Table 1. Parameters defining stand location, productivity, discount rate and the resulting sets of optimisation sub-problems.
Parameters defining stand location, productivity, demand to economic return
Stand location Latitude, °N lat = {60, 64}
Altitude, m.a.s.l. alt = {100, 200, 300, 400}
Stand productivity Site index, SIH(100) SIH = {T16, T18, T20, T22, T24, T26, T28}
  Discount rate, % r = {1.0, 1.5, 2.0, 2.5, 3.0}
The parameters above generate 280 combinations. For each of these, 2 × 4 sub-problems were solved separately.
Silvicultural decisions Regeneration method RM = {Planting, Seed-tree-method}
Number of thinnings TH = {0, 1, 2, 3}
m.a.s.l. = meters above sea level, SIH(100) = dominant height of stand in meters at an age of 100 years. The prefix T in e.g. T24 denotes Scots pine (“Tall” in Swedish).
Table 2. Decision variables.
Regeneration by planting Natural regeneration by seed trees
· Number of seedlings planted (seedlings ha–1) · Number of soil treatment patches (patches ha–1)
· Number of seed trees (stems ha–1)
· Seed tree period, years
· Intensity of pre commercial thinning, fraction of stems removed
For each thinning i = {0, 1, 2, 3}
· Age of thinning i, years
· Intensity of thinning i, fraction of basal area removed
· Diameter quota Q  =  Dt/Dr, where Dt is the diameter of stems removed by thinning and Dr is the diameter of the remaining stems
· Age of final harvest, years · Age of regeneration harvest, years
Table 3. Difference between the best scenario of planting and natural regeneration. Genetically unimproved planting material. Results for 8 different stand locations and 7 levels of productivity.
Latitude °N Altitude m.a.s.l. Discount rate Site index (SIH(100), m)
T16 T18 T20 T22 T24 T26 T28
60 100 1.0% –230 N1 –324 N1 –306 N1 –207 N1 –66 N1 90 P1 281 P1
1.5% –125 N0 –177 N1 –206 N1 –187 N1 –116 N1 6 P1 126 P1
2.0% –112 N0* –129 N0 –140 N1 –138 N1 –108 N1 –29 N1 61 P1
2.5% –100 N0* –112 N0* –125 N0* –118 N0 –103 N1 –56 N1 19 P1
3.0% –94 N0* –102 N0* –113 N0* –106 N0* –96 N0 –62 N1 –13 N1
200 1.0% –264 N1 –361 N1 –358 N1 –257 N1 –110 N1 47 P1 241 P1
1.5% –138 N0 –194 N1 –232 N1 –221 N1 –150 N1 –8 N1 127 P1
2.0% –125 N0* –138 N0 –156 N1 –162 N1 –131 N1 –56 N1 50 P1
2.5% –112 N0* –122 N0* –134 N0* –124 N0 –121 N1 –78 N1 8 P1
3.0% –105 N0* –112 N0* –123 N0* –116 N0* –106 N0 –72 N1 –23 N1
300 1.0% –293 N1 –398 N1 –417 N1 –313 N1 –158 N1 15 P1 185 P1
1.5% –157 N0 –214 N1 –260 N1 –256 N1 –184 N1 –45 N1 98 P1
2.0% –139 N0* –149 N0 –166 N1 –180 N1 –159 N1 –86 N1 38 P1
2.5% –125 N0* –133 N0* –141 N0 –135 N0 –133 N1 –91 N1 –2 N1
3.0% –117 N0* –122 N0* –128 N0* –126 N0* –116 N0 –82 N1 –33 N1
400 1.0% –298 N1 –428 N1 –470 N1 –370 N1 –208 N1 –25 N1 150 P1
1.5% –174 N0 –218 N1 –277 N1 –285 N1 –221 N1 –81 N1 74 P1
2.0% –155 N0* –162 N0 –167 N1 –186 N1 –184 N1 –103 N1 25 P1
2.5% –139 N0* –145 N0* –151 N0 –148 N0 –139 N1 –108 N1 –25 N1
3.0% –131 N0* –133 N0* –139 N0* –137 N0* –128 N0 –90 N0 –50 N1
64 100 1.0% –339 N1 –426 N1 –455 N1 –349 N1 –186 N1 –13 N1 75 P1
1.5% –159 N0 –205 N1 –236 N1 –258 N1 –207 N1 –60 N1 97 P1
2.0% –141 N0* –151 N0 –154 N0 –160 N1 –154 N1 –97 N1 43 P1
2.5% –127 N0* –137 N0* –141 N0 –136 N0 –119 N0 –77 N1 –5 N1
3.0% –120 N0* –126 N0* –131 N0* –128 N0* –116 N0 –76 N0 –33 N0
200 1.0% –371 N1 –430 N1 –486 N1 –414 N1 –242 N1 –66 N1 34 P1
1.5% –181 N1 –208 N1 –240 N1 –262 N1 –249 N1 –103 N1 73 P1
2.0% –158 N0* –166 N0 –168 N0 –164 N1 –159 N1 –111 N1 –10 N1
2.5% –143 N0* –150 N0* –155 N0 –150 N0 –132 N0 –83 N1 –14 N1
3.0% –135 N0* –139 N0* –143 N0* –140 N0* –129 N0 –87 N0 –45 N0
300 1.0% –378 N1 –427 N1 –486 N1 –496 N1 –308 N1 –114 N1 3 P1
1.5% –201 N0 –207 N1 –240 N1 –263 N1 –256 N1 –150 N1 40 P1
2.0% –178 N0* –179 N0 –180 N0 –168 N0 –161 N1 –113 N1 –12 N1
2.5% –163 N0* –163 N0* –166 N0 –160 N0 –141 N0 –90 N0 –20 N0
3.0% –154 N0* –151 N0* –154 N0* –150 N0* –137 N0 –95 N0 –51 N0
400 1.0% –362 N1 –373 N1 –474 N1 –510 N1 –391 N1 –187 N1 15 P1
1.5% –221 N0 –221 N0 –230 N1 –257 N1 –253 N1 –182 N1 –2 N1
2.0% –200 N0* –194 N0 –193 N0 –179 N0 –158 N1 –111 N1 –10 N1
2.5% –182 N0* –178 N0* –180 N0 –172 N0 –149 N0 –97 N0 –25 N0
3.0% –173 N0* –167 N0* –168 N0* –161 N0* –148 N0 –103 N0 –56 N0
Difference in net present value = (NPVPlanting – NPVNatural) in € ha–1. Thus, positive values mean that the best option for planting yields a higher net present value than the best natural regeneration. N denotes that natural regeneration is the optimal method, P denotes planting. The numbers 0 to 1 represents the optimal number of thinnings and * means that both methods result in negative land value.
1

