Economics of harvesting uneven-aged forest stands in Fennoscandia

Figures & data

Figure 1a–c. Diameter increment, ingrowth, and mortality of Norway spruce using growth models by Pukkala et al. (2009) and Bollandsås et al. (2008), with size-distribution x = [300,180,120,80,50,30,18,10,2,0,0,…].

Table 1. Saw log and pulpwood stumpage prices for Scots pine, Norway spruce, and birch, € m⁻³.

	Saw log	Pulpwood
Scots pine	55.90	16.11
Norway spruce	55.46	23.71
Birch	48.55	15.58

Figure 2a–d. Additive stand basal area development with no harvests. Single-species initial stands at H₁₀₀ = 24, mixed-species stand at H₁₀₀ = 20.

Figure 3. Average annual yields in volume maximization steady state for Scots pine, Norway spruce, and birch with harvesting intervals of 5–80 years.

Figure 4. Development of basal area for Scots pine, Norway spruce, and birch from four different initial stands toward the volume yield maximization steady state.

Table 2. The optimal steady-state solution when maximizing volume yield for Scots pine, Norway spruce, and birch using a 5-year harvesting interval.

H100	Average annual yield, m^3 ha^−1	No. of harvested trees, ha^−1 a^−1	No. of trees after harvests, ha^−1	Basal area before/after harvests, m^2 ha^−1	Average annual natural mortality, trees ha^−1	Average annual ingrowth, trees ha^−1	Diameter of harvested trees, cm
Scots pine
15	1.4	1.8	329	11.71/10.75	1.02	2.8	35–39.9
20	2.4	1.8	281	13.54/12.30	0.79	2.5	40–44.9
24	3.0	1.2	245	18.23/16.85	0.70	2.0	50–54.9
Norway spruce
15	2.1	3.6	679	15.76/14.30	2.56	6.0	30–34.9
20	4.0	4.2	784	24.49/22.02	3.37	7.9	35–39.9
24	6.4	6.2	802	27.33/23.87	3.47	9.7	35–39.9
27	7.3	7.2	808	28.55/24.57	3.50	10.7	35–39.9
Birch
20	2.3	2.6	795	20.60/19.14	6.48	9.1	35–39.9
24	3.5	3.4	747	21.68/19.76	5.90	9.4	35–39.9
27	3.9	3.8	726	22.01/19.87	5.64	9.5	35–39.9

Figure 5. Optimal steady-state structures when maximizing volume yield for Scots pine, Norway spruce, and birch with a 5-year harvesting interval. Size classes begin from a diameter of 7.5 cm and increase in 5 cm intervals.

Table 3. Optimal steady-state solutions when maximizing the net present value of forestry income with a 0% interest rate for Scots pine, Norway spruce, and birch using a 15-year harvesting interval

H100	Average annual yield, m^3 ha^−1	Revenues per harvest, € ha^−1	No. of harvested trees per harvest, ha^−1	No. of trees after harvests, ha^−1	Basal area before/after harvests, m^2 ha^−1	Average annual natural mortality, no. of trees ha^−1	Average annual ingrowth, no. of trees ha^−1	Diameter of harvested trees, cm
Scots pine
15	1.3	1112	24	320	13.26/10.42	1.04	2.7	35–49.9
20	2.3	1938	25	271	15.54/11.86	0.81	2.4	40–54.9
24	2.8	2330	23	241	17.79/13.53	0.69	2.2	45–59.9
Norway spruce
15	2.0	1623	48	678	18.26/13.99	2.72	5.9	30–44.9
20	4.0	3199	81	710	23.45/16.02	2.91	8.4	30–44.9
24	6.1	4696	83	792	33.09/23.07	3.85	9.4	35–49.9
27	7.1	5735	94	797	35.28/23.71	3.94	10.3	35–49.9
Birch
20	2.3	1603	37	771	22.71/18.37	6.52	9.0	35–49.9
24	3.5	2468	47	718	24.55/18.82	5.97	9.2	35–49.9
27	3.9	2754	53	695	25.25/18.86	5.72	9.3	35–49.9

Figure 6. Optimal steady-state structures when net present value of forestry income is maximized using a 0% discount rate for Scots pine, Norway spruce, and birch with a 15-year harvesting interval. Size classes begin from a diameter of 7.5 cm and increase in 5 cm intervals.

