全 文 ：第 20 卷　第 1 期　　　　　　　　　植　　　物　　　研　　　究 2000 年　1 月
Vol.20　No.1　　　　　　　BULLETIN OF BOTANICAL RESEARCH Jan., 　2000
北京东灵山地区辽东栎林种群空间分布分形分析
祖元刚　赵则海　丛沛桐　张文辉　陈伯林
(东北林业大学森林植物生态学开放研究实验室 ,哈尔滨　150040)
摘　要　通过植物个体的坐标点与模拟冠幅的分形维数的分析 ,对辽东栎林内不同
种群沿海拔梯度变化的空间分布格局和种群动态进行了比较和讨论 。结果表明:模
拟冠幅分形分析方法更适于分析具有大小不等 、复杂多样的冠幅的植物个体空间分
布格局。随着海拔的升高 ,不同种群的空间占据能力也随之变化 。辽东栎种群的空
间分布占绝对优势地位 ,分形维数可达 1.9811;五角枫种群则逐步下降 ,分形维数
最低为 0.1170。低海拔山坡六道木种群空间占据能力较强 ,高海拔山坡照山白种
群有较大的空间占据能力 。在一定的环境条件下 ,不同的种群可能具有相近的空间
占据能力 ,但对乔木层与灌木层来说 ,相同的分形维数的内涵是不同的 。冠幅的分
形维数作为表征植物种群空间占据能力的工具 ,是种群动态分析和种群分布格局研
究的的重要指标之一 。
关键词　分形维数;冠幅;空间占据能力;辽东栎林
FRACTAL ANALYSIS ON SPATIAL
DISTRIBUTION PATTERNS OF POPULATION FROM
QUERCUS LIAOTUNGGENSIS FOREST IN
DONGLINGMOUNTAIN , BEIJING CHINA
ZU Yuan-gang　ZHAO Ze-hai　
CONG Pei-tong　ZHANG Wen-hui　CHENG Bai-lin
(Open Research Labo rato ry of Forest Plant Ecolog y , Nor theast Forestry University , Harbin , 150040 , China)
Abstract 　 In this paper , the coordinate positions and crown breadth of plant individ-
uals have been analyzed by using their f ractal dimensions.The distributon patterns of
population and populat ion dynamic in the Quercus l iaotunggensis forests at different
altitudes are compared and discussed.The method of f ractal analysis of simulation
crow n breadth is considered as a bet ter method of studying spatial dist ribution of plant
This w ork w as supported by the state Natu rel Soience Foundation of R.P.China No.39893360收稿日期:1999-9-10
individuals w ith dif ferent and complex crow n breadth.As alt itude rises , the capacities
of spatial occupat ion of different populations are variable.Q.liaotunggensis popula-
tion maintains high level , w ith a f ractal dimension reached 1.9811;Acer mono popu-
lation go down w ith a f ractal dimension is minimum , 0.1170.Whereas Abelia bi f lora
population is strong at low altitude , Rhododendron m icranthum populat ion has
stronger capacity of spatial occupation at high altitude.On the given environmental
conditions , the capacity of spatial occupation of different populations become probably
similar.However , the same fractal dimension betw een arbor and shrub layer implies
different meaning.The fractal dimension of crow n breadth , imply ing the capacity of
spatial occupation of plant population , is one of the important indices in process of dy-
namic analysis and population dist ribution pattern.
Key words　fractal dimension;crow n breadth;spatial occupation capacity;Quercus
liaotunggensis.
