Resource communication. Individual tree growth model for radiata pine plantations in northwestern Spain

Ins i u o Nacional de In es igación y Tecnología Ag a ia y Alimen a ia (INIA) A ailable online a www.inia.es/ o es sys ems h p://dx.doi.o g/10.5424/ s/2012213-03109 Fo es Sys ems 2012 21(3), 538-542 ISSN: 2171-5068 eISSN: 2171-9845 Resou ce communica ion. Indi idual- ee g ow h model o adia a pine plan a ions in no hwes e n Spain F. C ecen e-Campo1, *, U. Dieguez-A anda1 and R. Rod iguez-Soallei o2 1 Depa amen o de Ingenie ía Ag o o es al, Uni e sidad de San iago de Compos ela. Escuela Poli écnica Supe io , Benigno Ledo s/n, Campus uni e si a io, 27002 Lugo, Spain 2 Depa amen o de P oducción Vege al, Uni e sidad de San iago de Compos ela. Escuela Poli écnica Supe io , Benigno Ledo s/n, Campus uni e si a io, 27002 Lugo, Spain Abs ac Indi idual- ee basal a ea and heigh inc emen models we e de eloped wi h da a om 130 pe manen plo s o Pinus adia a D. Don loca ed in Galicia (no hwes e n Spain). Mixed-models echniques we e used o model i ing. Co a ia es ac ing a ee and s and le el we e included as ixed e ec s. Es ima ed alues o s and a iables ob ained om agg ega- ion o indi idual- ee p edic ions we e used in model e alua ion. The de eloped models accoun ed o 54% o he a iabili y in basal a ea inc emen and 36% o he a iabili y in heigh inc emen , wi h mean e o s o 16 cm2 and 0.36 m, espec i ely. These models, along wi h an exis ing indi idual- ee mo ali y model, cons i u e a whole indi idual- ee g ow h model ha can be used o simula e o es managemen al e na i es, helping in o es manage s’ decision making. Key wo ds: mixed-e ec s modeling; Pinus adia a; Galicia. Resumen Comunicación de ecu so. Modelo de c ecimien o de á bol indi idual pa a plan aciones de pino adia a en el no oes e de España En es e es udio se han desa ollado modelos de inc emen o en sección no mal y al u a de á bol indi idual, u ilizan- do da os de 130 pa celas de Pinus adia a D. Don localizadas en Galicia. La écnica de modelos mix os se u ilizó en el ajus e de los modelos. Se incluye on co a iables que ac úan a ni el de á bol y a ni el de odal como e ec os ijos en los modelos. En la e aluación de los modelos se u iliza on es imaciones de a iables de odal ob enidas po ag egación de las p edicciones de á bol indi idual. Los modelos desa ollados explica on el 54% de la a iabilidad en el inc e- men o en sección no mal y el 36% de la a iabilidad en el inc emen o en al u a, con e o es medios de 16 cm2 y 0.36 m, espec i amen e. Es os modelos, jun o al modelo de mo alidad de á bol indi idual exis en e, o man un mo- delo de c ecimien o de á bol indi idual que puede u iliza se pa a simula al e na i as de ges ión o es al, ayudando a la oma de decisiones de los ges o es o es ales. Palab as cla e: modelo de e ec os mix os, Pinus adia a D. Don; Galicia. * Co esponding au ho : [email p o ec ed] Recei ed: 06-05-12. Accep ed: 01-08-12. In oduc ion Radia a pine (Pinus adia a D. Don) is he mos commonly used exo ic coni e in e o es a ions in Spain, especially in no he n Spain, whe e i co e s app oxima ely 270,000 ha (DGCN, 1998). In Galicia (no hwes e n Spain) i is es ima ed o co e 90,000 ha (Xun a de Galicia, 2001). Rela ed s udies mainly e e o s and g ow h and yield and o ecological and sil i- cul u al aspec s. Yield ables (Sánchez e al., 2003) and a dynamic s and g ow h model (Cas edo-Do ado e al., 2007) ha e been de eloped o Galicia. Indi idual- ee g ow h models p o ide mo e de ailed in o ma ion han o he modeling app oaches (Gadow and Hui, 1999; Ga cía, 2003) and usually pe o m be - e han s and g ow h models o sho e m p ojec ions (Bu kha , 2003). The objec i e o he p esen s udy was o de elop dis ance-independen indi idual- ee basal a ea and heigh inc emen models o e en-aged adia a pine 539 Indi idual- ee g ow h model o adia a pine plan a ions in no hwes e n Spain means o isual analysis o s uden ized esiduals. I necessa y, weigh ed eg ession was used. The weak au oco ela ion in he emeasu