Fo es s 2010, 1, 177-193; doi:10.3390/ 1030177
o es s
ISSN 1999-4907
www.mdpi.com/jou nal/ o es s
A icle
Unce ain y in Fo es Ne P esen Value Es ima ions
Ma kus Holopainen 1,*, An i Mäkinen 1, Jussi Rasinmäki 2, Ka i Hyy iäinen 3, Saeed Bayazidi 1,
Mikko Vas a an a 1 and Ilona Pie ilä 1
1 Depa men o Fo es Sciences, Uni e si y o Helsinki, La oka anonkaa i 7, 00014 Finland;
E-Mails: [email p o ec ed] (A.M.); [email p o ec ed] (S.B.);
[email p o ec ed] (M.V.); [email p o ec ed] (I.P.)
2 Simosol Oy, Asema-aukio 2, 11130 Riihimäki, Finland; E-Mail: jussi. asinm[email p o ec ed] (J.R.)
3 MTT, Economic Resea ch, La oka anonkaa i 9, 00790 Helsinki, Finland;
E-Mail: ka i.hyy iainen@m . i (K.H.)
* Au ho o whom co espondence; E-Mail: ma kus.holopain[email p o ec ed];
Tel.: +358-50-380 4984; Fax: +358-9-191 58100.
Recei ed: 9 Augus 2010; in e ised o m: 31 Augus 2010 / Accep ed: 10 Sep embe 2010/
Published: 27 Sep embe 2010
Abs ac : Unce ain y ela ed o in en o y da a, g ow h models and imbe p ice
luc ua ion was in es iga ed in he assessmen o o es p ope y ne p esen alue (NPV).
The deg ee o unce ain y associa ed wi h in en o y da a was ob ained om p e ious
a ea-based ai bo ne lase scanning (ALS) in en o y s udies. The s udy was pe o med,
applying he Mon e Ca lo simula ion, using s and-le el g ow h and yield p ojec ion models
and h ee al e na i e a es o in e es (3, 4 and 5%). Timbe p ice luc ua ion was po ayed
wi h geome ic mean- e e ing (GMR) p ice models. The analysis was conduc ed o ou
al e na i e o es p ope ies ha ing a ying compa men s uc u es: (A) a p ope y ha ing
an e en de elopmen class dis ibu ion, (B) sapling s ands, (C) young hinning s ands, and
(D) ma u e s ands. Simula ions esul ed in p edic ed yield alue (p edic ed NPV)
dis ibu ions a bo h s and and p ope y le els. Ou esul s showed ha ALS in en o y
e o s we e he mos p ominen sou ce o unce ain y, leading o a 5.1–7.5% ela i e
de ia ion o p ope y-le el NPV when an in e es a e o 3% was applied. In e es ingly,
ALS in en o y led o signi ican biases a he p ope y le el, anging om 8.9% o 14.1%
(3% in e es a e). ALS in en o y-based bias was he mos signi ican in ma u e s and
p ope ies. E o s ela ed o he g ow h p edic ions led o a ela i e s anda d de ia ion in
NPV, a ying om 1.5% o 4.1%. G ow h model- ela ed unce ain y was mos signi ican
OPEN ACCESS
Fo es s 2010, 1
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in sapling s and p ope ies. Timbe p ice luc ua ion caused he ela i e s anda d de ia ions
anged om 3.4% o 6.4% (3% in e es a e). The combined ela i e a ia ion caused by
in en o y e o s, g ow h model e o s and imbe p ice luc ua ion a ied, depending on he
p ope y ype and applied a es o in e es , om 6.4% o 12.6%. By applying he
me hodology desc ibed he e, one may ake in o accoun he e ec s o a ious unce ain y
ac o s in he p edic ion o o es yield alue and o supply he ou pu esul s wi h le els
o con idence.
