Optimal Management of Pinus radiata Silvopastoral Systems Established on Abandoned Agricultural Land in Galicia (North-Western Spain)

831 www.metla.fi/silvafennica · ISSN 0037-5330 The Finnish Society of Forest Science · The Finnish Forest Research Institute SI LV A FE N N I C A Silva Fennica 43(5) research articles Optimal Management of Pinus radiata Silvopastoral Systems Established on Abandoned Agricultural Land in Galicia (North-Western Spain) María Pasalodos-Tato, Timo Pukkala, Antonio Rigueiro-Rodríguez, Esther Fernández-Núñez and María Rosa Mosquera-Losada Pasalodos-Tato, M., Pukkala, T., Rigueiro-Rodríguez, A., Fernández-Núñez, E. & Mosquera-Losada, M.R. 2009. Optimal management of Pinus radiata silvopastoral systems established on abandoned agricultural land in Galicia (north-western Spain). Silva Fennica 43(5): 831–845. Timber production has been the main objective in forest production in Galicia for a long time. Nevertheless, factors such as fire risk and the need to obtain non-timber benefits make other production alternatives like silvopastoral systems worth of consideration. Integration of grazing in the production system not only diversifies products and benefits, but also decreases fire risk by enhancing fuel control. Nonetheless, few studies have examined the economic profitability of these systems. This article analyses the economics of silvopastoral systems established on abandoned agricultural soils afforested with Pinus radiata D. Don. Different tree planting densities, discounting rates, grass values and fire risk scenarios were analysed. The technique employed is based on the combination of an optimization algorithm and a simulator of stand growth and grass yield. The most profitable schedules were obtained with initial stand densities of 1500 trees per hectare. However, with high unit values of pasture production (high value of grass), schedules with an initial stand density of 500 trees per hectare were the most profitable. When the risk of fire was included in the analyses, silvopastoral systems were always more profitable than timber production systems. With an assumption that grazing reduces fire risk thinnings should be done earlier and heavier to reduce the expected losses due to fire and to promote grass production. This lengthens the pasture period. In general, rotation lengths of silvopastoral systems were shorter than in timber production. Keywords economic profitability, optimization, risk reduction, salvage, simulation Addresses Pasalodos: INIA, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria. Madrid, Spain; Rigueiro, Fernández & Mosquera: University of Santiago de Compostela, Lugo, Spain; Pukkala: University of East Finland, Joensuu, Finland E-mail [email protected] Received 5 April 2009 Revised 14 September 2009 Accepted 13 November 2009 Available at http://www.metla.fi/silvafennica/full/sf43/sf435831.pdf 832 Silva Fennica 43(5), 2009 research articles 1 Introduction The main use of Galician forest is timber production. Many forests are managed to maximise biomass production for pulp and board industries. Steady income from these management regimes is hampered by both forest fires (Núñez Regueira et al. 2003) and low timber prices. Therefore, there is a need to search for alternative regimes that would make income-generation less risky. Silvopastoral systems could be an appropriate alternative. Grazing has sometimes been considered to promote fire damages because fire has been carelessly employed by shepherds to promote the growth of more palatable grass species. However, if prescribed fires are excluded, grazing reduces the risk of fire by diminishing the fuel loads in the forest (Rigueiro-Rodríguez et al. 2005). Another advantage is the multiplicity of products that make silvopastoral systems economically safer under market uncertainty than the traditional timber production oriented forestry (Anderson and Sinclair 1993, Sharrow 1999). Furthermore, silvopastoral systems generate incomes much earlier (Sharrow 1999) than pure timber production systems. Finally, silvopastoral systems improve accessibility (Knowles 1991) and scenic value of the landscapes, enhancing their recreational use (Ruark et al. 2003, Alavalapati et al. 2004). Despite the advantages showed by the implementation of silvopastoral systems, not much research has focused on the optimal design of these systems. One of the very few examples is the study of Muchiri et al. (2002b), which optimized the management of an agroforestry system composed of maize and Grevillea robusta. This study is focused on silvopastoral systems established on abandoned agricultural lands. These lands are