Economics of even- and uneven-aged mixed species forestry Olli Tahvonen Janne Rämö University of Helsinki, Dept. of forest sciences

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1 Economics of even- and uneven-aged mixed species forestry Olli Tahvonen Janne Rämö University of Helsinki, Dept. of forest sciences

2 Introduction In Nordic countries forests are important as sources of wood and economic welfare, e.g. in Finland ~25% of export revenues come from forest products Present forest management: single species even-aged plantations with native species Biodiversity, climate change, recreation etc call to develop understanding on mixed species even- and uneven-aged forests But forest economics has concentrated on even-aged single species forestry Our objective: to develop economic models for mixed species stands that cover both even- and uneven-aged forestry Open questions: -what is optimal species mixture? -optimal thinning strategy? -optimal rotation? -even- or uneven-aged forestry?

3 Existing economic optimization studies on mixed species stands are few Valsta (1986) Buongiorno et al (1995, ): many results but the model used is not economically sound Getz and Haight (1989): model for white fir (Abies concolor) and red fir (Abies magnifica) -no harvesting cost -result: uneven-aged management but preferable to maintain only the white fir

4 This study: dynamic economic-ecological optimization model for boreal mixed species forests Three species: Norway spruce, birch, Scots pine Stand growth: transition matrix model Species interaction: total basal area determines regeneration, growth and mortality Economic objective: max of harvesting revenues net of harvesting and regeneration cost Long (infinite) time horizon Harvest type, timing and rotation are optimized dynamically without any restrictions In addition, the model determines optimal choice between even-and uneven-aged management

5 Ecological and economic data Detailed empirical harvesting cost models for even- and uneven-aged management: Nurminen et al Mixed species stand growth: Bollandsås et al 2008, Norwegian data, distance independent transition matrix model Optimization method Mixed integer large scale nonlinear problem Bi-level optimization Upper level: harvest timing 0/1 variables (integers) Lower level: number of trees harvested per size classes and species

6 A model for optimizing thinnings and rotation period and the choice between even- and uneven-aged management Based on Tahvonen JAERE 2015, For Pol & Econ 2015, Rämö and Tahvonen 2015 Tahvonen and Rämö 2015 J,T max subject to, st t h,,t t, 1 w R C C b R C C b T t 1 1 ˆ T hit ith hit t f hit cl hit T T t t1 i 1 i 1 T 1 1 b (1) x i 1,t 1 i x t 1 i1 x t 1 x t x i1t h i1t, t t 1,...,T, i 1, 2, 3, (2) xis 1,t 1 is xt xist 1 is 1 xt is 1 x t x is 1,t h is 1,t, i 1, 2, 3, s 1,...,n 1, t t 1,...,T, (3) h h, i 1, 2, 3, s 1,...,n, t t,...,t, (4) ist t ist 1 x 1, x ist 0, i 1, 2, 3, s 2,...,n, (5) i t 1 1 Note: When optimal rotation is finite even-aged management is optimal When optimal rotation is infinite uneven-aged management is optimal

7 Results: Case 1 The initial state of the stand can be freely chosen but assume 1. The stand initial age is 20 years (after a clearcut) 2. The stand has been regenerated to Scots pine (20 yrs ago) Initial state: Scots pine: 2250 seedlings Norway spruce: 100 seedlings (natural regeneration) Birch: 1000 seedlings (natural regeneration) 3. Site productivity is good (SI=17) 4. Interest rate is 1% and regeneration cost below 500 per hectare

8 Bare land value per hectare Rotation period years 30 Basal area m 3 per hectare per species Norway spruce Birch Scots pine Stand age, years Remarks: 1. Optimal rotation is 90 years =>even-aged forestry is optimal 2. Birch is almost totally harvested at the age of 35 years 3. Three thinnings from above are optimal before the clearcut

9 Results: Case 2 1. The stand initial age is 20 years (after clearcut) 2. The stand has been regenerated to Scots pine Initial state: Scots pine: 1750 seedlings Norway spruce: 100 seedlings (natural regeneration) Birch: 1000 seedlings (natural regeneration) 3. Site productivity is good (SI=17) 4. Interest rate is 3% and regeneration cost is 2000 per hectare

10 Bare land value per ha Rotation period Regeneration cost 2000 per hectare Regeneration cost 0 per hectare Optimal uneven-aged solution Remark: When regeneration cost is 2000 per hectare optimal rotation is infinitely long =>uneven-aged management is optimal

11 Characteristics of the optimal uneven-aged solution: Volumes m 3 per ha Optimal harvesting interval: years All harvests: optimal to thin from above Diameter of harvested trees: Spruce: cm Birch: co Pine: cm Spruce volume Birch volume Pine volume Time years Site fertility: good (SI=17), interest rate 3% Initial state: Norway spruce 100, Birch 1000, Pine 1750 (number of trees, in smallest size class)

12 Characteristics, cont. 40 Stand basal area m 2 per ha Time Site fertility: good (SI=17), interest rate 3% Initial state: Norway spruce 100, Birch 1000, Pine 1750 (number of trees, in smallest size class)

13 Characteristics, cont. 12 Ingrowth per year per ha Spruce Birch Pine Time years Site fertility: good (SI=17), interest rate 3% Initial state: Norway spruce 100, Birch 1000, Pine 1750 (number of trees, in smallest size class)

14 Characteristics, cont Harvest m 3 per ha per cutting Spruce Birch Pine Time years Site fertility: good (SI=17), interest rate 3% Initial state: Norway spruce 100, Birch 1000, Pine 1750 (number of trees, in smallest size class)

15 Characteristics, cont Revenues, costs per ha Gross revenues Net revenues Costs Time years Site fertility: good (SI=17), interest rate 3% Initial state: Norway spruce 100, Birch 1000, Pine 1750 (number of trees, in smallest size class)

16 Characteristics, cont. Stand structure at the optimal steady state 180 Number of trees per hectare per species cm Diameter class 42.5cm Norway spruce Norway spruce harvested trees Birch Birch, harvested trees Scots pine Scots pine, harvested trees

17 Interest rate 1% =>higher stand volume, longer harvesting interval Volumes per ha m Spruce volume Birch volume Pine volume Time years Note: Site index: SI=15 Initial state: Norway Spruce 100,,Birch 1000, Scots Pine 1750 Interest rate: 1%

18 Closing remarks Economics of mixed species forestry calls for reliable ecological models for stand growth Both transition matrix or single tree models can be applied Obtaining dynamic economic solutions calls for efficient optimization algorithms (and fast computers) When model includes natural regeneration and harvesting costs economically optimal solutions maintain mixed species structure (cf. Getz and Haigh 1989) Economic optimality between even-and uneven-aged forestry depends on a number of factors like natural regeneration, regeneration costs and interest rate, sawn timber price/pulp price, etc