Keywo ds: o es p ope y alua ion; ne p esen alue; unce ain y; o es managemen
planning; simula ion; g ow h and yield p edic ion; ai bo ne lase scanning; o es in en o y
1. In oduc ion
Es ima es o he economical alue o o es p ope y a e needed o many pu poses, e.g., in he eal
es a e business, land di isions and exchanges and o conside ing o es y in es men . In addi ion, he
In e na ional Financial Repo ing S anda ds (IFRS) equi e ha o es en e p ises p esen
sys ema ically compu ed es ima es o he alue o hei o es ed land annually.
One me hod o de i ing he economic alue o a o es s and o p ope y is o calcula e he
di e ence be ween he p esen alues (ne p esen alue, NPV) o all u u e expec ed e enues and
expenses. This app oach is e e ed o as he o es y yield alue me hod [1] and i is based on he
undamen al ideas o o es economics [2]. The es ima ion o u u e chains o o es s and managemen
and he low o e enues and expenses a e mos commonly pe o med on he basis o he ha es and
sil icul u e ecommenda ions p esen ed in he espec i e o es managemen plan. Re enues and
expenses a e es ima ed, based on he wood p oduc ion p edic ions ha a e commonly de e mined by
simula ion and op imiza ion compu a ions ca ied ou by speci ic o es -planning so wa e sys ems.
Decisi e issues ega ding he de e mina ion o o es y yield alue include de e mina ion o he
op imal o a ion leng h, he iming and in ensi y o ha es s, imbe s umpage p ices, sil icul u al cos s
and he applied in e es a e. The NPV o o es ed land is subjec o a ious unce ain ies. The sou ces
o unce ain y include g ow h and yield models used in he simula o s, de elopmen o imbe p ices,
he a e o in e es used and unce ain ies in he inpu da a.
Acquisi ion o o es -planning da a is cu en ly in a phase o adical change. In Finland, ope a i e
o es planning is e ol ing in o a me hodology by which s ock cha ac e is ics a e es ima ed by means
o ee-wise measu ed sample plo s and a ea-based s a is ical ea u es o ai bo ne lase scanning (ALS)
da a and digi al ae ial pho og aphs. Es ima ion o o es cha ac e is ics will be pe o med, using he
nonpa ame ic k-nea es neighbo (k-NN) o k-mos simila neighbo (k-MSN) me hod [3]. Wi h
espec o he es ima ion o s and mean cha ac e is ics (e.g., [4-7]) and ee species- o imbe
asso men -speci ic cha ac e is ics [8-11], i has become possible o achie e a leas he same le el o
accu acy using low-pulse ALS da a as ha ound in adi ional s andwise o es in en o y (SWFI).
O e iews on he use o ALS in o es in en o y can be ound in [12-15].
Cu en ly, a c ucial ques ion ha emains is how o in eg a e his new in en o y da a in o
o es -planning compu a ions. I is hen essen ial o be awa e o how in en o y da a ob ained a a ious
Fo es s 2010, 1
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accu acies a ec he simula ion end esul s, which ha e a signi ican in luence on he o es owne ’s
economic e u n. Thus, a s a ing poin o he s udy was he s a e o change cu en ly p esen in
ope a i e o es planning, in which adi ional compa men in en o ies a e being eplaced by
ALS-based in en o ies.
Reliable in en o y da a a e essen ial o o es y yield alue simula ions. In assessing he s a e o a
s and, he es ima es may di e signi ican ly om he eal si ua ion, due o he in en o y me hod used.
This aspec can be s udied using cos -plus-loss analyses, in which he expec ed losses due o
subop imal decisions a e added o he o al o es in en o y cos s ([16,17]). The cos -plus-loss
app oach was widely u ilized in ecen o es in en o y- and planning- ela ed esea ch (e.g., [18-24]).