fertile (stand dominant heights up to 30 meters at 20 years for Pinus radiata D. Don). Accordingly, this study analyses only good sites on which economically viable agroforestry is possible (Hawke 1991). Pinus radiata has been the most common tree species employed in silvopastoral systems. The system is established by planting trees and sowing grass at the same time. Therefore, there is forage production already in the first year suitable for instance to sheep grazing (Rigueiro-Rodríguez et al. 2002). A study carried out at the Department of Crop Production at the University of Santiago de Compostela (Spain) found that silvopastoral systems of this type need an area of about 200–300 hectares to make their implementation profitable. On this scale the management costs of the silvopastoral system (veterinary costs, shepherd costs and other related costs) become affordable. It has been claimed (Adams et al. 2001) that the establishment of conifer plantations on this type of terrains may decrease soil fertility in the Spanish Atlantic region due to a pH reduction. This impoverishment of soil fertility leads to a change in the type of understorey vegetation, from herbaceous vegetation with low fuel loads towards more inflammable shrub communities (Rigueiro-Rodríguez et al. 2005, MosqueraLosada et al. 2006). Therefore, it seems even more important to keep the herbaceous stratum at the understorey level by grazing in order to reduce the risk of fire as long as possible. For the optimal management of silvopastoral systems, the influence of trees on pasture production must be known. The key factor of the success of the system is to achieve a compromise between the two sources of economic benefit. Grazing is possible when the tree canopy allows light to reach the understorey layer. Canopy cover is commonly used to set the limits for pasture production (Knowles et al. 1998). Literature suggests that canopy covers higher than 50% drastically decrease the pasture production (Rigueiro-Rodríguez et al. 1998). Other studies suggest a maximum canopy cover of 70% (Knowles et al. 1998). Also green crown lengths (Percival and Knowles 1983, 1988), horizontal projection of the crowns (Sibbald et al. 1994) or stand density (Pearson et al. 1995, Burner and Brauer 2003, Rozados-Lorenzo et al. 2007) are variables that have been used to predict pasture production. Canopy cover is difficult to measure in the field and predict in simulations. Green crown length and horizontal projection of the crowns are also problematic because they are not measured in normal inventories. Stand density (number of trees per hectare) is not a good predictor neither because, by itself, it does not give enough information about competition in the stand. Therefore, we decided to model the dependence of pasture production on stand basal area and site index, which are easily obtained 833 Pasalodos-Tato, Pukkala, Rigueiro-Rodríguez, Fernández-Nùñez and Mosquera-Losada Optimal Management of Pinus radiata Silvopastoral… from regular inventories. Using this model with a growth and yield model for tree stand dynamics, we were able to calculate the profitability of the system. The aim was to study how the economic profitability and optimal management of silvopastoral systems established on abandoned agricultural terrains depend on site quality, grass value and planting density of trees. The effect of fire risk on the profitability of the silvopastoral systems was also studied. Moreover, we analysed the effects of an assumption that grazing reduces fire risk by diminishing fuel loads and promoting less inflammable species. The analyses of the study are divided into three parts: effect of (I) stand density and grass price, (II) fire risk and (III) the influence of grazing on fire risk, on the economic profitability and optimal management of silvopastoral systems. 2 Material and Methods 2.1 Simulation of the Tree Stand Dynamics Silvopastoral systems have three components, tree stand, forage and livestock. We used the model of Castedo-Dorado et al. (2007) for even-aged P. radiata stands in Galicia to simulate stand development in different management schedules. In this model, the initial stand conditions are defined by three state variables: number of trees per hectare, stand basal area and dominant height. The model uses three transition functions to project each state variable for a given time period. It also includes a function for predicting the initial stand basal area when no inventory data are available. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class by recovering the parameters of the Weibull function, using the moments of the first and second order of the distribution. By using a height-diameter function to estimate the height of the average tree in each diameter class, and a taper function, the total and merchantable stand volume are calculated. The model for the dominant height development is as follows: HH T T 21 2 1 1 1006738 1006738 =−− −−      − exp( .) exp( .) .. ./755 12 44 1 +X (1) with, XHL HL L 111 11 2 1 1 21 755 1 755 41244 =++ +−⋅ ((ln.) (ln.).) (2) LT 11 1006738=−−ln(exp( .)) (3) where H1 is the dominant height (m) at age T1 (years), and H2 is dominant height at age T2. Reduction in the number of trees per hectare (natural mortality) is predicted with: NN TT 21 0 3161 100 100 103161 1 053 1 053 21 =+− −−− − (..) ./. (4) where N2 is the number of trees per hectare at age T2 and N1 is the number of trees per hectare at age T1. The following function was used for basal area initialization: GSIN =−      −− + exp. . exp. . 4 331 114 3 276 1 1391 0 03594 44 331 114 3 0 03594 0 923 .. . . SI N T −                  −33             (5) where G is stand basal area (m2ha–1) at age T (years), N is the number of trees per hectare and SI is the site index (m), estimated using Eq. 1 at a reference age of 20 years. The function for basal area projection is: GY YT 21 12 0 9233 276 1 1391= () −− + () () − expexp ./ . (6) YT TG T 11 0 9233 1 0 9233 1 1 09 1 2 276 1 4 1391 = −+ () + ⋅ −. . . .ln 2233 1 0 9233 1 2 276 1+− () ()         .ln . TG (7) where G2 is the stand basal area (m2 ha–1) at a given projection age T2, and G1 is stand basal area (m2 ha–1) at age T1. The equation for predicting the arithmetic mean diameter, to be used to derive the diameter distribution with the parameter recovery approach, is: 834 Silva Fennica 43(5), 2009 research articles dd T NSI g =− −+ +     exp.. .. 0 1449 19 76 1 0 0001345 0 03264     (8) where d is the arithmetic mean diameter (cm) and dg the quadratic mean diameter (cm), dGN g=×40000 // π (9) The equation for predicting the height of a representative tree in each 1-cm diameter class is: hH d = + − () − − − 13 13 1 1 0 9339 0 9339 0 9339 0 06614 . .exp . .. . eexp. /. −           0 06614 109339 D (10) where h is the total tree height (m), d is diameter at breast height (cm), and D and H are, respectively, dominant diameter and dominant height of the stand. Both uniform and low thinnings can be simulated as intermediate treatments. Uniform thinnings remove an equal percentage of trees from every diameter class. When a low thinning is simulated, the remaining number of trees in diameter class i (ni) is calculated following the distribution independent approach proposed by Alder (1979): nNLFdFd ii L i L =−    −before (()() //1 1 1 (11) where Nbefore is the total number of trees per hectare before low thinning, L is low-thinning intensity expressed as one minus the proportion of removed trees (1–Nremoved/Nbefore) and F(di) is the cumulative frequency distribution at diameter di. The taper model proposed by Fang et al. (2000) fitted for P. radiata by Castedo et al. (2007) was used to calculate the stem volume of trees extracted in thinning operations or clear cuttings. The following top diameters were used: 35, 18 and 7 cm. The timber assortments therefore corresponded to the following over-bark stem diameters: (I) d ≥ 35 cm; (II) 35 cm > d ≥ 18 cm; and (III) 18 cm > d ≥ 7 cm. The following minimum piece lengths were assumed in this study: (I) 3.0 m; (II) 2.5 m; and (III) 1.0 m. If the piece was shorter, the volume was moved to the next (with a smaller minimum top diameter) timber assortment. 2.2 Simulation of Grass Production Pasture production is highly dependent on the stand development since pasture production is only possible when the canopy allows light to reach the understorey level. Site and stand characteristics were used as predictors to fit a model for the pasture production. We used data from an experiment in Castro de Riberas de Lea (Lugo) that consisted of the measurement of trees and pasture production in a silvopastoral system during seven years since tree planting (see Mosquera-Losada et al. (2006) and Fernández-Núñez et al. (2007)). The trial has plots of different site quality and two different planting densities (833 and 2500 trees ha–1). The pasture was a mixture of Lolium perenne L., Dactylis glomerata L., Trifolium repens and Trifolium pratense. The fitted regression model is as follows: ln .. .grassSIG () =− +−125009 012 (12) where grass is the annual grass production (dry mass) (t ha–1), SI is site index of Pinus radiata stand (m) (dominant height at the reference age of 20 years) and G is the basal area (m2 ha–1) of the tree stand. The R2 of the equation is 0.425. This equation shows that the higher the basal area is, the smaller the grass production becomes (Fig.1). Better sites produce more grass, as expected. The pasture was considered to generate income only when the grass yield was higher than 0.3 t ha–1. This is the minimum amount required for feeding one sheep per hectare per year (data provided by 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0 5 10 15 20 25 30 Basal area (m 2 ha –1 ) Grass production (t ha –1 a –1 ) SI 35 SI 30 SI 25 SI 20 FIELD DATA Fig. 1. Dependence of grass production on stand basal area for different site indices. 