ed da a was igno ed because he impac o a iance unde es ima ion is likely o be masked by i ing each indi idual ee as an independen obse a ion (Temesgen and Gadow, 2004). Model compa ison Th ee s a is ical c i e ia we e used o model com- pa ison: oo mean squa e e o (RMSE), he model e iciency (EF), simila o he coe icien o de e mina- ion o linea eg ession, and Akaike’s in o ma ion c i e ion (AIC, Akaike, 1974).Plo s o obse ed agains p edic ed inc emen s and plo s o esiduals agains p edic ed inc emen s we e also used o model com- pa ison and selec ion. Valida ion was no ca ied ou because an independ- en da ase was no a ailable, and o he alida ion me hods seldom p o ide any addi ional in o ma ion compa ed wi h he i ing s a is ics (Kozak and Kozak 2003). Anyway, he de eloped equa ions whe e used oge he wi h he indi idual- ee mo ali y equa ion o he species in he egion (C ecen e-Campo e al., 2009) o make simula ions using he i ing da a. As he ac- cu acy o he sys em (i.e., he indi idual- ee g ow h model) is mo e impo an han he accu acy o he in- di idual equa ions, eal alues o s ems pe hec a e (N) and s and basal a ea (G, m2ha–1), and he diame e and heigh dis ibu ions in he second and h ee in en o ies we e compa ed wi h he p edic ed alues. The Kol- mogo o -Smi no es was used o compa e eal and p edic ed diame e dis ibu ions. Di e en cu -o al- ues we e es ed o con e mo ali y es ima ions o li e/ dead ees (C ecen e-Campo e al., 2009). Resul s and discussion The models ha pe o med bes we e: ig d G BALMOD BAR= + + α α α α α α 0 3 4 5 1 2 exp ( ) [1] ih h d SI RBA D = + − α α α α α α 0 4 5 1 2 3 exp( ) [2] whe e ig is he annual basal a ea inc emen (cm2), BALMOD is he compe i ion index de eloped by Sch öde and Gadow (1999), BAR is a basal a ea a io (100 · g/G, whe e g is he basal a ea o he ee –m2), ih is he annual heigh inc emen (m), SI is he si e plan a ions in Galicia (no hwes e n Spain) o be com- bined wi h an exis ing mo ali y model and o m a whole indi idual- ee g ow h model. Me hodology Da a 130 plo s loca ed in Galicia, ep esen ing he exis ing ange o ages, s and densi ies and si es, we e used (s and basal a ea –G– anging om 6.6 o 70.6 m2ha–1, s ems pe hec a e –N– anging om 192 o 3,936, dominan heigh –H– anging om 6.8 o 35.2 m, and age – – ang- ing om 8 o 47 yea s). Diame e a b eas heigh (d, cm, 1.3 m abo e g ound) was measu ed in all he ees in each plo and o al ee heigh (h, m) was measu ed in 30 andomly selec ed ees and in he dominan ees ( he p opo ion o he 100 hickes ees pe ha). 79 plo s we e measu ed in wo occasions (1996 and 1999) and 51 plo s we e measu ed in h ee occasions (1996, 1999 and 2005). As he e-measu emen in e al was a iable (wi h ei he 3 o 6 yea s be ween successi e in en o ies), he me hod o calcula ing he a e age annual g ow h was used o calcula e he independen a iables (annual basal a ea and heigh inc emen s). Models Zeide (1993) showed ha many g ow h equa ions can be decomposed in o wo componen s when hey a e conside in he di e en ial o m, leading o simple basic models. These basic models we e p oposed o i ing o he da abase. The inclusion o s and and ee a iables and com- pe i ion indices in hese basic o ms was es ed using linea ans o ma ions and OLS echniques. Those al- e na i es wi h a a iance in la ion ac o la ge han 10 we e ejec ed (Mye s, 1990). Because o he speci ic co ela ion s uc u e o he expe imen al da a ( ees g ouped in plo s), he basic as- sump ion abou non-co ela ed esiduals did no hold. To compensa e o his, a nonlinea mixed model —including bo h ixed and andom componen s— was applied. The i s -o de me hod o Beal and Sheine (1982), a ailable in he NLMIXED p ocedu e o SAS/STAT® (SAS Ins i u e Inc. 2009) was used o model i ing. Di e en combina ions o model pa ame e s we e es ed o be mixed. He e ocedas ici y was analyzed by F. C ecen e-Campo e al. / Fo es Sys ems (2012) 21(3), 538-542 540 index (Diéguez-A anda e al., 2005), RBA – D is a basal a ea a io, aised o he powe o a diame e a io ([g/G]d/Dg, whe e Dg is quad