The g ow h o ees o imbe s ock is a highly signi ican ac o a ec ing o es y yield alue. F om
he s andpoin o o es p ope y alua ion, he a e o g ow h is a decisi e ac o wi h espec o
o a ion leng h and he e o e in luences yield alue compu a ions o a g ea ex en . Since ee g ow h is
di icul o measu e di ec ly, i mus be es ima ed by models based on o he measu able ee
cha ac e is ics. G ow h models can be di ided in o ee- and s and-le el models (e.g., [25]).
Fo es g ow h simula o s a e applied o upda ing measu ed o es esou ce da a and o p edic ing
u u e g ow h o assess sil icul u al measu es and ime o ha es s. G ow h simula o s inco po a e
nume ous models o p edic ing a ious o es cha ac e is ics and hei de elopmen . These models can
ne e comple ely po ay he unde lying phenomena and hei ou pu es ima es he e o e include a
deg ee o unce ain y. The deg ee o unce ain y is dependen on he unc ioning o indi idual models
and he in e ac ion be ween hem. Models applied o simula ing o es g ow h o m a complex en i y
ha o en complica es he analysis o indi idual model unce ain y ([25,26]).
Unce ain y ela ed o o es g ow h modeling has been s udied, e.g., by Ge ne and Dzialowy [27],
Mow e [28] and Kangas ([26,29]). These s udies ha e mainly ocused on he in luence o a ious
unce ain y componen s in g ow h model unc ioning. Howe e , Mäkinen e al. [25] and Mäkinen [30]
showed ha ins ead o analyzing indi idual models, he model chains implemen ed by he simula o s
should be sc u inized as a whole.
The de elopmen o imbe asso men p ices is one o he mos signi ican ac o s in o es p ope y
alua ion compu a ions. A majo pa o a s and’s yield alue is gene a ed a he inal ha es , in which
case he iming o he inal ha es and he p ices o he mos aluable imbe asso men s (saw-wood
and in e media e logs) a ha ime a e especially impo an . Saw-wood log ou u n is, in u n,
in luenced by he (company-speci ic) bucking ules and quali y c i e ia in e ec a ha ime. Timbe
p ices a he s and le el a e u he in luenced by ha es condi ions, size o he logging si e and
nea -hauling dis ance.
When es ima ing he alue o a o es p ope y, he mos common way o inco po a e imbe p ices
is o apply mean p ices based on he ealized p ices o he pas [31]. The basic assump ion hen is ha
u u e p ice de elopmen is in acco dance wi h pas de elopmen . A mo e ad anced, and also
complica ed, app oach is o y o p edic u u e imbe p ice de elopmen based on ealized pas p ice
de elopmen , by which long- e m ends can be depic ed and ac o s causing p ice peaks iden i ied.
Such p edic ions can be ca ied ou e.g., by using geome ic mean- e e ing (GMR, [32-34]) o
geome ic B ownian mo ion (GBM, [35-37]) p ice p ocesses.
This s udy builds on a pape by Holopainen e al. [38]. They s udied unce ain ies ela ed o
compa men le el ield in en o ies, a ea-based ALS-in en o ies, g ow h models and imbe p ice
Fo es s 2010, 1
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luc ua ions when compu ing ne p esen alue o e he o a ion leng h on he s and le el. Acco ding o
hei esul s, g ow h models applied in o es planning simula ion compu a ions p o ed o be he mos
signi ican sou ce o unce ain y in s and le el compu a ions. Howe e , a p ope y (o es a e) is he uni
in ope a ional o es alue es ima ions p oduced o he pu poses o e.g., eal es a e business, land
exchanges and land di isions. The e ec s o a ious sou ces o unce ain y on he alue o o es
p ope y canno be ob ained simply by agg ega ing he unce ain ies obse ed a s and le el, because
he de ia ions om a e age o ue alue es ima es be ween a ious s ands end o pa ly cancel ou
each o he [38]. Thus, addi ional model simula ions a e needed o ob ain he o e all le el o
unce ain y o ypical sized o es es a es.
