RESEARCH ARTICLE Open Access
In en o y o aspen ees in sp uce domina ed
s ands in conse a ion a ea
Ma i Mal amo
1*
, Annukka Pesonen
2
, Lau i Ko honen
1
, Ja i Kouki
1
, Mikko Vehmas
3
and Kalle Ee ikäinen
4
Abs ac
Backg ound: The occu ence o aspen ees inc eases he conse a ion alue o ma u e coni e domina ed o es s.
Aspens ypically occu as sca e ed indi iduals among majo ee species, and he e o e he in en o y o aspens is
challenging.
Me hods: We cha ac e ized aspen popula ions in a bo eal na u e ese e using diame e dis ibu ion, spa ial
pa e n, and o es a ibu es: olume, numbe o aspens, numbe o la ge aspen s ems and basal a ea median
diame e . The da a we e collec ed om h ee sepa a e o es s ands in Koli Na ional Pa k, eas e n Finland. A each
si e, we measu ed b eas heigh diame e and coo dina es o each aspen. The compa ison o in en o y me hods
o aspens wi hin he h ee s ands was based on simula ions wi h mapped ield da a. We mimicked s and le el
in en o y by loca ing a ying numbe s o ixed a ea ci cula plo s bo h sys ema ically and andomly wi hin he
s ands. Addi ionally, we also es ed i he use o ai bo ne lase scanning (ALS) da a as auxilia y in o ma ion would
imp o e he accu acy o he s and le el in en o y by applying he p obabili y p opo ional o size sampling o
assis he selec ion o ield plo loca ions.
Resul s: The esul s showed ha aspens we e always clus e ed, and he diame e dis ibu ions indica ed di e en
s and s uc u es in he h ee in es iga ed o es s ands. The eliabili y o he olume and numbe o la ge aspen
ees a ied om ela i e oo mean squa e e o igu es abo e 50% wi h ewe sample plo s (5–10) o alues o
25%–50% wi h 10 o mo e sample plo s. S and le el in en o y es ima es we e also able o de ec spa ial pa e n
and he shape o he diame e dis ibu ion. In addi ion, ALS-based auxilia y in o ma ion could be use ul in guiding
he in en o ies, bu cau ion should be used when applying he ALS-suppo ed in en o y echnique.
Conclusions: This s udy cha ac e ized Eu opean aspen popula ions o he pu poses o moni o ing and
managemen o bo eal conse a ion a eas. Ou esul s sugges ha i he numbe o sample plo s is adequa e,
i.e. 10 o mo e s and le el in en o y will p o ide accu a e enough o es a ibu es es ima es in conse a ion a eas
(minimum accu acy equi emen o RMSE% is 20%–50%). E en o he mo e ecologically aluable a ibu es, such as
diame e dis ibu ion, spa ial pa e n and la ge aspens, he es ima es a e accep able o conse a ion pu poses.
Keywo ds: Diame e dis ibu ion; His o ical con inui y; In en o y; LiDAR; Populus emula L; Simula ion;
Spa ial a angemen ; S and cha ac e is ics
Backg ound
One o he mos in e es ing mino ee species in bo eal
o es s o no he n Eu ope is he Eu opean aspen (Populus
emula L.). The impo ance o aspen is closely ela ed o
i s biodi e si y alues because i hos s pa icula ly di e se
g oups o associa ed species, many o which a e h ea -
ened in Fennoscandia (Esseen e al. 1992; Kouki e al.
2004). In addi ion, la ge-sized aspens ha e gene ally dis-
appea ed om managed o es s because hey ha e low
economic alue and a e in e media e hos s o he pine
us ungus (Melampso a pini o qua [B aun] Ros .) ha
causes se ious damage o young pine s ands (Ku kela 1973;
Heliö aa a and Väisänen 1984).
Al hough aspen is a ypical species in pos -dis u bance,
ea ly successional s ages, ecen s udies ha e indica ed
ha aspen can main ain i s popula ions in na u al old-
g ow h coni e ous o es s o up o se e al hund ed yea s,
* Co espondence: [email p o ec ed]
1
Uni e si y o Eas e n Finland, School o Fo es Science, P.O. Box 111,
FI-80101 Joensuu, Finland
Full lis o au ho in o ma ion is a ailable a he end o he a icle
© 2015 Mal amo e al.; licensee Sp inge . This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons
A ibu ion License (h p://c ea i ecommons.o g/licenses/by/4.0), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion
in any medium, p o ided he o iginal wo k is p ope ly c edi ed.