835 Pasalodos-Tato, Pukkala, Rigueiro-Rodríguez, Fernández-Nùñez and Mosquera-Losada Optimal Management of Pinus radiata Silvopastoral… the Department of Crop Production of Santiago de Compostela). 2.3 Study Cases The effect of stand density and unit value of pasture production was tested with two site indices for radiata pine, namely 29 and 25 meters at 20 years. These site indices are typical for silvopastoral systems. The studied planting densities ranged from the sparsest to the densest stockings used in forestry practise in the region: 500, 1500 and 2500 trees ha–1. Two site indices with three planting densities resulted in six different initial stands. In every stand we tested different number of thinnings (0–2) and different unit value of pasture production. The revenues from pasture come from the animals fed by the grass. Grass production was converted into fed livestock (lamb and sheep) to calculate the income using data of the Department of Crop Production at the University of Santiago de Compostela. The data indicate that one ton of grass can feed three sheeps. Taking into account that each sheep delivers 1.6 lambs per year on an average, one ton of grass generates an annual income of about 200 € when silage making and all the related costs such as veterinary, shepherd and silage are considered. This is called as the unit value of pasture production. This value was varied to see the effect of market fluctuations; the used unit values of pasture production were 100, 200 and 400 € t–1. Fire risk was assumed to have two components: probability of occurrence and damage. We tested four different probabilities of occurrence: 0, 1, 3 and 5%. When fire takes place we assumed that it ends the rotation prematurely and only a part of the growing stock volume can be harvested (salvaged). The proportion of salvaged timber describes the second component of risk: damage (salvage rate = 1 – damage rate). The proportion of timber that can be salvaged depended on the mean tree diameter (Pasalodos-Tato et al. 2009b) (Fig. 2): st d =−1092. (13) where d is the diameter at breast height measured in cm. In addition to loosing a part of timber in fire, the salvaged timber was depreciated by 25% (Arenas and Izquierdo 2007). This price reduction of salvaged timber was used in all optimisations. The optimizations were done for one site index (29 meters) and two different stand densities (500 and 1500 trees ha–1). Grazing may reduce fire risk by reducing fuel loads and promoting less inflammable species (Rigueiro-Rodríguez et al. 2005, RigueiroRodríguez et al. 2009). Even though the literature has mentioned this effect widely (Blackmore and Vitousek 2000, Elmore and Asner 2003, Casal et al. 2009) it is difficult to find quantitative information on it. Therefore, we used several reduction factors, namely 25, 50, 75 and 100% to reduce the probability of fire occurrence in every grazing year (grass yield ≥ 0.3 t ha–1). Two different stand densities (500 and 1500 trees ha–1), one site index (29 meters) and two different probabilities of fire occurrence (1 and 5%) were employed to analyse the effect of the reduction in fire risk due to grazing. 2.4 Objective Function Soil expectation value (SEV) calculated with 3% discounting rate was used as the objective variable. The SEV was calculated as the net present value (NPV) of all future net incomes: SEV NPV rR = −+ 11 1() (14) 0 20 40 60 80 100 0 10 20 30 40 50 60 70 Diameter at breast height (cm) Salvage proportion (%) Fig. 2. Dependence of the salvage proportion of the breast height diameter. 