2. Objec i e
The objec i e o he s udy was o analyze he e ec o unce ain y ac o s ela ed o in en o y da a,
g ow h models and imbe p ice luc ua ion on he p edic ion o o es p ope y-le el NPV. The e m
unce ain y he e e e s o he a ia ion in es ima ed o es NPVs caused by e o s in in en o y da a,
andom e o s in g ow h and yield p ojec ions and andom a ia ions in imbe asso men p ices. The
deg ee o unce ain y- ela ed in en o y da a was de i ed om p e ious s udies dealing wi h a ea-based
ALS in en o ies a he s and le el. The e ec s o imbe p ice luc ua ion we e depic ed wi h
s ochas ic GMR p ice models. Fo es p ope y-le el NPVs we e es ima ed using h ee al e na i e a es
o in e es (3%, 4% and 5%). The s udy was ca ied ou applying he Mon e Ca lo (MC) simula ion
me hod and using s and-le el g ow h and yield p ojec ion models.
3. Ma e ial and Me hods
3.1. Da a
The s a ing poin o he in es iga ion consis ed o ou simula ed o es p ope ies ha ing a ying
compa men s uc u es: a p ope y ha ing an e en de elopmen class dis ibu ion (A), sapling s ands
(B), young hinning s ands (C) and ma u e s ands (D). Va ia ion in basic s and cha ac e is ics in
p ope ies can be seen in Figu e 1. All p ope ies included some a ia ion be ween s and de elopmen
classes. In o es p ope y A, whe e de elopmen class dis ibu ion was e en, age, basal a ea, mean
diame e and mean heigh a ied om 5 o 144 yea s, 0 o 27.5 m2/ha, 0 o 29.0 cm and 0.6 o 26.0 m,
espec i ely. In sapling-domina ed o es p ope y B, he espec i e a ia ions we e 5–50 yea s,
0–22.0 m2/ha, 0–23.0 cm and 0.6–20.0 m. Young hinning s ands p edomina ed in o es p ope y C
and he a ia ions we e 15–55 yea s, 1.3–22.0 m2/ha, 3.2–23.0 cm and 3.2–20.0 m as in o es
p ope y D, which was domina ed by ma u e s ands wi h espec i e a ia ions o 30–114 yea s,
7.2–27.5 m2/ha, 8.4–29.0 cm and 7.7–25.0 m. We assumed ha hese s and cha ac e is ics we e
es ima ed wi h a ea-based ALS in en o y.
Fo es s 2010, 1
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Figu e 1. Va ia ion in s and cha ac e is ics wi hin he o es p ope ies: A (ha ing an e en
de elopmen class dis ibu ion), B (sapling s ands), C (young hinning s ands) and D
(ma u e s ands). Top le : age; op igh : basal a ea (BA); bo om le : mean diame e (Dg);
and bo om igh : mean heigh (Hg).
3.2. Simula ion o he Sou ces o Unce ain y
The ela i e impo ance o he h ee sou ces o unce ain y in o es NPV compu a ions was
de e mined by simula ing each s and wi hin each o es p ope y epea edly wi h he MC
me hod (e.g., [25,26,29,39]). In MC me hodology, con idence es ima es a e ob ained by gene a ing an
e o e m om he model's e o dis ibu ion o each ou pu es ima e. The model is un dozens o
hund eds o imes, he esul s o which a e used o de e mine he inal p edic ed alue e o s a is ics.
The unce ain y caused by andom a ia ion in u u e imbe asso men p ices is e e ed o as
UPRICE, he unce ain y caused by inpu da a e o s UINV and he unce ain y caused by andom e o s in
ABCD
0 20406080100120
Age, yea s
Age
ABCD
0 5 10 15 20 25 30
BA, m2/ha
BA
ABCD
0 5 10 15 20 25 30
Dg, cm
Dg
ABCD
0 5 10 15 20 25 30
Hg, cm
Hg

Fo es s 2010, 1
182
g ow h p ojec ions is e e ed o as UGROWTH. The sou ces o unce ain y we e included in he
simula ions sepa a ely and all h ee simul aneously, enabling us o de e mine how he di e en sou ces
o unce ain y a ec he NPV dis ibu ions. In addi ion, we simula ed each combina ion wi h in e es
a es o 3%, 4% and 5%. The calcula ions we e ca ied ou using SIMO simula ion and op imiza ion
so wa e (SIMO simula ion amewo k, [40,41]).
