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

831 www.me la. i/sil a ennica · ISSN 0037-5330 The Finnish Socie y o Fo es Science · The Finnish Fo es Resea ch Ins i u e SI LV A FE N N I C A Sil a Fennica 43(5) esea ch a icles Op imal Managemen o Pinus adia a Sil opas o al Sys ems Es ablished on Abandoned Ag icul u al Land in Galicia (No h-Wes e n Spain) Ma ía Pasalodos-Ta o, Timo Pukkala, An onio Riguei o-Rod íguez, Es he Fe nández-Núñez and Ma ía Rosa Mosque a-Losada Pasalodos-Ta o, M., Pukkala, T., Riguei o-Rod íguez, A., Fe nández-Núñez, E. & Mosque a-Losada, M.R. 2009. Op imal managemen o Pinus adia a sil opas o al sys ems es ablished on abandoned ag icul u al land in Galicia (no h-wes e n Spain). Sil a Fennica 43(5): 831–845. Timbe p oduc ion has been he main objec i e in o es p oduc ion in Galicia o a long ime. Ne e heless, ac o s such as i e isk and he need o ob ain non- imbe bene i s make o he p oduc ion al e na i es like sil opas o al sys ems wo h o conside a ion. In eg a ion o g azing in he p oduc ion sys em no only di e si ies p oduc s and bene i s, bu also dec eases i e isk by enhancing uel con ol. None heless, ew s udies ha e examined he economic p o i abili y o hese sys ems. This a icle analyses he economics o sil opas o al sys ems es ablished on abandoned ag icul u al soils a o es ed wi h Pinus adia a D. Don. Di e en ee plan ing densi ies, discoun ing a es, g ass alues and i e isk scena ios we e analysed. The echnique employed is based on he combina ion o an op imiza ion algo i hm and a simula o o s and g ow h and g ass yield. The mos p o i able schedules we e ob ained wi h ini ial s and densi ies o 1500 ees pe hec a e. Howe e , wi h high uni alues o pas u e p oduc ion (high alue o g ass), schedules wi h an ini ial s and densi y o 500 ees pe hec a e we e he mos p o i able. When he isk o i e was included in he analyses, sil opas o al sys ems we e always mo e p o i able han imbe p oduc ion sys ems. Wi h an assump ion ha g azing educes i e isk hinnings should be done ea lie and hea ie o educe he expec ed losses due o i e and o p omo e g ass p oduc ion. This leng hens he pas u e pe iod. In gene al, o a ion leng hs o sil opas o al sys ems we e sho e han in imbe p oduc ion. Keywo ds economic p o i abili y, op imiza ion, isk educ ion, sal age, simula ion Add esses Pasalodos: INIA, Ins i u o Nacional de In es igación y Tecnología Ag a ia y Alimen a ia. Mad id, Spain; Riguei o, Fe nández & Mosque a: Uni e si y o San iago de Compos ela, Lugo, Spain; Pukkala: Uni e si y o Eas Finland, Joensuu, Finland E-mail [email p o ec ed] Recei ed 5 Ap il 2009 Re ised 14 Sep embe 2009 Accep ed 13 No embe 2009 A ailable a h p://www.me la. i/sil a ennica/ ull/s 43/s 435831.pd 832 Sil a Fennica 43(5), 2009 esea ch a icles 1 In oduc ion The main use o Galician o es is imbe p o- duc ion. Many o es s a e managed o maximise biomass p oduc ion o pulp and boa d indus ies. S eady income om hese managemen egimes is hampe ed by bo h o es i es (Núñez Reguei a e al. 2003) and low imbe p ices. The e o e, he e is a need o sea ch o al e na i e egimes ha would make income-gene a ion less isky. Sil- opas o al sys ems could be an app op ia e al e - na i e. G azing has some imes been conside ed o p omo e i e damages because i e has been ca elessly employed