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.