UINV, UGROWTH and UPRICE we e simula ed in a manne simila o ha in [38]. The e ec o andom
a ia ion, i.e., measu emen and sampling e o s, in o es in en o y da a was aken in o accoun by
gene a ing ue alues om he es ima es in he simula ion inpu da ase , using so-called ue alue
models. In his con ex he e m ue alues e e o simula ed (no ac ual) ue s and a ibu e alues.
The ue alue models we e cons uc ed so ha ends, dis ibu ion shapes and co ela ions be ween he
a ious a ibu es we e aken in o accoun .
Da a o modeling ue alues o ALS in en o y we e based on a s udy a ea in no heas e n Finland
ha included 89 s ands. The alues o he a ibu es we e es ima ed and measu ed a he ee species
s a um le el and he es ima es we e based on he k-MSN p ocedu e ( o de ails see [42]. The da ase
used is desc ibed in u he de ail in Mäkinen e al. [43]. The unce ain y caused by he s and-le el
g ow h models was aken in o accoun by including a andom a ia ion componen in he g ow h
p ojec ions. A mo e de ailed desc ip ion o andom componen in he g ow h p edic ions can be ound
in [38]. Howe e , he au oco ela ion componen included in [38] was excluded om hese
simula ions.
Timbe p ices we e modeled using a GMR p ocess ha u ilized his o ical p ice s a is ics on eal
s umpage p ices in Finland be ween Janua y 1986 and Augus 2008. The p ice s a is ics we e gi en
sepa a ely o saw logs and pulpwood o he h ee main comme cial imbe species in Finland: Sco s
pine (Pinus syl es is L.), No way sp uce (Picea abies (L.) H. Ka s .) and bi ch (Be ula L.) [38].
The de elopmen o each s and was simula ed un il he nex egene a ion ha es , o a maximum o
100 yea s, using a one-yea imes ep, and epea ing he en i e simula ion p ocess 100 imes o each
sou ce o unce ain y and in e es a e combina ion.
The hinning schedules we e based on sil icul u al ecommenda ions o he o es y ex ension
o ganiza ion Tapio in Finland [44]. The egene a ion ha es s we e done as soon as he 5-yea mo ing
a e age o alue g ow h pe cen age, o so-called - alue, o he s and was less han he in e es a e
chosen. To es ima e he imbe asso men olumes and incomes om he ha es s, ee diame e
dis ibu ions we e cons uc ed o each s and be o e he ha es s, using he dis ibu ion models
by [45-47]. The alue o each diame e class was hen p edic ed wi h he ape cu e unc ions o [48]
and op imal s em bucking algo i hm o [49]. Decisions abou when o ha es and egene a e we e
made a single s and-le el and, in his case, wi hou any p ope y-le el cons ain s. This is, o cou se, a
simpli ica ion as in some cases he ha es and egene a ion decisions a e no o ally independen .
Howe e , we belie e ha his kind o simpli ica ion can be jus i ied as he decision make aims a
simply maximizing he NPV o he o es p ope y.
When summing s and le el da a o p ope y le el co ela ions we e accoun ed o by gene a ing 100
al e na i e andom imbe p ice scena ios (one o each MC i e a ion) and hus s ands ha we e
gene a ed du ing he same ime s ep and i e a ion had simila imbe p ices. This should gua an ee ha
he a ia ion a he p ope y-le el was app op ia e.