836 Silva Fennica 43(5), 2009 research articles where NPV is the net present value of one rotation, r is the discounting rate and R is the rotation length (years). The expression for the NPV is: NPV IICC r t Rwgwg t tttt =+−− + () = ∑ 01 (15) Where Iwt and Igt are the incomes and Cwt and Cgt are the costs derived from timber and pasture production in year t, respectively (see Tables 1 and 2). The incomes from timber production (Iwt) were calculated from: IsnvP wt jkj k k j J t=⋅      == ∑∑ 1 3 1 (16) where st is the proportion of salvage calculated from Eq. 13 (st = 1 if there is no fire), J is the number of diameter classes, nj is the number of trees in diameter class j, Pk is the unit price of timber assortment k and vkj is the volume of assortment k of a tree in diameter class j. The following road side timber prices were used: 90 € m–3 for grade I, 50 € m–3 for grade II and 18 € m–3 for grade III (see Pasalodos-Tato et al. 2009a, b). The unit price was reduced by 25% when fire ended the rotation. The costs of the silvopastoral system (both Cwt and Cgt) depended on site index (Table 1). Timber production costs were different when there was no grazing (Table 2). Regeneration cost (Tables 1 and 2) was assumed to be a linear function of the number of planted trees per hectare with the constant part representing the cost of site preparation and the variable part representing the planting cost per tree. In silvopastoral systems the regeneration cost is higher because of an additional cost of individual tree protectors to avoid the damages that sheeps can cause on the seedlings. The tree harvesting cost was calculated from (based on Ambrosio et al. 2000): HCostECost VFCost S =+ ⋅+ ⋅+78 33 167 0 30477 0 972 (.)/ .. ν              (17) where HCost is harvesting cost (€ ha–1), ECost is entry cost (€ ha–1), V is the total harvested volume (m3 ha–1), FCost is forwarding cost (€ m–3), S is slope (%), and ν is the mean volume of harvested trees (m3). It was assumed that the entry cost of moving the machinery to the forest (ECost) is 200 € ha–1. The forwarding cost was assumed to be 5 € m–3 and the slope was taken as 20%. 2.5 Integrating Fire Risk into Objective Function In order to include fire risk in the calculation of SEV we used the approach developed by Bright and Price (2000). The method consists of the sum of all possible outcomes, weighted by their probabilities. The expression for the expected SEV was (see Pasalodos-Tato et al. 2009a, b): Table 1. Years and costs of tending operations for silvopastoral systems. N is the number of planted trees per hectare. Year Operation Cost (€/ha) SI = 25 m 0 Tree planting+protectors 500+2.2 N 0 Grass sowing 100 6 Tree pruning 200 12 Tree pruning 200 SI = 29 m 0 Tree planting+protectors 500+2.2 N 0 Grass sowing 100 5 Tree pruning 200 10 Tree pruning 200 Table 2. Years and costs of tending operations for a timber-production schedule. N is the number of planted trees per hectare. Year Operation Cost (€/ha) SI = 25 m 0 Tree planting 500+1 N 2 Cleaning 150 4 Cleaning 150 6 Tree pruning 200 12 Tree pruning 200 SI = 29 m 0 Tree planting 500+1 N 2 Cleaning 150 4 Cleaning 150 5 Tree pruning 200 10 Tree pruning 200 837 Pasalodos-Tato, Pukkala, Rigueiro-Rodríguez, Fernández-Nùñez and Mosquera-Losada Optimal Management of Pinus radiata Silvopastoral… SEV NPV p r p r first t t t R R R = −+     ++ ()    = − ∑ 111 0 1 ()              (18) where pt is the probability that the stand burns in year t and survives the previous years, i.e., pt = (1 – pfire)t pfire, where pfire is the annual probability of fire occurrence, and pR pR = (1 – pfire)R is the probability that there is no fire before the rotation age. NPVfirst is calculated from: NPVpNPVpNPV first t t R tR R =⋅+⋅ = − ∑ 0 1 (19) where NPVt is the net present value if fire hits the stand at age t and ends the rotation prematurely, and NPVR is the net present value if there is no fire during the rotation (R). A thinning intensity higher than 30% was assumed to make the stand sensitive to windthrow and snow breakage (Castedo-Dorado et al. 2009). Therefore, a penalty function was added to the SEV of the management schedule as a means to avoid too heavy thinnings. The objective function (OF) which was maximized in optimization was therefore OF SEVPenaltym m M =− = ∑1 (20) with Penalty H HH m m m m = ≤ − −>     030 10000 30 100 30 30 if if % %%  (21) where H%m is thinning intensity in percent of removed stand basal area in thinning m and M is the number of thinnings. The penalty function implies that the penalty of harvesting too much at a time increases from 0 to 10 000 € ha–1 when the thinning percentage increases from 30 to 100. 