Table 4. Optimal steady-state solutions when maximizing the net present value of forestry income with a 3% interest rate for Scots pine, Norway spruce, and birch using a 15-year harvesting interval.

H100	Average annual yield, m^3 ha^−1	Revenues per harvest, € ha^−1	No. of harvested trees per harvest, ha^−1	No. of trees after harvests, ha^−1	Basal area before/after harvests, m^2 ha^−1	Average annual natural mortality, trees ha^−1	Average annual ingrowth, trees ha^−1	Diameter of harvested trees, cm
Scots pine
15	0.9	664	48	246	5.29/3.16	0.85	4.1	20–34.9
20	1.7	1368	45	233	7.44/4.44	0.69	3.7	25–39.9
24	1.9	1514	48	203	7.20/3.93	0.58	3.8	25–39.9
Norway spruce
15	1.6	1166	83	492	9.55/5.89	1.80	7.3	20–34.9
20	2.9	2144	128	507	12.21/6.30	1.88	10.4	20–34.9
24	5.5	4267	136	622	20.48/11.15	2.38	11.5	25–39.9
27	6.2	4836	152	623	21.83/11.29	2.41	12.5	25–39.9
Birch
20	2.0	1222	92	750	12.87/8.83	5.64	11.8	20–34.9
24	2.9	1767	111	677	13.31/8.24	5.00	12.5	20–34.9
27	3.1	1926	120	645	13.37/7.95	4.73	12.8	20–34.9

Figure 7. Basal area development for Scots pine, Norway spruce, and birch from four different initial stands toward the net present value of forestry income maximization steady state using a 3% interest rate and a 15-year harvesting interval.

Figure 8. Optimal steady-state structures when net present value of forestry income is maximized using a 3% interest rate for Scots pine, Norway spruce, and birch with a 15-year harvesting interval. Size classes begin from a diameter of 7.5 cm and increase in 5 cm intervals.

Table 5. Optimal steady states based on the single-tree model. The site for Scots pine is H₁₀₀ = 20 and H₁₀₀ = 24 for Norway spruce. An interest rate of 3% and a harvesting interval of 15 years.

H100	Average annual yield, m^3 ha^−1	Revenues per harvest, ha^−1	No. of harvested trees per harvest, ha^−1	No. of trees after harvests, ha^−1	Basal area before/after harvests, m^2 ha^−1	Average annual natural mortality, trees ha^−1	Average annual ingrowth, trees ha^−1	Diameter of harvested trees, cm
Scots pine
20	1.5	1082	49	224	6.27/3.22	0.84	4.0	24–27
Norway spruce
24	4.5	3379	148	585	15.24/7.70	2.45	12.5	24–28

Figure 9. Optimal steady-state structures obtained with the single-tree model for Scots pine at H₁₀₀=20 and for Norway spruce at H₁₀₀ = 24, using a 3% interest rate and a 15-year harvesting interval.

Figure 10. Single-tree steady-state structures combined in 5 cm size classes.

Table 6. Comparison of the dynamic optimization results for Norway spruce at H₁₀₀ = 24 and the Investment Efficient (IE) model. Harvesting interval:15 years.