Mal amo e al. Fo es Ecosys ems (2015) 2:12
DOI 10.1186/s40663-015-0037-4
e en hough hey may slowly decline in abundance (Lilja
e al. 2006; Vehmas e al. 2009b). In pa icula , old and
la ge-sized aspen ees, which a e mos aluable o bio-
di e si y, a e mos ly ound in ma u e and old-g ow h
mixed o es s whe e hey g ow in small g oups o as
sca e ed indi iduals (Tikka 1954; Sy jänen e al. 1994).
Because he spa io empo al con inui y o ecologically im-
po an cha ac e is ics is ega ded as impo an o conse -
a ion pu poses (S okland e al. 2002; Kouki e al. 2004) he
abili y o in en o y and moni o aspen ees is essen ial
o he managemen o conse a ion a eas.
Se e al a iables can be used o desc ibe aspens in
s and-le el o es in en o ies. Fi s , he exis ence o
aspen can be eco ded. Secondly, de ail on he amoun
and size o aspen ees is o in e es ; in s and-le el in en-
o ies, hey a e usually desc ibed using basal a ea, mean
diame e , and mean heigh (Koi uniemi and Ko honen
2006). Thi dly, om a biodi e si y poin o a iew, in o -
ma ion on size a ia ion and spa ial dis ibu ion is highly
ele an (Kouki e al. 2004). The de e mina ion o spa ial
dis ibu ion equi es ha he ees a e indi idually mapped,
which is usually p ac ically impossible o conduc in ield
su eys, excep o esea ch pu poses. Co espondingly,
he ee heigh dis ibu ions a e usually no assessed due
o he labo ious ield measu emen s, whe eas diame e
dis ibu ions can be ob ained. Wi h his in o ma ion, some
indica o s o he na u alness o he o es s uc u e, such
as he shape o he diame e dis ibu ion, o he gi en
aspen popula ion can be assessed. Fu he mo e, i is easy
o de ine he p opo ion o la ge aspens when hei diame-
e s a b eas heigh (dbh) a e, o ins ance, g ea e han
25 cm.
The p oblem ela ed o he assessmen o aspen a
s and-le el in en o ies is ha he low densi y o he
aspen ees esul s in high es ima es o sampling e o s.
I is also possible ha aspens a e no sepa a ed om
o he economically less-impo an deciduous species in
ee s ock desc ip ions o o es managemen . In alid-
a ion s udies o he in en o ies by compa men s, he
oo mean squa e e o s (RMSEs) ob ained o he o al
g owing s ock olume ha e anged om 15% −38% (Poso
1983; Haa a and Ko honen 2004). Howe e , species-
speci ic e o s a e conside ably highe , being 29%, 43%
and 65% o Sco s pine (Pinus syl es is L.), No way
sp uce (Picea abies L.), and he g oup consis ing o sil e
bi ch (Be ula pendula Ro h) and downy bi ch (B. pubes-
cens Eh h), espec i ely (Haa a and Ko honen 2004).
While he e o s a e usually accep able o he dominan
coni e ous species, mino deciduous ee species a e de-
sc ibed oo inaccu a ely o many pu poses. Fo Eu opean
aspen, he ela i e RMSE can be se e al hund eds o pe -
cen (A o Haa a, pe sonal comm.).
Ai bo ne lase scanning (ALS) -based echnology has
been success ully applied o s and-le el in en o ies du ing
ecen yea s (Næsse 2007; Mal amo and Packalen 2014).
Fo es cha ac e is ics a e usually es ima ed wi h 100%
co e age o he in en o y a ea by u ilising he a ea-based
app oach (ABA), i.e. s a is ical ela ionships be ween o -
es a ibu es and ALS me ics a he plo le el. The i s
applica ions es ima ed o es cha ac e is ics as a whole,
bu he in en o y sys em by Packalén and Mal amo
(2007), which also u ilizes ae ial pho og aphs and elies on
non-pa ame ic impu a ion, was he i s species-speci ic
es ima o o o es a ibu es. Howe e , deciduous ee
species a e usually pooled in o one single g oup (Packalén
and Mal amo 2007). Thus, he p e iously de eloped ALS
based in en o y app oaches a e no app op ia e o p o-
iding species-speci ic in o ma ion on aspen. In s udies by
B eidenbach e al. (2010) and Pippu i e al. (2013) species-
speci ic ALS in en o y has also been applied o iden i y
aspens, bu he RMSE alues ha e been o e 100%.
