全 文 ：植　　　物　　　研　　　究
BULLETIN OF BOTAN ICAL RESEARCH
第 17卷　第 4期 1997年　 10月
Vol. 17　 No. 4 Oct. , 　 1997
THE VERTICAL BELTS OF NATURAL VEGETATION
PARTITIONING OF THE GUANDI MOUNTAINS BY USING
ORDERED PLOT CLUSTERING, SHANXI,NORTH CHINA
⒇
Feng Zhang1　 Tieliang Shang- guan1　 Anders Telenius2
( 1. Depar tment of Life Science, Shanxi Univ er sity , Taiyuan 030006, P. R. China )
( 2. Depar tment of Bo tany , Univ er sity o f Stockholm, S- 106 91 Stockholm, Sweden)
Abstract　 In this paper, o rdered plo t clustering ( OPC) , a non- hiera rchical ag-
g lomerativ e alg orithm based on the algo ri thm of the“ go ld- parti tioning method"
( Fisher s method) , is introduced to vertical bel t parti tio n of Guandi M ountains,
Shanx i. The result o f the ver tical bel t parti tioning is as follow s: 1. deciduous
broadleave forest belt ( 800 - 1600m above sea lev el ) , including 2 subbelts: I.
tempera te coni ferous fo rest subbel t ( 800- 1400m above sea lev el ) , andⅡ . decid-
uous bro adleave forest subbelt ( 1400- 1600m above sea lev el ) ; 2. coni ferous and
broadleave mixed- forest bel t ( 1600- 1750m above sea level) ; 3. co ld- temperate
coni ferous forest bel t ( 1750- 2600m above sea lev el ) ; 4. subalpine shrub and
meadow belt ( 2600- 2831m above sea lev el) .
The results obtained by O PC analy sis are then compared to TW IN SPAN us-
ing data on the f lo ristic composi tion o f v ertical bel ts of the Guandi M ountains,
Shanx i, No rth China. The resul t of analysis by OPC is considered as superior to
that by TW IN SPAN because some TW IN SPAN plo t g roups canno t be explained
acco rding to existing vegeta tion dist ribution, cont ra ry to the OPC result.
Key words　Ordered plot clustering , TW IN SPAN, Non- hierarchical agg lomera-
tiv e alg orithm, Vertical belt of natural v egetation, Gold parti tio ning
method, Guandi Mountains, Shanxi
　　 Introduction
Hierarchical agg lomera tiv e algo ri thms, such as TW INSPAN ( Hill 1979) , system
clustering ( Lance & Williams 1967; Orlo ci 1978) and various fuzzy clustering methods
⒇ 1996年 12月收稿。
( Zhang 1985, 1992, Zhang & Shangguan 1986, 1991a ) , and non - hierarchical alg o-
ri thms, e. g . , fuzzy c- means algo ri thms ( Ha thaway& Bezdek 1988; Equihua 1990) , al-
so known as fuzzy ISODATA ( Li 1989) and stepwise clustering ( Zhang & Shangguan
1994, 1996) , have been ex tensiv ely applied to v egetation analysis fo r a long time. In all o f
these methods, the probability for any tw o a rbit rari ly chosen plo ts to finally end up in the
same g roup is equal. This lack of bias prio r to o r during analy sis is usually advantag e, but
advantag e is turned to a disadvantag e in the case o f sequential ly o rdered plo ts ( plots f rom
a successiv e sequence, t ransects along an alti tude g radient , etc. ) , w hich cannot be anal-
y sed by methods of this kind.
The aim o f this paper is to int roduce a new non- hiera rchical alg orithm, o rdered plo t
clustering ( O PC) ( Fisher 1958, Fisher & Ness 1971, Tang 1986, Lang & Tang 1989) ,
sui table for applica tion to sequentially o rdered da ta sets. This new method and
TW IN SPAN are then applied to separation of the vegetation belts in the Guandi M oun-
tains in Shanxi , No rth China.
Materials and Methods
Study site
The Guandi Mountains are situated in the centre of the Luliang Range a t the boundary
betw een Jiaocheng , W enshui , Fang shan and Lufan Counties in Shanxi , No rth China ( 37°
20′～ 38°20′N, 110°18′～ 111°18′E) . The highest peak, Xiaow enshan, reaches 2831m above
sea level ( a. s. l. ) . M ean annual tempera ture is 3～ 4℃ . Monthly mean tempera ture in
January and July a re - 10. 6℃ and 16. 1℃ , respectiv ely. Annual precipi ta tion is 830. 8mm
( the only sta tion is located at 1600m a. s. l. ) . The major soi l types ( in sequence f rom
mountain fo ot to hi lltop) are mountain cinnamon soil, brow n fo rest soi l and mountain
meadow soi l ( Zhang & Shangguan 1992; Zhang 1994) .