by shephe ds o p omo e he g ow h o mo e pala able g ass species. Howe e , i p esc ibed i es a e excluded, g azing educes he isk o i e by diminishing he uel loads in he o es (Riguei o-Rod íguez e al. 2005). Ano he ad an age is he mul iplici y o p oduc s ha make sil opas o al sys ems economically sa e unde ma ke unce ain y han he adi ional imbe p oduc ion o ien ed o es y (Ande son and Sinclai 1993, Sha ow 1999). Fu he mo e, sil opas o al sys ems gene a e incomes much ea - lie (Sha ow 1999) han pu e imbe p oduc ion sys ems. Finally, sil opas o al sys ems imp o e accessibili y (Knowles 1991) and scenic alue o he landscapes, enhancing hei ec ea ional use (Rua k e al. 2003, Ala alapa i e al. 2004). Despi e he ad an ages showed by he imple- men a ion o sil opas o al sys ems, no much esea ch has ocused on he op imal design o hese sys ems. One o he e y ew examples is he s udy o Muchi i e al. (2002b), which op i- mized he managemen o an ag o o es y sys em composed o maize and G e illea obus a. This s udy is ocused on sil opas o al sys ems es ablished on abandoned ag icul u al lands. These lands a e e ile (s and dominan heigh s up o 30 me e s a 20 yea s o Pinus adia a D. Don). Acco dingly, his s udy analyses only good si es on which economically iable ag o o es y is possible (Hawke 1991). Pinus adia a has been he mos common ee species employed in sil- opas o al sys ems. The sys em is es ablished by plan ing ees and sowing g ass a he same ime. The e o e, he e is o age p oduc ion al eady in he i s yea sui able o ins ance o sheep g azing (Riguei o-Rod íguez e al. 2002). A s udy ca ied ou a he Depa men o C op P oduc ion a he Uni e si y o San iago de Compos ela (Spain) ound ha sil opas o al sys ems o his ype need an a ea o abou 200–300 hec a es o make hei implemen a ion p o i able. On his scale he man- agemen cos s o he sil opas o al sys em ( e e i- na y cos s, shephe d cos s and o he ela ed cos s) become a o dable. I has been claimed (Adams e al. 2001) ha he es ablishmen o coni e plan a- ions on his ype o e ains may dec ease soil e ili y in he Spanish A lan ic egion due o a pH educ ion. This impo e ishmen o soil e ili y leads o a change in he ype o unde s o ey eg- e a ion, om he baceous ege a ion wi h low uel loads owa ds mo e in lammable sh ub communi- ies (Riguei o-Rod íguez e al. 2005, Mosque a- Losada e al. 2006). The e o e, i seems e en mo e impo an o keep he he baceous s a um a he unde s o ey le el by g azing in o de o educe he isk o i e as long as possible. Fo he op imal managemen o sil opas o al sys ems, he in luence o ees on pas u e p o- duc ion mus be known. The key ac o o he success o he sys em is o achie e a comp omise be ween he wo sou ces o economic bene i . G azing is possible when he ee canopy allows ligh o each he unde s o ey laye . Canopy co e is commonly used o se he limi s o pas u e p oduc ion (Knowles e al. 1998). Li - e a u e sugges s ha canopy co e s highe han 50% d as ically dec ease he pas u e p oduc ion (Riguei o-Rod íguez e al. 1998). O he s ud- ies sugges a maximum canopy co e o 70% (Knowles e al. 1998). Also g een c own leng hs (Pe ci al and Knowles 1983, 1988), ho izon al p ojec ion o he c owns (Sibbald e al. 1994) o s and densi y (Pea son e al. 1995, Bu ne and B aue 2003, Rozados-Lo enzo e al. 2007) a e a iables ha