1.Introduction
The study of spatial dist ribution pattern of different plant populations is an important re-
search field of the phy toecology at present time.The capacity of spatial occupation of different
plant individual has a large dif ference in the phytobiocoenose and its spatial dist ribution is in
possession of non -linear characters because their characters of grow th and development and
habitat conditions have differences in communi ty.The component of plant individual , crow n
structure and horizontal dist ributions of plant populations are in possession of f ractal charac-
ters〔1 , 2〕.Although there are lots of bigger dif ferences among the individuals of dif ferent popula-
tions or those of different time of g row th and development in the same population , their mo r-
phosis are in possession of self-similarity on variable scale and scale invariabili ty in a given
scale range.The fractal analy sis indicats that the spatial distribut ion pattern of populations is
possession of conspicuous spatial heterogenei ty in a given scale range〔3 , 4〕.Ma Keming &Zu
Yuangang had studied the horizontal dist ribution pat tern of Picea korainsis population by the
fractal analy sis method of average crown breadth
〔5〕.The complexity of crow n breadth s size
and shape of arbor o r shrub need to be solved when we utilize some fractal analysis methods to
study the spatial dist ribution pat tern of population.The fractal analysis method of average
crow n breadth isn t fit to describe capaci ty of spatial occupation of plant population with dif fer-
ent crow n breadth.This paper discussed the method of f ractal analysis , which can simulate
horizontal projection of crow n breadth of plant individuals.The spatial dist ribution pattern of
six impo rtant arbor and shrub populations in the Q .liaotunggensis broad leaves forest in
Dongling M ountain of Beijing China was studied by this method.The aim is to reveal the dis-
tribution characters of dif ferent populations in the Q .l iaotunggensis fo rest and explain the ca-
pacity of spatial occupation.
1131 期　　　　　　　　祖元刚等:北京东灵山地区辽东栎林种群空间分布分形分析
2.Methods
The Q .liaotunggensis broad leaves forest distributes sonnenseite , semi-sonnenseite and
semi-shaddy slope from altitude 800m to 1600m in the area of Beijing Dongling Mountain〔6〕.
Several typical sample plots of Q .liaotunggensis broad leaves forest were disposed recent ly by
Xiaolongmen forestry farm , 40°00′N , 115°26′E.The sample plots lay in semi-sonnensei te
w ith 40 deg ree of slope , alti tude f rom 1175m to 1315m.5 quadrats of 6×10m2 were selected
and their number marks of quadrat are 1 , 2 , 3 , 4 , and 5 as alti tude.The parameters of every
individual of arbo r or brush in the quadrat such as coordinates , crown breadth , chest diameter ,
base diameter and height etc.which w ere recorded.The simulation process of individual crow n
breadth of plant population had been completed wi th computer.The box fractal dimension
could be calculated by equat ion as follow s:
Db =-l i m
m※0
log(N)
log(m)
　　Db is box f ractal dimension;N is lattice number of crow n breadth occupation of individu-
als of plant population;m is scale.In this paper , Db is intercept the linear reg ression of log
(m)and log (N)in order to simplify calculation.Because of the minimum crown breadth is
g reater than 0.1m in field investigation , the calculating step size of fi tting crow n breadth set-
tled on 0.1m.
3.Results and discussion
3.1　Comparing of f ractal analy sis results betw een methods of coordinate point and simu-
lation crow n breadth.
In this paper , taking characters of ho rizontal dist ribution and fractal results betw een Q.