Interest rate	Optimization framework	Basal area before/after harvests, m^2 ha^−1	Annual yield, m^3 ha^−1	Trees after harvests, ha^−1	Harvested trees per harvest, ha^−1	Size of harvested trees, cm	Revenues per harvest, € ha^−1	Objective value, € ha^−1
3%	Dynamic	15.24/7.75	4.5	595	144	24–28	3330	6664^a
	IE	14.59/6.84	3.5	565	156	23–27	3180	4410
5%	Dynamic	10.46/4.69	3.5	496	172	19–23	2475	3326^a
	IE	13.10/5.8	3.2	534	164	22–26	2867	1710

^a Objective function value when IE after-harvest steady state is taken as the initial state. Other figures for the dynamic optimization framework are steady state results.

Table

		Diameter at breast height, cm
Norway spruce		7.5	12.5	17.5	22.5	27.5	32.5	37.5	42.5	47.5	52.5	57.5	62.5
H100 = 15	Pulpwood	0.01214	0.05485	0.13494	0.06132	0.05286	0.04370	0.03921	0.03420	0.03224	0.03001	0.02723	0.02617
	Saw log	0	0	0	0.19151	0.35321	0.54620	0.76099	0.99508	1.24309	1.49430	1.75811	2.01921
H100 = 20	Pulpwood	0.01285	0.06061	0.15062	0.06857	0.06052	0.04872	0.04593	0.04370	0.03787	0.03573	0.03329	0.03035
	Saw log	0	0	0	0.21435	0.39553	0.61681	0.85638	1.11749	1.40218	1.68841	1.97974	2.28072
H100 = 24+	Pulpwood	0.01374	0.06664	0.16690	0.08080	0.06482	0.05975	0.04978	0.05039	0.04324	0.03925	0.03317	0.03073
	Saw log	0	0	0	0.23419	0.44578	0.68392	0.96304	1.25313	1.57421	1.89981	2.21442	2.56544
		Diameter at breast height, cm
Birch		7.5	12.5	17.5	22.5	27.5	32.5	37.5	42.5	47.5	52.5	57.5	62.5
H100 = 20	Pulpwood	0.01445	0.06552	0.15522	0.07000	0.05743	0.04731	0.04769	0.04179	0.03290	0.03096	0.03058	0.02474
	Saw log	0	0	0	0.21483	0.39299	0.59908	0.82020	1.06492	1.32770	1.59244	1.85821	2.12589
H100 = 24+	Pulpwood	0.01591	0.07464	0.18005	0.07854	0.06655	0.05827	0.04978	0.04865	0.04463	0.03891	0.03685	0.03268
	Saw log	0	0	0	0.25137	0.45137	0.69732	0.96304	1.24859	1.55035	1.86531	2.18117	2.49693
		Diameter at breast height, cm
Scots pine		7.5	12.5	17.5	22.5	27.5	32.5	37.5	42.5	47.5	52.5	57.5	62.5
H100 = 15	Pulpwood	0.01169	0.05517	0.13018	0.04226	0.02884	0.02522	0.02129	0.01975	0.01560	0.01291	0.01046	0.00823
	Saw log	0	0	0	0.20034	0.35433	0.54088	0.75996	1.01160	1.29577	1.61250	1.96176	2.36358
H100 = 20	Pulpwood	0.03342	0.06370	0.09685	0.03738	0.02917	0.02690	0.02597	0.02551	0.02525	0.02509	0.02498	0.02490
	Saw log	0	0	0.09244	0.25616	0.46094	0.70979	0.99370	1.32168	1.69072	2.10083	2.55120	3.04424
H100 = 24	Pulpwood	0.10194	0.12840	0.13353	0.11102	0.08415	0.06490	0.05270	0.04499	0.03996	0.03655	0.03415	0.03241
	Saw log	0	0	0.09764	0.27034	0.48515	0.74205	1.04106	1.38216	1.76537	2.29067	2.65807	3.16758

Pukkala T, Lähde E, Laiho O. 2009. Growth and yield models for uneven-sized forest stands in Finland. For Ecol Manage. 258:207–216.

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Bollandsås OM, Buongiorno J, Gobakken T. 2008. Predicting the growth of stands of trees of mixed species and size: a matrix model for Norway. Scand J For Res. 23:167–178.

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