ha e been used o p edic pas u e p oduc ion. Canopy co e is di icul o measu e in he ield and p edic in simula ions. G een c own leng h and ho izon al p ojec ion o he c owns a e also p oblema ic because hey a e no measu ed in no mal in en o ies. S and den- si y (numbe o ees pe hec a e) is no a good p edic o nei he because, by i sel , i does no gi e enough in o ma ion abou compe i ion in he s and. The e o e, we decided o model he dependence o pas u e p oduc ion on s and basal a ea and si e index, which a e easily ob ained 833 Pasalodos-Ta o, Pukkala, Riguei o-Rod íguez, Fe nández-Nùñez and Mosque a-Losada Op imal Managemen o Pinus adia a Sil opas o al… om egula in en o ies. Using his model wi h a g ow h and yield model o ee s and dynam- ics, we we e able o calcula e he p o i abili y o he sys em. The aim was o s udy how he eco- nomic p o i abili y and op imal managemen o sil opas o al sys ems es ablished on abandoned ag icul u al e ains depend on si e quali y, g ass alue and plan ing densi y o ees. The e ec o i e isk on he p o i abili y o he sil opas o al sys ems was also s udied. Mo eo e , we analysed he e ec s o an assump ion ha g azing educes i e isk by diminishing uel loads and p omo ing less in lammable species. The analyses o he s udy a e di ided in o h ee pa s: e ec o (I) s and densi y and g ass p ice, (II) i e isk and (III) he in luence o g azing on i e isk, on he economic p o i abili y and op imal managemen o sil opas o al sys ems. 2 Ma e ial and Me hods 2.1 Simula ion o he T ee S and Dynamics Sil opas o al sys ems ha e h ee componen s, ee s and, o age and li es ock. We used he model o Cas edo-Do ado e al. (2007) o e en-aged P. adia a s ands in Galicia o simula e s and de elopmen in di e en managemen sched- ules. In his model, he ini ial s and condi ions a e de ined by h ee s a e a iables: numbe o ees pe hec a e, s and basal a ea and dominan heigh . The model uses h ee ansi ion unc ions o p ojec each s a e a iable o a gi en ime pe iod. I also includes a unc ion o p edic ing he ini ial s and basal a ea when no in en o y da a a e a ailable. Once he s a e a iables a e known o a speci ic momen , a dis ibu ion unc ion is used o es ima e he numbe o ees in each diame e class by eco e ing he pa ame e s o he Weibull unc ion, using he momen s o he i s and second o de o he dis ibu ion. By using a heigh -diame e unc ion o es ima e he heigh o he a e age ee in each diame e class, and a ape unc ion, he o al and me chan able s and olume a e calcula ed. The model o he dominan heigh de elop- men is as ollows: HH T T 21 2 1 1 1006738 1006738 =−− −−      − exp( .) exp( .) .. ./755 12 44 1 +X (1) wi h, XHL HL L 111 11 2 1 1 21 755 1 755 41244 =++ +−⋅ ((ln.) (ln.).) (2) LT 11 1006738=−−ln(exp( .)) (3) whe e H1 is he dominan heigh (m) a age T1 (yea s), and H2 is dominan heigh a age T2. Reduc ion in he numbe o ees pe hec a e (na u al mo ali y) is p edic ed wi h: NN TT 21 0 3161 100 100 103161 1 053 1 053 21 =+− −−− − (..) ./. (4) whe e N2 is he numbe o ees pe hec a e a age T2 and N1 is he numbe o ees pe hec a e a age T1. The ollowing unc ion was used o basal a ea ini ializa ion: 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) whe e G is s and basal a ea (m2ha–1) a age T (yea s), N is he numbe o ees pe hec a e and SI is he si e index (m), es ima ed using Eq. 1 a a e e ence age o 20 yea s. The unc ion o basal a ea p ojec ion 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) whe e G2 is he s and basal a ea (m2 ha–1) a a gi en p ojec ion age T2, and G1 is s and basal a ea (m2 ha–1) a age T1. The equa ion o p edic - ing he a i hme ic mean diame e , o be used o de i e he diame e dis ibu ion wi h he pa am- e e eco e y app oach, is: 834 Sil a Fennica 43(5), 2009 esea ch a icles dd T NSI g =− −+ +     exp.. .. 