Economics of even- and uneven-aged mixed species forestry Olli Tahvonen Janne Rämö University of Helsinki, Dept. of forest sciences
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?
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
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
Ecological and economic data Detailed empirical harvesting cost models for even- and uneven-aged management: Nurminen et al. 2006 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
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 1 3 3 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
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
Bare land value per hectare 28000 27800 27600 27400 27200 27000 26800 26600 26400 40 60 80 100 120 140 160 Rotation period years 30 Basal area m 3 per hectare per species 25 20 15 10 5 0 20 40 60 80 100 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
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
4700 4600 Bare land value per ha 4500 4400 4300 4200 4100 40 60 80 100 120 140 160 180 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
Characteristics of the optimal uneven-aged solution: Volumes m 3 per ha 180 160 140 120 100 80 60 40 20 Optimal harvesting interval: 15-20 years All harvests: optimal to thin from above Diameter of harvested trees: Spruce: 27.5-42.5cm Birch: 22.5-37.5co Pine: 22.5-37.5cm 0 0 100 200 300 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)
Characteristics, cont. 40 Stand basal area m 2 per ha 30 20 10 0 0 100 200 300 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)
Characteristics, cont. 12 Ingrowth per year per ha 8 4 0 0 100 200 300 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)
Characteristics, cont. 180 160 Harvest m 3 per ha per cutting 140 120 100 80 60 40 20 0 0 50 100 150 200 250 300 350 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)
Characteristics, cont. 12000 10000 Revenues, costs per ha 8000 6000 4000 2000 0 0 50 100 150 200 250 300 350 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)
Characteristics, cont. Stand structure at the optimal steady state 180 Number of trees per hectare per species 160 140 120 100 80 60 40 20 0 7.5cm 1 2 3 4 5 6 7 8 Diameter class 42.5cm Norway spruce Norway spruce harvested trees Birch Birch, harvested trees Scots pine Scots pine, harvested trees
Interest rate 1% =>higher stand volume, longer harvesting interval 250 200 Volumes per ha m 3 150 100 50 0 0 50 100 150 200 250 300 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%
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