Fo es s 2010, 1
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3.3. Analysis o he Unce ain y
The unce ain y in he NPV simula ion was analyzed by de e mining he dis ibu ions o he NPVs
and compa ing hem wi h he e e ence NPVs simula ed om ue alues, sepa a ely o each sou ce o
unce ain y and in e es a e combina ion. The simula ion compu a ions esul ed in p edic ed yield
alue (p edic ed NPV) dis ibu ions a he p ope y le el.
Fo each p ope y i, he mean and sd o he NPV dis ibu ion, meaniNPV and sdiNPV, espec i ely,
we e calcula ed wi h Equa ions (1) and (2).
󰇛󰇜1
100

 (1)
󰇛󰇜1
100

 (2)
The bias, i.e., he di e ence be ween he e e ence NPVs and means o he NPV dis ibu ions o
each p ope y i, was calcula ed as biasiNPV = meaniNPV − np iREF and he ela i e, o pe cen ual, bias
was calcula ed as bias%iNPV = (meaniNPV − np iREF)/np iREF × 100. We we e also in e es ed in he
ela i e a ia ion and hus he ela i e sd (%) was calcula ed wi h Equa ion (3).
%󰇧
 󰇨100

 1
100 (3)
4. Resul s
The e ec s o unce ain y ela ed o in en o y da a, g ow h models and imbe p ice luc ua ion on
o es p ope y-le el NPVs a e summa ized in Table 1. The e ec o each indi idual sou ce o e o
and he combined e ec we e de i ed o each o es p ope y ype. Compu a ions we e ca ied ou
using h ee di e en a es o in e es (3%, 4% and 5%). The e ec o he applied a e o in e es on he
pe -hec a e NPVs is p esen ed in Table 2. Fo es p ope ies A, B, C, and D s andwise NPV a ia ion
SDs and biases a e p esen ed in Figu e 2 and Figu e 3.
As p esen ed in Table 1, o es in en o y- ela ed e o s we e he mos signi ican sou ce o
unce ain y in all o he o es p ope y ypes analyzed. In en o y- ela ed e o s led o a o es
p ope y-le el ela i e s anda d de ia ion anging om 5.1% o 7.5% when an in e es a e o 3% was
applied. The espec i e biases a ied om 8.9% o 14.1%. The e ec o in en o y- ela ed bias was
emphasized, especially in he case o he ma u e s and p ope y (D).
Fo es s 2010, 1
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Table 1. A e ages o he ela i e biases (BIAS%NPV) and s anda d de ia ions (SD%NPV) o he simula ed NPV dis ibu ions o he 25 hec a e
o es p ope y wi h gi en sou ce o unce ain y and in e es a e combina ion.
Ac i e sou ces o unce ain y In e es a e
3 % 4 % 5 %
Fo es p ope y Uin en o
y
U
g
ow h U
p
ice meanNPV BIAS%NPV SD%NPV meanNPV BIAS%NPV SD%NPV meanNPV BIAS%NPV SD%NPV
A • 142,140.9 12.2 5.1 123,038.6 14.4 6.5 112,439.9 18.1 7.6
A • 128,507.9 1.4 1.7 109,728.8 2.1 1.3 97,236.1 2.1 1.4
A • 124,846.2 −1.5 3.4 106,930.3 −0.5 2.4 95,661.8 0.5 2.0
A • • • 143,469.5 13.2 6.5 125,119.5 16.4 6.4 115,839.1 21.7 6.8
B • 87,042.1 8.9 7.4 63,659.0 16.5 9.9 49,849.9 24.3 11.1
B • 79,864.9 −0.1 4.1 55,853.2 2.2 3.6 41,231.2 2.8 4.4
B • 76,160.0 −4.7 5.8 52,502.4 −3.9 4.7 39,230.1 −2.1 4.8
B • • • 84,661.3 5.9 9.3 62,515.1 14.4 9.8 49,896.3 24.5 12.6
C • 120,940.7 13.5 7.5 95,619.7 19.7 9.4 80,878.8 29.6 12.0
C • 107,330.0 0.7 3.2 81,492.2 2.0 3.1 64,357.0 3.2 3.3
C • 103,493.5 −2.9 6.4 78,387.9 −1.9 4.9 62,126.2 −0.4 4.6
C • • • 118,141.0 10.9 9.4 95,007.3 19.0 9.7 80,928.5 29.7 10.9
D • 204,107.4 14.1 5.8 186,286.6 15.4 7.2 177,365.5 18.6 8.1
D • 183,501.9 2.6 1.5 165,762.0 2.7 1.3 153,543.8 2.7 1.3
D • 179,539.0 0.4 3.6 162,407.2 0.6 2.3 151,240.5 1.2 1.9
D • • • 209,108.8 16.9 7.3 191,775.9 18.8 7.4 184,321.2 23.3 7.3
The ac i e unce ain y sou ces in each combina ion a e ma ked wi h •.