0 1449 19 76 1 0 0001345 0 03264     (8) whe e d is he a i hme ic mean diame e (cm) and dg he quad a ic mean diame e (cm), dGN g=×40000 // π (9) The equa ion o p edic ing he heigh o a ep e- sen a i e ee in each 1-cm diame e class is: hH d = + − () − − − 13 13 1 1 0 9339 0 9339 0 9339 0 06614 . .exp . .. . eexp. /. −           0 06614 109339 D (10) whe e h is he o al ee heigh (m), d is diame e a b eas heigh (cm), and D and H a e, espec- i ely, dominan diame e and dominan heigh o he s and. Bo h uni o m and low hinnings can be simu- la ed as in e media e ea men s. Uni o m hin- nings emo e an equal pe cen age o ees om e e y diame e class. When a low hinning is simula ed, he emaining numbe o ees in diame e class i (ni) is calcula ed ollowing he dis ibu ion independen app oach p oposed by Alde (1979): nNLFdFd ii L i L =−    −be o e (()() //1 1 1 (11) whe e Nbe o e is he o al numbe o ees pe hec a e be o e low hinning, L is low- hinning in ensi y exp essed as one minus he p opo - ion o emo ed ees (1–N emo ed/Nbe o e) and F(di) is he cumula i e equency dis ibu ion a diame e di. The ape model p oposed by Fang e al. (2000) i ed o P. adia a by Cas edo e al. (2007) was used o calcula e he s em olume o ees ex ac ed in hinning ope a ions o clea cu ings. The ollowing op diame e s we e used: 35, 18 and 7 cm. The imbe asso men s he e o e co - esponded o he ollowing o e -ba k s em diame- e s: (I) d ≥ 35 cm; (II) 35 cm > d ≥ 18 cm; and (III) 18 cm > d ≥ 7 cm. The ollowing minimum piece leng hs we e assumed in his s udy: (I) 3.0 m; (II) 2.5 m; and (III) 1.0 m. I he piece was sho e , he olume was mo ed o he nex (wi h a smalle minimum op diame e ) imbe asso men . 2.2 Simula ion o G ass P oduc ion Pas u e p oduc ion is highly dependen on he s and de elopmen since pas u e p oduc ion is only possible when he canopy allows ligh o each he unde s o ey le el. Si e and s and cha - ac e is ics we e used as p edic o s o i a model o he pas u e p oduc ion. We used da a om an expe imen in Cas o de Ribe as de Lea (Lugo) ha consis ed o he measu emen o ees and pas u e p oduc ion in a sil opas o al sys em du ing se en yea s since ee plan ing (see Mos- que a-Losada e al. (2006) and Fe nández-Núñez e al. (2007)). The ial has plo s o di e en si e quali y and wo di e en plan ing densi ies (833 and 2500 ees ha–1). The pas u e was a mix u e o Lolium pe enne L., Dac ylis glome a a L., T i- olium epens and T i olium p a ense. The i ed eg ession model is as ollows: ln .. .g assSIG () =− +−125009 012 (12) whe e g ass is he annual g ass p oduc ion (d y mass) ( ha–1), SI is si e index o Pinus adia a s and (m) (dominan heigh a he e e ence age o 20 yea s) and G is he basal a ea (m2 ha–1) o he ee s and. The R2 o he equa ion is 0.425. This equa ion shows ha he highe he basal a ea is, he smalle he g ass p oduc ion becomes (Fig.1). Be e si es p oduce mo e g ass, as expec ed. The pas u e was conside ed o gene a e income only when he g ass yield was highe han 0.3 ha–1. This is he minimum amoun equi ed o eeding one sheep pe hec a e pe yea (da a p o ided 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 a ea (m 2 ha –1 ) G ass p oduc ion ( ha –1 a –1 ) SI 35 SI 30 SI 25 SI 20 FIELD DATA Fig. 1. Dependence o g ass p oduc ion on s and basal a ea o di e en si e indices. 