Prior to human interv ention, the Guandi M ountains w ere covered by w arm- temper-
ate deciduous broadleaved fo rests. Due to human disturbance, the deciduous broadleaved
fo rests have to a larg e ex tent been replaced by cold- tempera te coni ferous fo rests, cla ssi-
fied as forma tions Larix principis- rupprecht ii , Picea wilsonii and Picea meyeri ( Zhang&
Shangguan 1992; Zhang 1994) . Other commonly occurring vegetation types are w arm-
tempera te coniferous fo rests ( Fo rm. Pinus tabulaeform is and Form. Platycladus
oriental is ) , deciduous broadleaved fo rests ( Fo rm. Quercus liaotungensis , Fo rm. Populus
davidiana , Fo rm. Betula platyphylla and Fo rm. Populus cathayana ) , deciduous
broadleaved shrubs ( Form. Caragana jubata , Fo rm. Potent illa fruticosa , Form. Hip-
pophae rhamnoides , Form. Rosa xanthina ( Zhang& Shangguan 1991b) , Form. Ostryopsis
davidiana ( Shangguan & Zhang 1989) , Fo rm. Spiraea trilobata , Form , Vitex negundo
va r. heterophylla , and Fo rm. Ziz iphus jujuba var. spinosa) , g rasslands ( Fo rm. Artemisia
spp. and Fo rm. Bothriochloa ischaemum ) and subalpine meadow s ( Form. Carex spp. and
Form. Kobresia spp. ( Zhang 1994) ) .
Data col lection
448 植　　物　　研　　究　　　　　　　　　　　　　　　 17卷
In June 1993 and July 1994, 41 plo ts, containing 57 carpophy tes species ( 13 t ree
species, 26 shrub species and 18 herb species) , w ere placed in various communi ties along a
t ransect running perpendicular to the contour lines f rom 800m to 2831m a. s. l. . Plot size
w as dependent on vegeta tion st ructure: 400m2 in fo rests ( 28 plo ts) , 25m2 in shrubs ( 8
plo ts) and 1 m2 in vegetation devoid of shrub o r t ree layers ( 5 plo ts) . In each plo t , the f re-
quency, and the g round cover of all component species w as reco rded. The g round cover o f
each species w ere estimated and adjusted to relativ e cover value ( sum 100% in each
lay er) . The diameter a t breast heigh t of the t rees, the stem diameter at g round level and
the heigh t o f the shrubs w ere reco rded using st ring and ruler. The impo rtance value o f
t rees ( IV t ) w as calculated acco rding to ( 1):
IVt= ( relativ e cover+ relativ e f requency+ relativ e dominant ) /300 ( 1)
w here the relativ e cover is the cover of each species divided by the to tal cover of all
species, the relative frequency is th e percentag e of plots ( out of 28) in w hich each species
occurs, and the relativ e dominant equals the total stem area of each species at breast
height divided by the to tal stem a rea o f all species at breast heigh t.
The importance value o f shrubs ( IV S ) was calcula ted by acco rding to Zhang & Shang-
guan ( 1994) as:
IV S= ( rela tiv e height+ relativ e cover) /200 ( 2)
w here the rela tiv e height is the total height of each species divided by the sum of heights o f
all shrub species.
The relativ e g round cover o f each herb species w as added, and the cumulativ e value
used as a numerical index.
Data analy sis
Ordered plot clustering
The O PC procedure divides n o rdered plo ts into m g roups by minimizing hetero geneity
w ithin each g roup acco rding to the gold- pa rtitioning method ( Fisher s method ) ( Fisher
1958, Fisher& Ness 1971) . It can be described as follow s:
Data set containing p species in n plo ts have been collected in the field, deno ted ma-
trix X. m may be chosen as in stepw ise clustering ( Zhang& Shangguan 1994) , w here m is
set equal to the number o f v egeta tion types t radi tionally discerned.
The index o f heterogenei ty wi thin an arbi tra ry g roup, D( i , j) , containing the j- i+ 1
plo ts ( f rom plot i to plot j) i s described as:
D( i , j)=∑j
k= i
∑p
l= 1
( xkl- x-l )
1
( xk1- x-1 ) ( 3)
w here Xk1 is the impo rtance value of kth species in l th plot , x-1 i s the mean column vecto r o f
the plot g roup.