ALS can also p o ide in o ma ion abou indi idual
ees, which can be agg ega ed o he s and le el. In a
s udy by Säynäjoki e al. (2008), single aspen ees we e
de ec ed om dense ALS da a. The in en o y sys em
was, howe e , a he complex, including, o ins ance,
isual in e p e a ions by ae ial images o sepa a e con-
i e ous ees om deciduous ees. As a esul , he clas-
si ica ion accu acy o la ge (dbh > 25 cm) aspen ees
was 78.6%. In addi ion, disc imina ion o aspen can be
di icul because he ALS in ensi y me ics ha a e im-
po an in species de ec ion o e lap wi h sp uce and bi ch
(Ø ka HO e al. 2007; Ko pela e al. 2010).
Despi e he ecen ad ances in ee-le el iden i ica ion,
i is challenging o ob ain s and-le el in o ma ion on
aspen in emo e sensing-based o es in en o ies. Co -
espondingly, he accu acy es ima es ha e been a he
low o aspen, o i has been comple ely igno ed in ad-
i ional ield in en o ies. Since he end in o es in en-
o ies is owa d emo e sensing applica ions, a e and
sca e ed ee species, such as aspen, could become
neglec ed in in en o ies. On he o he hand, he e is
an inc easing need o ha e o es in en o y in o ma-
ion on aspen, especially in conse a ion a eas whe e
he occu ence and long- e m pe sis ence o sca e ed
aspen ees may be c ucial o many conse a ion-
dependen species.
The goal o his s udy was o cha ac e ise aspen popu-
la ions in a bo eal na u e ese e. The s udy da a a e
based on mapped indi idual aspens in h ee sepa a e
sp uce domina ed o es s ands. In his unique da a se
he aspen popula ions ha e de eloped wi hou he e -
ec s o ac i e o es sil icul u e du ing ecen decades.
We cha ac e ised aspen using diame e dis ibu ion,
spa ial pa e n o ees and o es a ibu es olume
(V,m
3
∙ha
–1
), numbe o s ems (N,ha
–1
), numbe o s ems
o la ge aspens (N
dbh >25cm
,ha
–1
) and basal a ea median
diame e (D
g
M, cm). Fu he mo e, we applied s and le el
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 2 o 12
in en o y simula ions o examine he accu acy o he
es ima es o hese cha ac e is ics. Finally, p obabili y p o-
po ional o size (PPS) sampling using ALS me ics as
auxilia y in o ma ion was e alua ed as a me hod o im-
p o e in en o y es ima es.
Me hods
S udy a ea and ield measu emen s
The s udy a ea was loca ed in Koli Na ional Pa k (NP) in
eas e n Finland (29°50′E, 63°5′N). The a ea is cha ac-
e ised as a highly a iable bo eal landscape, whe e he al i-
ude a ies om 94 −347 m abo e sea le el (Lyy ikäinen
1991; Kä kkäinen 1994). The a ea lies in he ansi ional
a ea be ween he sou he n and middle bo eal ege a ion
zones (Kalliola 1973). Mos o es s in he a ea a e domi-
na edbyNo waysp uce(Picea abies L. Ka s .) and Sco s
pine (Pinus syl es is L.) wi h a highly a iable admix-
u e o sil e bi ch, downy bi ch, Eu opean aspen, and
g ey alde (Alnus incana [L.] Moench) (Lyy ikäinen 1991;
G önlund and Hakalis o 1998).
In a s udy by Vehmas e al. (2009b), he his o ical con-
inui y o aspen was s udied based on in en o y egis-
e s, and some a eas whe e la ge aspens ha e su i ed
om 1910 we e ound wi hin he cu en Koli NP. Th ee
o he la ges o hese s ands we e selec ed o his s udy
(Figu es 1 and 2). O he s ands we e e y small sized, in-
cluded only a ew aspens o had highly i egula shape.
The o al a ea o o es s and 1 was 8.05 ha, whe eas
s ands 2 and 3 co e ed 5.96 and 12.93 ha o o es ,
espec i ely (Table 1). Wi hin he h ee s ands, bo h dbh
and GPS posi ion we e eco ded o all li ing aspen ees
ha ing a dbh la ge han 5 cm in 2006. S em olumes o
Figu e 1 The loca ion o he s udy a ea.