835 Pasalodos-Ta o, Pukkala, Riguei o-Rod íguez, Fe nández-Nùñez and Mosque a-Losada Op imal Managemen o Pinus adia a Sil opas o al… he Depa men o C op P oduc ion o San iago de Compos ela). 2.3 S udy Cases The e ec o s and densi y and uni alue o pas- u e p oduc ion was es ed wi h wo si e indices o adia a pine, namely 29 and 25 me e s a 20 yea s. These si e indices a e ypical o sil o- pas o al sys ems. The s udied plan ing densi ies anged om he spa ses o he denses s ockings used in o es y p ac ise in he egion: 500, 1500 and 2500 ees ha–1. Two si e indices wi h h ee plan ing densi ies esul ed in six di e en ini ial s ands. In e e y s and we es ed di e en numbe o hinnings (0–2) and di e en uni alue o pas- u e p oduc ion. The e enues om pas u e come om he animals ed by he g ass. G ass p oduc- ion was con e ed in o ed li es ock (lamb and sheep) o calcula e he income using da a o he Depa men o C op P oduc ion a he Uni e si y o San iago de Compos ela. The da a indica e ha one on o g ass can eed h ee sheeps. Taking in o accoun ha each sheep deli e s 1.6 lambs pe yea on an a e age, one on o g ass gene a es an annual income o abou 200 € when silage making and all he ela ed cos s such as e e ina y, shep- he d and silage a e conside ed. This is called as he uni alue o pas u e p oduc ion. This alue was a ied o see he e ec o ma ke luc ua ions; he used uni alues o pas u e p oduc ion we e 100, 200 and 400 € –1. Fi e isk was assumed o ha e wo componen s: p obabili y o occu ence and damage. We es ed ou di e en p obabili ies o occu ence: 0, 1, 3 and 5%. When i e akes place we assumed ha i ends he o a ion p ema u ely and only a pa o he g owing s ock olume can be ha es ed (sal aged). The p opo ion o sal aged imbe desc ibes he second componen o isk: damage (sal age a e = 1 – damage a e). The p opo ion o imbe ha can be sal aged depended on he mean ee diame e (Pasalodos-Ta o e al. 2009b) (Fig. 2): s d =−1092. (13) whe e d is he diame e a b eas heigh measu ed in cm. In addi ion o loosing a pa o imbe in i e, he sal aged imbe was dep ecia ed by 25% (A enas and Izquie do 2007). This p ice educ ion o sal aged imbe was used in all op imisa ions. The op imiza ions we e done o one si e index (29 me e s) and wo di e en s and densi ies (500 and 1500 ees ha–1). G azing may educe i e isk by educing uel loads and p omo ing less in lammable species (Riguei o-Rod íguez e al. 2005, Riguei o- Rod íguez e al. 2009). E en hough he li e a u e has men ioned his e ec widely (Blackmo e and Vi ousek 2000, Elmo e and Asne 2003, Casal e al. 2009) i is di icul o ind quan i a i e in o ma- ion on i . The e o e, we used se e al educ ion ac o s, namely 25, 50, 75 and 100% o educe he p obabili y o i e occu ence in e e y g az- ing yea (g ass yield ≥ 0.3 ha–1). Two di e en s and densi ies (500 and 1500 ees ha–1), one si e index (29 me e s) and wo di e en p obabili ies o i e occu ence (1 and 5%) we e employed o analyse he e ec o he educ ion in i e isk due o g azing. 