Type | Habitat Type | ||
---|---|---|---|
Useable | Preferred | Refuge | |
Lowland spruce | 61 | ||
Mixedwood conifers | 71 | ||
Other lowland conifers | 51 | 41 * | |
Jack pine dominant | 41 | 61 | 41 * |
Jack pine mixed wood | 41 | 61 | 41 |
Black spruce dominant or black spruce mixed wood | 61 | 41 | |
Black spruce lowland | 41 | 101 | 41 * |
Treed bog and fen | Permanent | Permanent |
Problem | Protected Habitat Amount | Total Harvest Revenue | Protected Area Proportion Target | Actual Protected Area Proportion | Protected Area Proportion per Region | Harvest Revenue Loss Ratio per Region * | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
FMU 1 Trout | FMU 2 Lac Seul | FMU 3 Caribou | Min-Max Range | FMU 1 Trout | FMU 2 Lac Seul | FMU 3 Caribou | Min-Max Range | |||||
Protected area proportion target S = 0.65 | ||||||||||||
Problem 1: Socially optimal habitat protection | 88.3 | 1987.4 | 0.65 | 0.67 | 0.668 | 0.596 | 0.909 | 0.313 | 0.457 | 0.335 | 0.715 | 0.38 |
Problem 2: Bi-level habitat protection | 82.9 | 2294 | 0.65 | 0.67 | 0.632 | 0.631 | 0.89 | 0.259 | 0.289 | 0.317 | 0.694 | 0.405 |
Problem 3: Socially optimal habitat protection with equal protected area % in FMUs d | 86.7 | 1786.9 | 0.65 | 0.67 | 0.674 | 0.675 | 0.673 | 0.002 | 0.469 | 0.463 | 0.477 | 0.014 |
Problem 4: Bi-level habitat protection problem with equal protected area % in FMUs d | 79.6 | 2203.7 | 0.65 | 0.66 | 0.655 | 0.655 | 0.654 | 0.001 | 0.33 | 0.364 | 0.172 | 0.192 |
Problem 5: Socially optimal habitat protection with equal proportional revenue loss in FMUs d | 83.8 | 2205.1 | 0.65 | 0.66 | 0.655 | 0.621 | 0.749 | 0.128 | 0.345 | 0.338 | 0.338 | 0.007 |
Problem 6: Bi-level habitat protection with equal proportional revenue loss in FMUs d | 79.9 | 2300 | 0.65 | 0.65 | 0.644 | 0.631 | 0.729 | 0.098 | 0.308 | 0.317 | 0.317 | 0.009 |
Problem 7: Maximum harvest revenue | 78.9 | 2509.3 | 0.65 | 0.64 | 0.51 | 0.65 | 0.948 | 0.438 | 0.111 | 0.353 | 0.884 | 0.773 |
Protected area proportion target S = 0.4 | ||||||||||||
Problem 1: Socially optimal habitat protection | 62.9 | 2993.9 | 0.4 | 0.42 | 0.478 | 0.294 | 0.6 | 0.31 | 0.224 | 0.004 | 0.336 | 0.34 |
Problem 2: Bi-level habitat protection | 57.3 | 3308.6 | 0.4 | 0.42 | 0.494 | 0.248 | 0.691 | 0.44 | 0.101 | 0.005 | 0.227 | 0.23 |
Problem 3: Socially optimal habitat protection with equal protected area % in FMUs d | 61.5 | 2737.9 | 0.4 | 0.41 | 0.414 | 0.415 | 0.409 | 0.01 | 0.202 | 0.165 | 0.132 | 0.07 |
Problem 4: Bi-level habitat protection problem with equal protected area % in FMUs d | 52.2 | 3245.6 | 0.4 | 0.40 | 0.397 | 0.397 | 0.404 | 0.01 | 0.012 | 0.051 | 0.001 | 0.05 |
Problem 5: Socially optimal habitat protection with equal proportional revenue loss in FMUs d | 61.2 | 3170 | 0.4 | 0.41 | 0.429 | 0.341 | 0.586 | 0.25 | 0.086 | 0.005 | 0.27 | 0.27 |
Problem 6: Bi-level habitat protection with equal proportional revenue loss in FMUs d | 52.8 | 3259 | 0.4 | 0.40 | 0.397 | 0.4 | 0.421 | 0.02 | 0.013 | 0.042 | 0.001 | 0.04 |
Problem 7: Maximum harvest revenue | 54.1 | 3320.5 | 0.4 | 0.40 | 0.384 | 0.311 | 0.661 | 0.35 | 0.002 | 0.007 | 0.133 | 0.13 |
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Yemshanov, D.; Haight, R.G.; Liu, N.; Rempel, R.S.; Koch, F.H.; Rodgers, A. Balancing Large-Scale Wildlife Protection and Forest Management Goals with a Game-Theoretic Approach. Forests 2021, 12, 809. https://doi.org/10.3390/f12060809
Yemshanov D, Haight RG, Liu N, Rempel RS, Koch FH, Rodgers A. Balancing Large-Scale Wildlife Protection and Forest Management Goals with a Game-Theoretic Approach. Forests. 2021; 12(6):809. https://doi.org/10.3390/f12060809
Chicago/Turabian StyleYemshanov, Denys, Robert G. Haight, Ning Liu, Robert S. Rempel, Frank H. Koch, and Art Rodgers. 2021. "Balancing Large-Scale Wildlife Protection and Forest Management Goals with a Game-Theoretic Approach" Forests 12, no. 6: 809. https://doi.org/10.3390/f12060809
APA StyleYemshanov, D., Haight, R. G., Liu, N., Rempel, R. S., Koch, F. H., & Rodgers, A. (2021). Balancing Large-Scale Wildlife Protection and Forest Management Goals with a Game-Theoretic Approach. Forests, 12(6), 809. https://doi.org/10.3390/f12060809