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 3 o 12
he allied aspens we e calcula ed using Laasasenaho’s
(1982) olume unc ion o Sco s pine, since published
equa ions we e no a ailable o Eu opean aspen (Kinnunen
e al. 2007). The choice o olume model was based on
expe opinion. Sum cha ac e is ics we e con e ed o
pe -hec a e le els, and D
g
Mwas calcula ed o he h ee
s ands (Table 1). In addi ion, o al s and olume and
basal a ea we e aken om he exis ing s and egis e
da a and upda ed in o aspen measu emen da e (see
Vehmas e al. 2009b).
Addi ionally, 15 ec angula sample plo s loca ed in
Koli NP ha did no o e lap wi h he h ee s ands p e i-
ously desc ibed we e used o ind he bes -co ela ing
ALS me ic wi h aspen olume. These da a we e used in
PPS sampling. These plo s we e o iginally es ablished o
examine single- ee de ec ion o aspen om emo e sens-
ing da a and included a leas one aspen ee (Säynäjoki
e al. 2008). The dbh was measu ed and s em olumes
calcula ed o all ees. Mo e de ailed in o ma ion o he
da a ob ained om he 15 sample plo s can be ound in
Säynäjoki e al. (2008).
Lase da a
The geo- e e enced ALS poin cloud da a om Koli NP
we e collec ed on 13 July 2005 using an Op ech ALTM
3100 scanne ope a ing a a mean al i ude o 900 m
abo e g ound le el (a.g.l), which esul ed in a nominal
sampling densi y o ca. 4 measu emen s∙m
–2
. Bo h he
i s and las pulse da a we e eco ded, and he las pulse
da a we e employed o gene a e a digi al e ain model
(DTM) by he me hod explained in Axelsson (2000)
using a g id cell size o 1 m. Abo e g ound heigh s (i.e.,
canopy heigh s) o he lase poin s we e ob ained by
Figu e 2 The s udy s ands (A= s and 1, B= s and 2, C=s and 3) wi h aspen ee loca ions.
Table 1 A eas and o es a ibu es o Eu opean aspen
and s and o als o he h ee s udy s ands
A ibu e S and
123
A ea (ha) 8.05 5.96 12.94
D
g
M(cm) 22.4 39.1 49.7
G(m
2
∙ha
–1
) 3.8 1.9 6.0
V(m
3
∙ha
–1
) 22.2 12.4 35.7
N(ha
–1
) 148.6 21.3 54.1
N
dbh>25cm
(ha
–1
) 16.0 15.3 32.9
G
o al
(m
2
∙ha
–1
) 23.2 34.3 36.8
V
o al
(m
3
∙ha
–1
) 168.9 363.1 422.2
A ea deno es he size o he s and, D
g
M, cm deno es basal a ea median
diame e o aspen, G,m
2
∙ha
–1
deno es basal a ea o aspen, V,m
3
∙ha
–1
deno es
olume o aspen, N,ha
–1
deno es numbe o s ems o aspen, N
dbh>25cm
ha
–1
deno es numbe o s ems o la ge aspens, G
o al
,m
2
∙ha
–1
deno es basal a ea
o he o al g owing s ock and V
o al
,m
3
∙ha
–1
deno es olume o he o al
g owing s ock.
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 4 o 12
sub ac ing he DTM a he co esponding loca ion. In
his s udy, he pulse da a ob ained wi h he ALS senso
was eclassi ied o “ i s echo”o “las echo”. I is wo h
no ing he e ha he o iginal single echoes we e dupli-
ca ed o bo h i s and las echo classes, whe eas he
in e media e echoes we e comple ely igno ed. Fo mo e
de ails on he o iginal ALS da a, see Vehmas e al.
(2009a).
The heigh dis ibu ion o he i s and las pulse can-
opy heigh hi s was used o calcula e plo -wise pe cen-
iles o 0, 1, 5, 10, 20, …, 90, 95, 99, and 100% heigh s
(h
0
,h
1
,…,h
100
) (Næsse 2004), and cumula i e p opo -
ional c own densi ies (p
0
,p
1
,…,p
100
) we e calcula ed
o he espec i e quan iles. The heigh dis ibu ions
con ained only hose lase poin s ha we e classi ied as
abo e-g ound hi s; a h eshold alue o 0.1 m was used.
The h
5
, o example, deno es he heigh a which he ac-
cumula ion o lase hi heigh s in he ege a ion was 5%,
and, co espondingly, p
5
deno es he p opo ion o lase
hi s ha accumula ed a he 5% heigh . In addi ion, he
ollowing a iables we e calcula ed by sample plo s: he
lase pulse in ensi ies accumula ing in pe cen iles (i
10
,
i
30
,…,i
90
), he a e age in ensi y alue o abo e-g ound
hi s, he p opo ion o g ound hi s e sus canopy hi s
using a h eshold alue o 0.1 m ( eg), and he a e age
heigh (h
mean
) and s anda d de ia ion o he abo e-
g ound hi s (h
sd
). The in ensi y alues we e used as ou -
pu ed by he senso wi hou calib a ion. All me ics
we e calcula ed sepa a ely o he i s and he las pulse
da a.