A = a p ope y ha ing an e en de elopmen class dis ibu ion,
B = a sapling s and p ope y,
C = a young hinning s and p ope y,
D = a ma u e s and p ope y.
Fo es s 2010, 1
185
Table 2. A e ages o he ela i e biases (BIAS%NPV) and s anda d de ia ions (SD%NPV) o he simula ed NPV dis ibu ions pe hec a e wi h
gi en sou ces o unce ain y and in e es a e combina ion.
Ac i e sou ces o unce ain y In e es a e
3 % 4 % 5 %
Fo es p ope y Uin en o
y
U
g
ow h U
p
ice meanNPV BIAS%NPV SD%NPV meanNPV BIAS%NPV SD%NPV meanNPV BIAS%NPV SD%NPV
A • 5,685.6 12.2 25.9 4,921.5 14.4 30.4 4497.6 18.1 33.6
A • 5,140.3 1.4 15.3 4,389.2 2.1 15.5 3889.4 2.1 18.8
A • 4,993.8 −1.5 9.9 4,277.2 −0.5 9.1 3826.5 0.5 8.7
A • • • 5,738.8 13.2 32.8 5,004.8 16.4 35.3 4633.6 21.7 39.3
B • 3,481.7 8.9 22.9 2,546.4 16.5 27.7 1994.0 24.3 29.6
B • 3,194.6 −0.1 20.6 2,234.1 2.2 20.5 1649.2 2.8 24.6
B • 3,046.4 −4.7 12.6 2,100.1 −3.9 11.6 1569.2 −2.1 11.6
B • • • 3,386.5 5.9 34.8 2,500.6 14.4 38.1 1995.9 24.5 41.8
C • 4,837.6 13.5 29.7 3,824.8 19.7 35.0 3235.2 29.6 40.8
C • 4,293.2 0.7 17.7 3,259.7 2.0 16.9 2574.3 3.2 20.2
C • 4,139.7 −2.9 11.2 3,135.5 −1.9 9.8 2485.0 −0.4 9.3
C • • • 4,725.6 10.9 37.1 3,800.3 19.0 41.1 3237.1 29.7 46.4
D • 8,164.3 14.1 30.4 7,451.5 15.4 35.4 7094.6 18.6 40.9
D • 7,340.1 2.6 8.6 6,630.5 2.7 9.2 6141.8 2.7 11.1
D • 7,181.6 0.4 7.9 6,496.3 0.6 6.6 6049.6 1.2 6.0
D • • • 8,364.4 16.9 31.2 7,671.0 18.8 33.7 7372.8 23.3 39.1
The ac i e unce ain y sou ces in each combina ion a e ma ked wi h •.
A = a p ope y ha ing an e en de elopmen class dis ibu ion,
B = a sapling s and p ope y,
C = a young hinning s and p ope y,
D = a ma u e s and p ope y.
Fo es s 2010, 1
192
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