An erro r function Δ〔 f ( m , n)〕 of the classi fica tion w hen n plo ts a re divided into m
g roups is defined as:
Δ〔f ( m , n)〕=∑m
t= 1
D(it , it+ 1- 1) ( 4)
w here it , it+ 1- 1 a re the fi rst and the last sequence numbers of the each g roup. The low er
4494期　　　　　　　　　　 Feng Zhang a l et: The vertica l belts o f natura l v egeta tion
D(it , it+ 1- 1) is, the mo re bet ter th e classi fica tion.
Let the ini tial classification be denoted f0 ( m , n) , and denote the erro r function o f this
classi fica tion Δ〔 f0 ( m , n)〕 . The minimal error functionΔ〔 f0 ( m , n)〕 can likewise be ob-
tained using the recurrence formula:
Δ〔f0 ( m, n)〕= min{Δ〔 f0 ( m- 1, j- 1)〕+ D( j, n) } ( m < j< n) ( 5)
The upper and low er limits of each plo t g roup can be found by minimizingΔ〔f0 ( m , n)〕
fo r each m < n- 1.
TW IN SPAN
Based on recipro cal average o rdina tion, TW IN SPAN ( Hill 1979) is reg arded as one o f
the best hierarchical classi fica tion methods, w hich i ts procedure can be found in Hill s
( 1979) paper. The data set w as also analyzed by TW IN SPAN, and the results of the tw o
methods were compared.
Results
The 41 plo ts were div ided into 5 plot g roups in w hich the first tw o g roups w ere be-
longed to the first v ertical belt in the case o f O PC and by TW IN SPAN ( Table 1) . The five
vertical bel ts o r sub- belts a re described as:
Table 1　 The vertical belt division of the carpophytes flora in 41 situated along an ele-
vation gradient f rom 800 to 2831m a. s. l. in the Guandi Mountains in
Shanxi, North China as produced by OPC and TWINSPAN
V er tical belt s and sub- belt s OPC
Plot No.
TWINSPAN
G1
G2
G3
G4
G5
1— 13
14— 17
18— 21
22— 37
38— 41
1— 4, 6— 10, 12, 13, 41
14, 16, 17, 19
15, 18, 20, 21, 36
22— 35, 37
5, 11, 38— 40
1. Deciduous broadleave fo rest bel t ( 800- 1600m a. s. l. ) . Deciduous broadleaved
fo rests are the zonal v egetation type o f low er Guandi Mountains, in w hich the representa-
tiv e vegeta tion type is Form. Quercus l iaotungensis; in addition, Fo rm. Pinus tabulae-
form is can be found frequently. Fo rm. Quercus liaotungensis is considered as the climax
communi ty at this alti tude, but due to repeated human interference, the primary vegeta-
tion types a re st rongly reduced and frequent ly replaced by seconda ry deciduous
broadleaved forest, temperate coni ferous forest , shrub and g rassland. Th e belt is com-
posed of 2 sub- belts:
1. 1 ( G1 ) Tempera te coni ferous fo rest sub- blet ( 800- 1400m a. s. l. ) . Fo rm. Pinus
tabulaeform is i s the representativ e vegetation type of this sub- bel t ei ther as y oung natu-
rally recruited seconda ry forest or planted since the 1950s. Quercus liaotungensis i s f re-
quently found in this Fo rm. as an accompanying species. The primary vegeta tion in the
sub - belt is Form. Quercus liaotungensis . Mo reover, Fo rm. Platy cladus oriental is i s
450 植　　物　　研　　究　　　　　　　　　　　　　　　 17卷
found on limestone soi l. How ever, sh rubs and g rasses are also common, e. g. , Rosa xan-
thina , Ostryopsis davidiana, Vitex negundo var. heterophylla , Spiraea trilobata, Hip-
pophae rhamnoides , Ziziphus jujuba var. spinosa , Bothriochloa ischaemum and Artemisia
spp. V arious cul tiva ted plants a re a lso commonly found, e. g. , Zea mays , Setaria ital ica
etc. .
1. 2　 ( G2 ) Deciduous bro adleaved fo rest sub- bel t ( 1400- 1600m a. s. l. ) . The rep-
resenta tiv e v egetation belong s to Fo rm. Quercus liaotungensis. Due to log ging and picking
w ood fo r fuel, Quercus l iaotungensis i s o ften stunted. M oreover , mix ed fo rests w ith Quer-
cus liaotungensis and Pinus tabulaeformis occur lo cally. Af ter the dest ruction of the prima-
ry fo rests, this area is f requently invaded by Populus davidiana and i ts accompanying
species. Furthermo re, Fo rm. Hippophae rhamnoides can also be found in most arid slopes
w ith light soil. The majo r crops occurring in this sub - bel t are Avena nuda, Solanum
tuberosum , Vicia f aba and Linum usitat issimum.