S and le el in en o y
The me hods o aspen in en o y we e s udied based on
simula ions using ield da a om he h ee s ands whe e
all aspens we e mapped. We simula ed s and le el in en-
o y by placing ci cula plo s o size 400 m
2
( adius
11.28 m) in o he s ands bo h sys ema ically and an-
domly. The size o he plo was chosen o co espond o
he g id cell size in PPS sampling (see me hodology
below). Fi e, en, i een, o wen y plo s we e loca ed in
each s udy s and o di e en sampling in ensi ies. All
sampling al e na i es we e epea ed 2500 imes. In he
simula ions, plo s we e only included i he cen e poin
o he plo was wi hin he s udy s and. Fo plo s loca ed
a he edge o he s and, an edge co ec ion was applied
by mul iplying he a ibu e alue o an edge plo by i s
expansion ac o (Bee s 1966):
A ibu e ¼A ibu eEdge plo Plo size
Edge plo size ð1Þ
whe e, a ibu e is a ibu e alue a e co ec ion, a i-
bu e
Edge plo
is a ibu e alue o he edge plo , plo size
is size o he sample plo , i.e., 400 m
2
, and edge plo size
is he size o he edge plo wi hin he s and.
This co ec ion was made o sum a ibu es V,N, and
N
dbh>25cm
bu no o D
g
M. This edge co ec ion is
sligh ly biased bu leads o conside ably mo e accu a e
esul s han wi hou applying any co ec ion (Sch eude
e al. 1993). Finally, he es ima es o o es a ibu es
we e calcula ed as sample means o each sample.
Fu he mo e, we also es ed i he use o ALS da a as
auxilia y in o ma ion would imp o e he accu acy o he
s and le el in en o y by applying PPS sampling. The
basic idea o his app oach is o use he ALS me ic o
guide he selec ion o ield plo loca ions (Pesonen e al.
2010a, b). We applied he same numbe o sample plo s
as in he case o sys ema ic and andom sampling, bu
sampling p obabili ies a ied acco ding o ALS in o ma-
ion. This was done o choose he mos p omising plo
loca ions o aspen plo s. Fi s , p obabili y laye s we e
p oduced, i.e., he auxilia y da a alues we e di ec ly
calcula ed o he whole s and ha was di ided in o a
g id o 20 m × 20 m sample uni s. When applying PPS
sampling, he sample uni s we e squa e and a e e e ed
o as g id cells. ALS based auxilia y da a alues we e cal-
cula ed o each sample uni (i=1,…,N
g id
, whe e N
g id
is he o al numbe o sample uni s in a s and), and
he p obabili ies o each uni ibeing selec ed we e
de e mined. The selec ion p obabili ies o he sample
uni s (p
i
) we e calcula ed by di iding he auxilia y
da a alue x
i
o he sample uni iby he sum o he
auxilia y da a alues o e he whole a ea o he p ob-
abili y laye (p
i
=x
i
/∑x
i
). These selec ion p obabili ies
we e inally u ilised in sampling 5, 10, 15 o 20 sample
uni s. The calcula ions we e epea ed 2500 imes.
Shape o he diame e dis ibu ion
In s ands 1 and 3 he shape o he diame e dis ibu ion
es ima ed using he simula ed ixed- adius, plo -based
in en o y app oach was compa ed wi h he ac ual em-
pi ical dis ibu ion acco ding o he de eloped ules. The
unimodal o m o diame e dis ibu ion (s and 2) was
no conside ed. In he compa ison o measu ed and es i-
ma ed diame e dis ibu ions, he goal was o examine i
he sampled dis ibu ions ollowed he unde lying ac ual
size dis ibu ion o aspen. The sampled diame e dis i-
bu ions we e de e mined in 5- (bimodal s and) o 10-cm
(descending s and) diame e classes wi hin he ange
om 10 −95 cm (See Figu e 3 o ac ual dis ibu ions).
Fo descending diame e dis ibu ions, he ollowing ule
was applied:
Numbe o s ems in 10–20-cm dbh class > numbe
o s ems in 20–30-cm dbh class > numbe o s ems in
30–40-cm dbh class.