Fig. 1. Average age of regeneration harvest for all latitudes and altitudes and three discount rates. min denotes the minimum harvest age (Skogsstyrelsens föreskrifter… 2009). The bars denote maximum and minimum values.

2

Fig. 2. Break-even site index at latitude 60°N and a discount rate of 2.5%. The break-even site index was calculated by linear interpolation except for the two points lying above SIH 28. Here linear extrapolation was used.

Table 4. Difference in net present value between the best option for planting and for natural regeneration. Scenarios for two levels of genetic gain to growth compared to natural regeneration; and a scenario of higher mortality for seed trees compared to unimproved planting material. Latitude 60°N, Altitude 100 m.a.s.l. Compare to the first five rows in Table 3.
Scenario Discount
rate 		Site index (SIH(100), m)
T16 T18 T20 T22 T24 T26 T28
Genetically improved seedlings,+2% to site index 1.0% –178 N1 –235 N1 –151 N1 28 P1 271 P1 553 P1 908 P1
1.5% –108 N0 –145 N1 –134 N1 –67 N1 74 P1 261 P1 474 P1
2.0% –106 N0* –117 N0 –101 N1 –72 N1 –2 N1 136 P1 283 P1
2.5% –100 N0* –107 N0* –107 N0* –77 N0 –35 N1 54 P1 165 P1
3.0% –98 N0* –102 N0* –106 N0* –85 N0* –56 N0 8 P1 81 P1
Genetically improved seedlings,+5% to site index 1.0% –76 N1 –67 N1 138 P1 447 P1 847 P1 1345 P1 1956 P1
1.5% –62 N0 –61 N1 8 P1 163 P1 414 P1 711 P1 1105 P1
2.0% –79 N0* –73 N0 –15 N1 62 P1 208 P1 430 P1 676 P1
2.5% –84 N0* –80 N0* –48 N0* 9 P0 105 P1 266 P1 419 P1
3.0% –88 N0* –84 N0* –64 N0* –26 N0* 37 P0 156 P1 252 P1
Higher rate of annual mortality for seed trees, 1% instead of 0.5% 1.0% –201 N1 –294 N1 –271 N1 –167 N1 –21 N1 131 P1 332 P1
1.5% –103 N0 –152 N1 –177 N1 –155 N1 –79 N1 47 P1 171 P1
2.0% –94 N0* –110 N0 –121 N1 –117 N1 –86 N1 –2 N1 91 P1
2.5% –90 N0* –99 N0* –109 N0* –98 N0 –86 N1 –32 N1 45 P1
3.0% –85 N0* –90 N0* –97 N0* –87 N0* –77 N0 –39 N1 12 P1
Difference in net present value = (NPVPlanting – NPVNatural) in € ha–1. Thus, positive values mean that the best option for planting yields a higher net present value than the best option for natural regeneration. N denotes that natural regeneration is the optimal method, P denotes planting. The numbers 0 to 1 represents the optimal number of thinnings and * means that both methods result in negative land value.