2.4 Objec i e Func ion Soil expec a ion alue (SEV) calcula ed wi h 3% discoun ing a e was used as he objec i e a i- able. The SEV was calcula ed as he ne p esen alue (NPV) o all u u e ne incomes: SEV NPV R = −+ 11 1() (14) 0 20 40 60 80 100 0 10 20 30 40 50 60 70 Diame e a b eas heigh (cm) Sal age p opo ion (%) Fig. 2. Dependence o he sal age p opo ion o he b eas heigh diame e . 836 Sil a Fennica 43(5), 2009 esea ch a icles whe e NPV is he ne p esen alue o one o a- ion, is he discoun ing a e and R is he o a ion leng h (yea s). The exp ession o he NPV is: NPV IICC Rwgwg =+−− + () = ∑ 01 (15) Whe e Iw and Ig a e he incomes and Cw and Cg a e he cos s de i ed om imbe and pas u e p oduc ion in yea , espec i ely (see Tables 1 and 2). The incomes om imbe p oduc ion (Iw ) we e calcula ed om: Isn P w jkj k k j J =⋅      == ∑∑ 1 3 1 (16) whe e s is he p opo ion o sal age calcula ed om Eq. 13 (s = 1 i he e is no i e), J is he numbe o diame e classes, nj is he numbe o ees in diame e class j, Pk is he uni p ice o imbe asso men k and kj is he olume o asso men k o a ee in diame e class j. The ollowing oad side imbe p ices we e used: 90 € m–3 o g ade I, 50 € m–3 o g ade II and 18 € m–3 o g ade III (see Pasalodos-Ta o e al. 2009a, b). The uni p ice was educed by 25% when i e ended he o a ion. The cos s o he sil opas o al sys em (bo h Cw and Cg ) depended on si e index (Table 1). Timbe p oduc ion cos s we e di e en when he e was no g azing (Table 2). Regene a ion cos (Tables 1 and 2) was assumed o be a linea unc ion o he numbe o plan ed ees pe hec a e wi h he cons an pa ep esen ing he cos o si e p epa a- ion and he a iable pa ep esen ing he plan ing cos pe ee. In sil opas o al sys ems he egen- e a ion cos is highe because o an addi ional cos o indi idual ee p o ec o s o a oid he damages ha sheeps can cause on he seedlings. The ee ha es ing cos was calcula ed om (based on Amb osio e al. 2000): HCos ECos VFCos S =+ ⋅+ ⋅+78 33 167 0 30477 0 972 (.)/ .. ν              (17) whe e HCos is ha es ing cos (€ ha–1), ECos is en y cos (€ ha–1), V is he o al ha es ed olume (m3 ha–1), FCos is o wa ding cos (€ m–3), S is slope (%), and ν is he mean olume o ha es ed ees (m3). I was assumed ha he en y cos o mo ing he machine y o he o es (ECos ) is 200 € ha–1. The o wa ding cos was assumed o be 5 € m–3 and he slope was aken as 20%. 2.5 In eg a ing Fi e Risk in o Objec i e Func ion In o de o include i e isk in he calcula ion o SEV we used he app oach de eloped by B igh and P ice (2000). The me hod consis s o he sum o all possible ou comes, weigh ed by hei p ob- abili ies. The exp ession o he expec ed SEV was (see Pasalodos-Ta o e al. 2009a, b): Table 1. Yea s and cos s o ending ope a ions o sil- opas o al sys ems. N is he numbe o plan ed ees pe hec a e. Yea Ope a ion Cos (€/ha) SI = 25 m 0 T ee plan ing+p o ec o s 500+2.2 N 0 G ass sowing 100 6 T ee p uning 200 12 T ee p uning 200 SI = 29 m 0 T ee plan ing+p o ec o s 500+2.2 N 0 G ass sowing 100 5 T ee p uning 200 10 T ee p uning 200 Table 2. Yea s and cos s o ending ope a ions o a imbe -p oduc ion schedule. N is he numbe o plan ed ees pe hec a e. Yea Ope a ion Cos (€/ha) SI = 25 m 0 T ee plan ing 500+1 