I his ule was ul illed by he es ima e, i was classi-
ied as a ealis ic es ima e o he unde lying empi ical
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 5 o 12

dis ibu ion. Co espondingly, in he case o bimodal
dis ibu ion, he ollowing ule was applied:
The i s mode in he dis ibu ion is wi hin dbh classes
om 10 −20 cm, and he second mode in he dis ibu-
ion is a e he 25–30-cm dbh class.
Spa ial pa e n o aspens
The spa ial pa e n o he aspens wi hin he h ee s udy
s ands was de e mined by applying Ripley’s K( ) unc ion
(Ripley 1981). I desc ibes he expec ed numbe o ees
a dis ance om a andomly selec ed ee. I he alue
o he unc ion is la ge han wha would be expec ed
based on andom spacing, he spa ial pa e n is clus-
e ed; i smalle , i is sys ema ic. We applied he lib a y
spa s a (Baddeley and Tu ne 2005) in s a is ical so -
wa e R o calcula e he K( ) alues o each o he h ee
s ands. Iso opic co ec ion was applied o minimize edge
e ec s in he calcula ion (Ripley 1988).
The spa ial pa e ns de i ed o he en i e s ands we e
compa ed wi h es ima es ob ained om he simula ed
0
100
200
300
400
500
600
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
F equency
Diame e class midpoin , cm
A
0
5
10
15
20
25
30
10 15 20 25 30 35 40 45 50 55 60 65 70 75
F equency
Diame e class midpoin , cm
B
0
20
40
60
80
100
120
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
F equency
Diame e class midpoin , cm
C
Figu e 3 Diame e dis ibu ion o s ands 1–3(A= s and 1, B= s and 2, C=s and 3).
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 6 o 12
samples.The e o e, a Fishe index (I) was calcula ed o
each s and-wise simula ion ob ained using he ollowing
equa ion:
I¼s2
n
−
n;ð2Þ
whe e s2
nis he a iance o he plo -wise numbe s o
aspens in he sample o 20 plo s and 
nis he mean o
he plo -wise numbe s o aspens. The I alues g ea e
han 1 indica e clus e ed spa ial pa e ns.
Reliabili y cha ac e is ics
The simula ion esul s we e alida ed in e m o ela i e
RMSE.
RMSE%¼100x
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
N
i¼1
y−
X
n
i¼1
y
^
i
n
0
B
B
B
@
1
C
C
C
A
2
N
u
u
u
u
u
u
u
yð3Þ
and bias
bias%¼100x
X
N
i¼1
y−
X
n
i¼1
⌢
yi
n
0
B
B
B
@
1
C
C
C
A
N
yð4Þ
whe e Nis he numbe o simula ions, yis he obse ed
alue o he s and, ŷ
i
is he p edic ed alue o sample
plo simula ion i, and nis numbe o sample plo s in
one sample.
Finally, in he case o he ALS-guided in en o y, he
ela i e imp o emen in olume es ima e compa ed o
selec ing sample uni s o 20 m × 20 m wi h equal p ob-
abili ies was calcula ed.
Resul s
Reliabili y igu es o a ibu es o simula ed s and le el
in en o ies
In gene al, he esul s a e mo e accu a e by means o
RMSE% when he numbe o sample plo s inc eases
(Table 2). An excep ion is s and 3 wi h sys ema ic place-
men o plo s whe e accu acy dec eased in he case o
20 plo s. This is ela ed o he shape o he s and and,
hus, o he dec eased possibili ies o loca e he sys em-
a ic sample plo ne wo k o he na ow, densely s ocked
sou he n pa o he s and in simula ions. In gene al, he
esul s a e also sligh ly mo e accu a e o sys ema ic
han andom plo loca ions especially in he case o s ands
1 and 2. The biases a e in mos cases below 2% and he e
a e only a ew cases whe e he alues a e o e 5%.
In he case o RMSE% o V, which is usually ega ded
as he mos impo an s and a ibu e, he igu es a e a-
he high wi h smalle numbe o sample plo s and s ill
emain app oxima ely a he le el o 25%–40% e en wi h
20 sample plo s (Table 2). In s and 2 he RMSE% alues
we e la ge o Vand also o Ncompa ed o s ands 1
and 3. This ou come may be ela ed o he smalle quan-
i ies o aspen in s and 2 (see Table 1). F om he eco-
logical poin o a iew, N
dbh>25cm
is he mos impo an
o es a ibu e. Especially in s and 1, bu also in s and 2,
mos o he aspens had smalle dbh alues, less han 25
cm (Table 1, Figu e 3) and co espondingly he RMSE%
igu es a e high. On he o he hand, he RMSE% igu es
a e lowe in s and 3 whe e he diame e dis ibu ion
(Figu e 3C.) shows ha a ema kable p opo ion o as-
pens ha eside in he g oup o ees is in he dbh-class
la ge han 25 cm. Finally, in gene al he esul s a e mos
accu a e o D
g
M.