2.6 Decision Variables Decision variables such as the number and intensity of thinnings, and rotation length define the management schedule. Optimizing a management schedule is equal to finding optimal values for decision variables. Due to the fact that the number of thinnings is not a continuous variable schedules that have a different number of thinnings must be treated as different optimization problems. In this study management schedules were optimized with 0, 1 and 2 thinnings, which are all feasible options for Pinus radiata silvopastoral system. The simulated thinnings were combinations of uniform and low thinning. Therefore the management regime was defined by the number of thinnings and the following decision variables: For thinnings: – Stand age at the first thinning and number of years between the first and the second thinning. – Percentage of uniform thinning (% of number of trees) – Percentage of low thinning (% of trees removed after uniform thinning) For final felling – Number of years since the last thinning The number of optimized decision variables was therefore 3 × M + 1 where M is the number of thinnings. 2.7 Optimisation Method The optimisation algorithm used was the direct search method of Hooke and Jeeves (1961). This method uses a form of coordinate optimization and does not require explicit evaluation of any partial derivative of the objective function. The direct search method compares each new trial solution with the best obtained up to that time. The search has two components, the exploratory search and the pattern search. For a given base point, the exploratory search examines points around that base point in the direction of the coordinate axes (decision variables). The pattern search moves the base point in the direction defined by the given (current) base point and the best point found in exploratory search. 838 Silva Fennica 43(5), 2009 research articles 3 Results 3.1 Profitability of Silvopastoral Systems After running the optimisation for the six different initial stands (2 site indices with 3 planting densities) with three different thinning schedules (0, 1 and 2 thinnings), we chose that number of thinnings that gave the maximum SEV. The optimal schedules had one thinning with initial density 500 trees ha–1 and two thinnings with the other planting densities with both site indices (25 and 29 m). Silvopastoral system was always more profitable than mere timber production, planting density 1500 trees ha–1 being the most profitable (Fig. 3). SI 25 m SI 29 m revenues from grass revenues from timber 500 trees ha –1 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 Unit value of pasture production (€ t –1 ) Unit value of pasture production (€ t –1 ) Unit value of pasture production (€ t –1 ) Unit value of pasture production (€ t –1 ) Unit value of pasture production (€ t –1 ) Unit value of pasture production (€ t –1 ) SEV (€ ha –1 ) SEV (€ ha –1 ) SEV (€ ha –1 ) SEV (€ ha –1 ) SEV (€ ha –1 ) SEV (€ ha –1 ) -30000 -20000 -10000 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 1500 trees ha –1 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 2500 trees ha –1 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 0 10000 20000 30000 40000 50000 60000 no grass 100 200 400 Fig. 3. Soil expectation value of the optimal silvopastoral schedules for different initial stand densities when different grass prices are considered. 839 Pasalodos-Tato, Pukkala, Rigueiro-Rodríguez, Fernández-Nùñez and Mosquera-Losada Optimal Management of Pinus radiata Silvopastoral… The establishment of pasture improved profitability most with the lowest density, 500 trees ha–1. The improvement was up to 50% with a unit value of pasture production of 200 € t–1. SEV improved 15% with planting density 1500 trees per hectare and 4–7 % with 2500 trees per hectare. The optimal rotation lengths without pasture were 40 and 42 years, respectively, for planting densities 500 and 1500 trees per hectare in site index 25 m, and 38 years for both densities in site index 29 m. In general, rotation lengths decreased with the inclusion of pasture. This decrease was more noticeable with lower planting densities (Fig. 4). 500 trees ha –1 1500 trees ha –1 Basal area Grass production 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (years) Basal area (m 2 ha –1 ) Basal area (m 2 ha –1 ) Basal area (m 2 ha –1 ) Basal area (m 2 ha –1 ) Basal area (m 2 ha –1 ) Grass production (t ha –1 ) Grass production (t ha –1 ) Grass production (t ha –1 ) Grass production (t ha –1 ) Grass production (t ha –1 ) Grass production (t ha –1 ) Basal area (m 2 ha –1 ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Unit value of grass production 400 € t –1 Unit value of grass production 200 € t –1 Unit value of grass production 100 € t –1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 1 2 3 4 5 Age (years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Fig. 4. Development of stand basal area and annual grass yield in the optimal management schedule for different silvopastoral systems for different stand densities and unit value of grass production when site index is 29 meters.