a ic mean diame e –cm) and αi a e ixed pa ame e s, common o he popula ion. The esul s o he bes mixed-e ec s models a e shown in Table 1. All pa ame e s we e signi ican a he 0.01 le el. The plo s o esiduals agains p edic ed alues showed homogeneous a iance pa e ns. An a emp was made o ela e he andom pa ame e s o s and a iables bu no signi ican ela ionships we e ound. Wyko (1990) and Monse ud and S e ba (1996) ound ha mos o he a iance explained in basal a ea inc emen was due o size ac o s (diame e , c own a io), and hen compe i ion a iables, p ima ily basal a ea in la ge ees (BAL). The o al a iance explained was be ween 20% and 63%, om which only 2-6% was explained by si e ac o s. The same was ound in his s udy. The heigh inc emen model showed poo e esul s. Simila ly, Hasenaue and Monse ud (1997) could only explain 14% o he obse ed a ia ion. Tanaka (1988) explained so li le a ia ion in heigh inc emen (R2 < 0.01) ha a pu ely s ochas ic heigh inc emen model was de- eloped ins ead. O he s udies de eloped non-linea heigh -diame e models o ob ain heigh es ima ions (e.g., Mab u i a and Miina, 2002; Palahí e al., 2003), ins ead o de eloping a heigh inc emen model. O he au ho s (e.g., No d-La sen, 2006; Bu kha e al., 2003) ob ained simila esul s han in his s udy, explaining 37% and 46% o he obse ed a ia ion, espec i ely. The abili y o he models de eloped he e o handle hin- ning e ec s is associa ed wi h he a ia ion in s and a i- ables and compe i ion indices ha he emo al o some ees causes. Pas esea ch has shown ha a ue hinning e ec was a ely signi ican (e.g., Pukkala, 1989), and was hen only a mino e ec (Monse ud and S e ba, 1996). The ixed pa s o Eqs. (1) and (2) a e p oposed o indi idual- ee basal a ea and heigh annual inc e- men es ima ions o adia a pine s ands in Galicia, wi h he pa ame e es ima es shown in Table 1. These models plus he exis ing indi idual- ee mo ali y model (C ecen e-Campo e al., 2009) con o m a whole indi idual- ee g ow h model ha can be used o o ecas o es managemen al e na i es, gi ing accu a e esul s (Table 2) o he en i e o a ion age Table 1. Pa ame e es ima es and goodness-o - i s a is ics o he indi idual- ee basal a ea and heigh inc emen models Model Fixed e ec s Va iance componen s RMSE EF Pa m. Es ima e S d. E . Pa m. Es ima e S d. E . Basal a ea α00.2822 0.0288 σ2210.0 2.9 14.82 (16.21*) 0.6196 (0.5448*) α12.845 0.064 σ2 b00.01470 0.00121 α2–0.8608 0.0546 σ2 b40.006326 0.001178 α3–0.05018 0.00257 σ2 b51.676 0.242 α4–0.04286 0.01142 σ2 b0b4–0.004530 0.000950 α5–1.471 0.0170 σ2 b0b5–0.1444 0.0119 σ2 b4b50.03648 0.01112 Heigh α00.05284 0.01268 σ20.1011 0.0021 0.3123 (0.3575*) 0.5157 (0.3647*) α1–0.5727 0.07344 σ2 b10.2644 0.0041 α20.5482 0.05977 σ2 b20.2198 0.0032 α31.080 0.087 σ2 b1b2–0.2375 0.0017 α4–0.03272 0.00353 α5–50.01 5.46 bi: andom pa ame e ela ed wi h he ixed αi pa ame e ; σ2: e o a iance o he model; σ2 bi: a iance associa ed wi h he andom pa- ame e bi; σbibj: co a iance be ween andom pa ame e s bi and bj. *These s a is ics we e calcula ed wi h only he ix pa o he models. Table 2. S a is ics ob ained wi h he indi idual- ee g ow h model o s and basal a ea (G) and ees pe hec a e (N) p o- jec ion using se e al cu -o alues cu -o n RMSE G RMSE N 0.80 9 2.413 98.21 0.81 9 2.399 95.56 0.82 12 2.387 92.77 0.83 17 2.363 88.62 0.84 17 2.341 85.56 0.85 25 2.337 84.77 0.86 27 2.315 82.07 0.87 33 2.308 82.06 0.88 35 2.313 84.29 0.89 39 2.316 89.15 0.90 43 2.331 97.34 n: numbe o plo s (ou o 130) ha ailed o pass he Kol- mogo o -Smi no es . 541 Indi idual- ee g ow h model o adia a pine plan a ions in no hwes e n Spain o he species in he egion, i.e., 25-45 yea s depend- ing on si e quali y. F om applica ion, a ixed cu -o alue o 0.84 gi es a good comp omise be ween G and N es ima ions and he numbe o plo s ha passed he Kolmogo o -Smi no es (Table 2). Resul s o 50 yea s o p ojec ion using a cu -o o 0.84 a e shown (Fig. 1) in o de o show he biological ealism o he model. 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