In he case o PPS sampling, he chosen auxilia y in-
o ma ion me ic om ALS was h
mean
2
, which is based
on he co ela ion es ima e (0.76) be ween aspen Vand
his ALS me ic in 15 sample plo s o Koli NP. Co e-
sponding co ela ions be ween his ALS me ic and g id
cell le el alues in he s udy a ea we e also calcula ed,
and he e ec o he PPS sampling on he eliabili y o V
es ima es in gene al is p esen ed in Table 3. As shown,
he co ela ion was close o ze o in s and 2 and he
e ec o PPS sampling is nega i e in his case. Rega ding
he wo o he s ands he co ela ions be ween ALS me ic
and olume we e g ea e han 0.3, and he imp o emen s
in olume es ima es we e mo e han 10% and 3%, espec -
i ely. The mino imp o emen in s and 3 may be ela ed
o he exis ence o e y la ge aspens.
Shape o he diame e dis ibu ion es ima e
The shape o he diame e dis ibu ion o aspen was uni-
modal and skewed o he igh in s and 2, descending in
s and 1, and bimodal in s and 3 (Figu e 3A–C). The
shape o sample plo based diame e dis ibu ion es i-
ma es ob ained om he simula ions was examined in
s ands 1 and 3, including ecologically in e es ing descend-
ing and bimodal dis ibu ions, espec i ely. Examina ion
was implemen ed by classi ying he diame e dis ibu ion
es ima e o each simula ion acco ding o he ules p esen-
ed in he me hods.In s and 1 he p opo ion o ixed-
adius plo es ima es, which co ec ly classi ied he
descending s uc u e, anged om 50% −80% o 5 −20
plo s (Table 4). This was he case bo h o sys ema ically
and andomly loca ed plo s. Fo s and 3 wi h a bimodal
s uc u e, he p opo ion o co ec ly classi ied plo s wi h
di e en numbe o sample plo s co esponded o hose o
s and 1, bu he success a es we e lowe .
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 7 o 12
Spa ial pa e n o ees
The analysis based on mapped aspen da a wi h Ripleys
K- unc ion showed ha in all h ee s ands he aspens a e
clus e ed, because he expec ed alue o o he ees close
o each ee is la ge han a Poisson dis ibu ion would
sugges (Figu e 4A–C). Co espondingly, he analysis
based on sampling simula ions and Fishe ’s index showed
ha in each case he a e age alue showed ha spa ial
pa e n was clus e ed (Table 5). Also he p opo ion o
simula ions showing clus e ed spa ial pa e n was always
o e 50%, e en wi h jus i e sample plo s.
Discussion
This s udy conside ed s and le el aspen popula ions in a
bo eal na u e ese e. The analysis was based on diam-
e e dis ibu ion, spa ial pa e n o aspen ees and eli-
abili y igu es o o es a ibu e es ima es o s and le el
in en o y. Ou unique da a included mapped aspen ees
Table 3 Co ela ion and he imp o emen in he RMSE o
V(%) due o he use o ALS auxilia y in o ma ion in PPS
sampling
S a is ical a iable S and
123
Co ela ion 0.35 0.04 0.33
Imp o emen in he RMSE o V(%) 10.6 –7.0 3.2
Table 4 P opo ion (%) o co ec ly classi ied diame e
dis ibu ion ypes in 2500 simula ions
S and Numbe o plo s In en o y me hod
Sys ema ic Random
1 5 51.2 54.9
10 65.4 66.9
15 76.0 75.0
20 78.8 78.6
3 5 35.3 36.7
10 52.2 49.9