2. ( G3 ) Coni ferous and broadleaved mixed- fo rest bel t ( 1600- 1750m a. s. l) . This
belt is lo cated a t the t ransi tio n f rom decidouous bro adleaved fo rest to cold - temperate
coni ferous fo rest vegetation. The major v egetation types consist of Fo rm. Larix principis
- rupprechtii , Form. Picea wilsonii , Form. Picea mayeri , Form. Betula platyphylla and
Form. Populus davidiana; the lat ter tw o fo rmations occur where the o riginal coniferous
fo rests have been dest royed. M oreover , Fo rm. Populus cathayana can be found in stream
banks.
3. ( G4 ) Cold- temperate coniferous fo rest bel t ( 1750- 2600m a. s. l. ) . This is the
predominant v egeta tion type in Guandi Mountains. The major v egetation types a re com-
posed of Fo rm. Larix principis- rupprechtii on southern slopes, Fo rm. Picea wilsonii and
Form. Picea meyeri in northern slopes. All th ree forma tions show clo se resemblance to
each other in the mountain. Fo rm. Larix principis- rupprechtii covers the larg est area.
4. ( G5 ) Subalpine shrub and meadow belt ( 2600- 2831m a. s. l. ) . The predominant
v egetation types a re Fo rm. Carex spp. and Form. Kobresia spp. . In this bel t, they cover
lag er areas tha t a re used a s pastures during summer and autumn. Mo reover, Fo rm. Cara-
gana jubata and Fo rm. Potentilla fruticosa can be found locally.
Discussion
The vertical belts o f Guandi Mountains w ere studied by Fu and Li ( 1976) , which
w ere as follow s: 1. open fo rest , shrub and cul tiv ated land bel t ( 800- 1400m a. s. l. ) ; 2.
coni ferous forest belt in hill and middle mountains ( 950- 1700m a. s. l. ) ; 3. small-
leaved forest belt ( 1600- 2150m a. s. l. ) ; 4. coni ferous forest belt ( 1850- 2600m a. s.
l. ) ; 5. suba lpine shrub and meadow belt ( 2600- 2785m a. s. l. ) . How ever, the resul t o f
O PC is di fferent f rom that of Fu and Li ( 1976) due to that the lat ter has some disadvan-
tages. Fi rstly , open fo rest , shrub and cultiv ated land belt is no t co rrect ly. Acco rding to
the principle of v ertical belt parti tio ning (Wu 1980) , the belt par titio ning should be ac-
corded wi th prima ry vegetation. If prima ry vegetation is dest roy ed, i ts characteristics and
4514期　　　　　　　　　　 Feng Zhang a l et: The vertica l belts o f natura l v egeta tion
t races should be explo red, and then vertical belt i s named af ter the primary vegeta tion.
Thus, open fo rest , sh rub and cultiv ated land having second vegetation feature evidently is
no t reg arded as the name o f v er tical belt. Secondly , small- leaved fo rest belt i s not ex act-
ly. In fact, i t i s no t exist that small- leaved fo rest is composed of Betula platyphylla and
Populus davidiana as dominants. Af ter co ld - temperate coniferous fo rest i s broken,
Form. Betula platyphyl la and Fo rm. Populus davidiana appear as pioneer communities,
and then they fo rm coniferous and broadleaved mixed- forest landscape w ith Fo rm. Larix
principis- rupprechtii , Form. Picea wilsonii and Fo rm. Picea meyeri tog ether, therefore,
w hich should be named coni ferous and broadleaved mixed - fo rest bel t. Thirdly, the
ranges as some bel ts w ere not in accordance wi th the current po si tio n of the belts, e. g. ,
coni ferous fo rest belt and subalpine sh rub and meadow belt.
The vertical belt pa rtitioning of a mountain into di fferent forma tions commonly dif fer
st rongly betw een investiga to rs and methods. Fo r example, the belts of the Luya M oun-
tain, Shanxi, North China w ere di fferent ly parti tio ned by Fu and Li ( 1976) and Zhang
( 1989) , bo th nomencla ture, component species of some belts, and latitudinal seg regation
a re conco rded. Apart f rom the co ld- temperate coni ferous fo rest belt ( 1750- 2600m a. s.
l. in easter n slopes) and the subalpine shrub and meadow belt ( 2450- 2772m a. s. l. in
w estern slopes) , the o ther v ertical belts a re dif ferent f rom each o ther, for instance, the
belt betw een 1300m and 1600m a. s. l. is named as the sh rub, steppe and cultiva ted vege-
tation bel t by Fu and Li ( 1976) , but is named as the deciduous broadleaved fo rest bel t
( 1350- 1700m a. s. l. in west slopes) and the forest- steppe belt ( 1300- 1500m a. s. l.
in eastern slopes) by Zhang ( 1989) . M oreover , the coniferous and broadleaved mixed -
fo rest belt is located betw een 1500- 1800m a. s. l. by the former autho r, and betw een
1700- 1850m a. s. l. by the lat ter. These div erg ent results can be avoided wi th the verti-
cal bel ts parti tion by OPC.