N 2 Cleaning 150 4 Cleaning 150 6 T ee p uning 200 12 T ee p uning 200 SI = 29 m 0 T ee plan ing 500+1 N 2 Cleaning 150 4 Cleaning 150 5 T ee p uning 200 10 T ee p uning 200 837 Pasalodos-Ta o, Pukkala, Riguei o-Rod íguez, Fe nández-Nùñez and Mosque a-Losada Op imal Managemen o Pinus adia a Sil opas o al… SEV NPV p p i s R R R = −+     ++ ()    = − ∑ 111 0 1 ()              (18) whe e p is he p obabili y ha he s and bu ns in yea and su i es he p e ious yea s, i.e., p = (1 – p i e) p i e, whe e p i e is he annual p ob- abili y o i e occu ence, and pR pR = (1 – p i e)R is he p obabili y ha he e is no i e be o e he o a ion age. NPV i s is calcula ed om: NPVpNPVpNPV i s R R R =⋅+⋅ = − ∑ 0 1 (19) whe e NPV is he ne p esen alue i i e hi s he s and a age and ends he o a ion p ema u ely, and NPVR is he ne p esen alue i he e is no i e du ing he o a ion (R). A hinning in ensi y highe han 30% was assumed o make he s and sensi i e o wind h ow and snow b eakage (Cas edo-Do ado e al. 2009). The e o e, a penal y unc ion was added o he SEV o he managemen schedule as a means o a oid oo hea y hinnings. The objec i e unc ion (OF) which was maximized in op imiza ion was he e o e OF SEVPenal ym m M =− = ∑1 (20) wi h Penal y H HH m m m m = ≤ − −>     030 10000 30 100 30 30 i i % %%  (21) whe e H%m is hinning in ensi y in pe cen o emo ed s and basal a ea in hinning m and M is he numbe o hinnings. The penal y unc ion implies ha he penal y o ha es ing oo much a a ime inc eases om 0 o 10 000 € ha–1 when he hinning pe cen age inc eases om 30 o 100. 2.6 Decision Va iables Decision a iables such as he numbe and in en- si y o hinnings, and o a ion leng h de ine he managemen schedule. Op imizing a managemen schedule is equal o inding op imal alues o decision a iables. Due o he ac ha he numbe o hinnings is no a con inuous a iable schedules ha ha e a di e en numbe o hinnings mus be ea ed as di e en op imiza ion p oblems. In his s udy managemen schedules we e op imized wi h 0, 1 and 2 hinnings, which a e all easible op ions o Pinus adia a sil opas o al sys em. The simula ed hinnings we e combina ions o uni o m and low hinning. The e o e he manage- men egime was de ined by he numbe o hin- nings and he ollowing decision a iables: Fo hinnings: – S and age a he i s hinning and numbe o yea s be ween he i s and he second hinning. – Pe cen age o uni o m hinning (% o numbe o ees) – Pe cen age o low hinning (% o ees emo ed a e uni o m hinning) Fo inal elling – Numbe o yea s since he las hinning The numbe o op imized decision a iables was he e o e 3 × M + 1 whe e M is he numbe o hinnings. 2.7 Op imisa ion Me hod The op imisa ion algo i hm used was he di ec sea ch me hod o Hooke and Jee es (1961). This me hod uses a o m o coo dina e op imiza ion and does no equi e explici e alua ion o any pa ial de i a i e o he objec i e unc ion. The di ec sea ch me hod compa es each new ial solu ion wi h he bes ob ained up o ha ime. The sea ch has wo componen s, he explo a o y sea ch and he pa e n sea ch. Fo a gi en base poin , he explo a o y sea ch examines poin s a ound ha base poin in he di ec ion o he coo dina e axes (decision a iables). The pa - e n sea ch mo es he base poin in he di ec ion de ined by he gi en (cu en ) base poin and he bes poin ound in explo a o y sea ch. 838 Sil a Fennica 