15 55.2 54.7
20 65.1 61.7
Table 2 Rela i e RMSE and bias (in b acke s) alues o he o es a ibu es in h ee s udy s ands
S and Sampling a e (%) Sampling al e na i e Numbe o plo s RMSE (%) (bias %)
VND
g
MN
dbh>25cm
1 2.48 Random 5 62.0 (–3.4) 64.3 (–5.0) 56.9 (–10.6) 81.8 (–2.4)
4.97 Random 10 43.8 (–3.3) 45.6 (–2.9) 35.2 (–6.0) 58.2 (–3.5)
7.45 Random 15 35.2 (0.6) 36.2 (0.2) 23.5 (–3.6) 47.7 (–0.5)
9.94 Random 20 30.5 (–1.4) 31.0 (–1.2) 15.5 (–2.1)) 41.8 (–2.1)
Sys ema ic 5 50.8 (–3.0) 56.0 (–4.4) 48.2 (–6.8) 74.3 (–1.2)
Sys ema ic 10 34.5 (–0.1) 40.1 (–1.4) 35.8 (–6.1) 48.5 (0.1)
Sys ema ic 15 25.9 (–2.3) 21.5 (–1.5) 17.8 (–1.8) 49.7 (–4.2)
Sys ema ic 20 24.5 (–1.8) 25.5 (–1.2) 13.5 (–2.5) 38.5 (–2.8)
2 3.36 Random 5 85.7 (–0.2) 83.8 (0) 29.4 (1.3) 87.1 (–0.8)
6.72 Random 10 59.8 (1.2) 59.7 (0.6) 24.5 (–1.4) 60.6 (0.2)
10.08 Random 15 50.0 (–0.2) 49.2 (0) 21.1 (–1.3) 50.1 (–0.2)
13.45 Random 20 41.8 (0.7) 42.7 (–0.6) 18.7 (–0.4) 42.8 (–0.1)
Sys ema ic 5 84.4 (–3.8) 98.2 (–8.2) 28.6 (0.9) 91.9 (–5.9)
Sys ema ic 10 53.2 (0) 47.6 (–2.4) 23.6 (–0.6) 52.2 (–1.4)
Sys ema ic 15 37.6 (1.4) 38.3 (–0.5) 18.5 (–0.3) 42.2 (0.5)
Sys ema ic 20 30.6 (0.1) 31.1 (–0.6) 16.9 (–0.2) 34.6 (–0.3)
3 1.55 Random 5 51.1 (0.2) 64.5 (–0.5) 21.0 (0.5) 52.8 (–0.1)
3.09 Random 10 36.0 (–0.2) 46.3 (–1.8) 13.1 (0.5) 37.7 (–0.7)
4.64 Random 15 29.0 (–0.5) 37.3 (–1.0) 10.1 (–0.1) 30.1 (–0.5)
6.18 Random 20 25.2 (0.1) 31.7 (–0.8) 8.5 (0.1) 25.6 (0.2)
Sys ema ic 5 53.6 (–1.2) 58.4 (2.9) 18.5 (0.5) 52.9 (–0.5)
Sys ema ic 10 33.6 (–0.4) 35.5 (–0.7) 12.8 (–1.6) 36.4 (–0.6)
Sys ema ic 15 26.7 (0) 29.8 (–0.7) 7.7 (–0.2) 24.2 (0)
Sys ema ic 20 33.8 (0.1) 35.7 (0.4) 7.2 (–0.5) 31.9 (–0.2)
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 8 o 12
in h ee sp uce domina ed o es s ands whe e local
aspen popula ions ha e su i ed du ing he pas 100
yea s (Vehmas e al. 2009b). These s ands also ep esen
a ou able g owing en i onmen s o aspen. The p opo -
ion o aspen in hese s ands is conside ably highe han
he a e age alue o 1.5% in Finland (Tomppo e al. 2001)
being 16.3%, 5.5% and 16.2% o basal a ea in s ands 1, 2
and 3, espec i ely. These s a is ics a e o he o es a ea
in gene al, bu in conse a ion a eas he p opo ion o
aspen is usually conside ably la ge . I also should be
no ed ha ou s udy s ands we e a he la ge in size com-
pa ed o he a e age s and size, which is ca. 2 ha in sou h-
e n Finland. Howe e , wi h espec o he s a e-owned
o es s and conse a ion a eas whe e aspen is common,
he s and sizes used in his s udy we e b oadly simila .
The accep able le el o o es a ibu e esul s is, o
cou se, dependen on he need o in o ma ion, bu
acco ding o in en o y by compa men s, he RMSE
Figu e 4 Ripley’s K unc ion o s ands 1–3(A= s and 1, B= s and 2, C=s and 3). The dashed line desc ibes he expec ed alue o ees based
on Poisson dis ibu ion wi h adius , and solid line he es ima e ob ained using Ripley’s K unc ion and iso opic edge co ec ion.
Mal amo e al. Fo es Ecosys ems (2015) 2:12 Page 9 o 12