In o rder to compa re OPC with TW IN SPAN , a 5× 5 contingency table ( Table 2) w as
Table 2　 The 5× 5 contingency table constructed to compare the classifications of the
vertical belts partition of GuandiMountains, Shanxi, North China as gener-
ated by OPC vs. TWINSPAN
O PC TWIN SPAN
1 2 3 4 5
1
2
3
4
5
11
0
0
0
2
0
3
1
0
0
0
1
3
1
0
0
0
0
15
0
1
0
0
0
3
constructed using the classi fications generated by each method, signi ficance of associa tions
betw een classi fica tions w as tested by theχ2- test of independence ( Feoli & Orlo ci 1979,
Wildi 1989, Zhang & Shangguan 1996) , χ2= 80. 58 ( p < 0. 001, df= 16) indicating very
452 植　　物　　研　　究　　　　　　　　　　　　　　　 17卷
closely simi lar results by the two methods. How ever, i f w e look at the result by
TW IN SPAN, some unreasonable results can be found. Fo r example, plot 5 a t 1000m a.
s. l. a nd 11 at 1300m a. s. l. are mainly composed of Fo rm. Bothriochloa ischaemum and
Form. Artemisia spp. , respectiv ely. In practice, these fo rmations can be found in the
tempera te coniferous forest sub- belt a s a resul t o f human disturbances. Under natural
conditions, their component species most ly w ould ra ther appear in steppe zone, but they
a re fell into subalpine sh rub and meadow bel t by TW INSPAN instead of falling into tem-
pera te coni ferous forest sub- bel t. Mo reover, the par ti tio ning results of plo t 15, 19, 36
and 41 by TW INSPAN were also unrea sonable.
Al l non- hierarchical ag glomerative algo ri thms, except O PC, sha re one of the signi fi-
cant characteristics that the posi tions for any tw o o r more a rbit rari ly chosen plots during
clustering process is equali ty and the probabi li ty fo r them to finally fall into same g roup is
equal; moreover, the result of classification has maximal homogenei ty wi thin g roup and
calculation is easier and quicker. How ever, not only the result o f O PC has maximal homo-
genei ty wi thin g roup and calcula tion is easier and quicker, but O PC has another feature
w hich the posi tions fo r any tw o or mo re arbi trarily cho sen plots during clustering process
is not equality and the probability fo r them to finally fall into same g roup is no t equal.
O PC is ca rried out acco rding to criterion of plo t order in space o r time sequence f rom the
fi rst to last one, therefore, the resul t of O PC accords w ith vegetation distribution. It i s
show ed that O PC can be applied to the div ision of organism development stages and of v eg-
eta tion successiv e series as w ell as the parti tio ning o f v ertical belts o f v egeta tion.
Acknowledgement
We thank Dr Irene Bisang for helpful comments on the manuscript. The pro ject i s
part ly financed by Shanxi Returned Oversea Scholar Fundation, China.
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454 植　　物　　研　　究　　　　　　　　　　　　　　　 17卷
刘家熙: 北京铁线蕨属孢子形态的研究 图版Ⅰ
Liu Jia- xi: Studies on the Spo re Mo rpholog y o f Adiantum L . in Beijing Pla teⅠ
See explanat ion at the end of text
刘伟华等: 发根土壤杆菌 Ri质粒对黄瓜进行遗传转化的研究 图版Ⅰ
Liu Wei- hua et al: Genetic T ransfo rmation of Cucumbe r by Ag roacterium Rhizogenes With Ri- Plasmid
Pla teⅠ
See explanat ion at the end of text
刘家熙: 北京铁线蕨属孢子形态的研究 图版Ⅰ
Liu Jia- xi: Studies on the Spo re Mo rpholog y o f Adiantum L . in Beijing Pla teⅠ
See explanat ion at the end of text
刘伟华等: 发根土壤杆菌 Ri质粒对黄瓜进行遗传转化的研究 图版Ⅰ
Liu Wei- hua et al: Genetic T ransfo rmation of Cucumbe r by Ag roacterium Rhizogenes With Ri- Plasmid
Pla teⅠ
See explanat ion at the end of text