43(5), 2009 esea ch a icles 3 Resul s 3.1 P o i abili y o Sil opas o al Sys ems A e unning he op imisa ion o he six di e - en ini ial s ands (2 si e indices wi h 3 plan ing densi ies) wi h h ee di e en hinning schedules (0, 1 and 2 hinnings), we chose ha numbe o hinnings ha ga e he maximum SEV. The op imal schedules had one hinning wi h ini ial densi y 500 ees ha–1 and wo hinnings wi h he o he plan ing densi ies wi h bo h si e indices (25 and 29 m). Sil opas o al sys em was always mo e p o i able han me e imbe p oduc ion, plan ing densi y 1500 ees ha–1 being he mos p o i able (Fig. 3). SI 25 m SI 29 m e enues om g ass e enues om imbe 500 ees ha –1 0 10000 20000 30000 40000 50000 60000 no g ass 100 200 400 Uni alue o pas u e p oduc ion (€ –1 ) Uni alue o pas u e p oduc ion (€ –1 ) Uni alue o pas u e p oduc ion (€ –1 ) Uni alue o pas u e p oduc ion (€ –1 ) Uni alue o pas u e p oduc ion (€ –1 ) Uni alue o pas u e p oduc ion (€ –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 g ass 100 200 400 1500 ees ha –1 0 10000 20000 30000 40000 50000 60000 no g ass 100 200 400 0 10000 20000 30000 40000 50000 60000 no g ass 100 200 400 2500 ees ha –1 0 10000 20000 30000 40000 50000 60000 no g ass 100 200 400 0 10000 20000 30000 40000 50000 60000 no g ass 100 200 400 Fig. 3. Soil expec a ion alue o he op imal sil opas o al schedules o di e en ini ial s and densi ies when di e en g ass p ices a e conside ed. 839 Pasalodos-Ta o, Pukkala, Riguei o-Rod íguez, Fe nández-Nùñez and Mosque a-Losada Op imal Managemen o Pinus adia a Sil opas o al… The es ablishmen o pas u e imp o ed p o i a- bili y mos wi h he lowes densi y, 500 ees ha–1. The imp o emen was up o 50% wi h a uni alue o pas u e p oduc ion o 200 € –1. SEV imp o ed 15% wi h plan ing densi y 1500 ees pe hec a e and 4–7 % wi h 2500 ees pe hec a e. The op imal o a ion leng hs wi hou pas u e we e 40 and 42 yea s, espec i ely, o plan ing densi ies 500 and 1500 ees pe hec a e in si e index 25 m, and 38 yea s o bo h densi ies in si e index 29 m. In gene al, o a ion leng hs dec eased wi h he inclusion o pas u e. This dec ease was mo e no iceable wi h lowe plan ing densi ies (Fig. 4). 500 ees ha –1 1500 ees ha –1 Basal a ea G ass p oduc ion 0 10 20 30 40 50 60 70 80 0 10 20 30 40 Age (yea s) Basal a ea (m 2 ha –1 ) Basal a ea (m 2 ha –1 ) Basal a ea (m 2 ha –1 ) Basal a ea (m 2 ha –1 ) Basal a ea (m 2 ha –1 ) G ass p oduc ion ( ha –1 ) G ass p oduc ion ( ha –1 ) G ass p oduc ion ( ha –1 ) G ass p oduc ion ( ha –1 ) G ass p oduc ion ( ha –1 ) G ass p oduc ion ( ha –1 ) Basal a ea (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 (yea s) 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 (yea s) 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 (yea s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Uni alue o g ass p oduc ion 400 € –1 Uni alue o g ass p oduc ion 200 € –1 Uni alue o g ass p oduc ion 100 € –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 (yea s) 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 (yea s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Fig. 4. De elopmen o s and basal a ea and annual g ass yield in he op imal managemen schedule o di e en sil opas o al sys ems o di e en s and densi ies and uni alue o g ass p oduc ion when si e index is 29 me e s.