liaotunggensis population and L .bicolor population in sample plo t 5 as an example , we w ant
to explore some dif ferences of f ractal methods of coo rdinate point and simulation crow n
breadth.In Fig.1(a)and Fig .1(c), the individual quantity of Q .liaotunggensis population is
less than that of L .bicolor population in horizontal coo rdinate point graph.The fractal dimen-
sion of Q.liaotunggensis population is 0.3059 and the f ractal dimension of L .bicolor popula-
tion is 0.9583 w ith calculating method of coordinate point (Fig.2(a)and(b)).This fractal
analy sis result seems to indicate L .bicolor population is in possession of st ronger capacity of
horizontal spatial occupation than Q .liaotunggensis populat ion.In fact , i t can not fi t the
practical situat ion on the nature condition.And yet the f ractal analysis method of simulation
crow n breadth has used simulation crow n breadth(see Fig.1(b)and(d), Fig2(c)and(d)),
i ts f ractal analy sis result almost coincide w ith actual observat ion recording.The fractal dimen-
sion of Q.liaotunggensis population reaches 1.3784 and that of L .bicolor population reaches
1.2264 , which indicates the capacity of horizontal spatial occupation of Q.liaotunggensis
population is st ronger than that of L .Bicolor.It is clear that the fractal analy sis method of
adopting coo rdinate point of spatial dist ribution is unsuitable for the plant individuals with dif-
114 植　　物　　研　　究　　　　　　　　　　　　　　　20 卷
ferent crow n breadth.Although the quantity of Q .l iaotunggensis population is less than that
of L .Bicolor , the spatial occupation of Q.liaotunggensis population is bigger than that of
L .Bicolor because the individual of Q.liaotunggensis possesses bigger crow n breadth than
that of L .Bicolor.So it is inevitable that the fractal dimension of Q .liaotunggensis popula-
tion is bigger than that of L .Bicolor by using f ractal analy sis method of simulat ion crow n
breadth.In general , the f ractal analy sis method of simulation crown breadth is bet ter to reveal
some law s of ho rizontal distribution pat tern of arbor and shrub population.Certainly , in order
to study the spatial heterogeneity and capacity of spatial occupation , we can adopt the fractal
analy sis method of coo rdinate point to calculate f ractal dimension.Usually its conclusion is de-
pendable.Especially some herbaceous monoco tyledon plants that it is possession of small crow n
breadth w hich can be igno red such as sedge family , g ramineae may be studied as well.
3.2　Change of spatial occupation capacity of different populations at altitudes in Q .Liao-
tunggensis forest.
The altitude variance is small in the sample area in which the Q .Liaotunggensis is domi-
nant species.There is dense vegetation and its canopy densi ty is more than 85 percent in the
sample area.There are some arbor species such as F .Rhynchophyl la , A .mono and a small
amounts of auxiliary species such as Betula dahurica , B .Platyphyl la , Cory lus mandshurica
and Prunus dav idiana that distributes in arborous layer.A great variety of shrubs distribute in
the sample plots.
Fig.1　Comparing between distribution of coo rdinate point and tha t of simulation crown breadth in quadrat
5.
(a)coordinate point of Q.laiotunggensis(b)simulation crow n breadth of Q .Laiotunggensis(c)coordinate point
of L .Bicolor (d)simulat ion crown breadth of L .Bicolor
Among them , A .bi f lora , L .Bicolor and R .micranthum are the best representativ-
eness and there distribute any other shrub populations such as R .micranthum , S .Triloba-
ta , Deutzia parvi f lora in sample plots.In this paper , three arbo r populations(i.e.Q .Liao-
tunggensis , F.Rhynchophy lla and A.mono)and three shrub populations(i.e.A.bi f lora ,
L .Bicolor and R .Micranthum)were studied by the f ractal analy sis of simulation crow n
breadth (see Fig.3).Q.Liaotunggensis population almost covers in the whole quadrat and its
fractal dimensions are 1.9396 at 1175m , 1.8785 , at 1210m and 1.9811 at 1280m respective-
1151 期　　　　　　　　祖元刚等:北京东灵山地区辽东栎林种群空间分布分形分析
Fig.2　fractal dimension comparing o f fractal analysis of coo rdinate point and of simulation crow n breadth
in quadra t 5
(a)fractal analysis of coordinate point of Q.laiotunggensis
(b)f ractal analysis of coordinate point of L .Bicolor
(c)f ractal analysis simulation crow n breadth of Q.Laiotu nggensis
(d)f ractal analysis of simulation crow n breadth of .Bicolor
ly .Q .Liaotunggensis population is in possession of dominance of spatial occupation capacity
in the w hole sample area.There are some characters such as ai r moist , slow wind velocity and
thick soil at low altitude (i.e.at between altitude 1175m and 1201m).Fractal dimension of
each population varies generally f rom 1.0000 to 1.7000.Therefore , those populations have
strong spatial occupation capacity so that the canopy density reaches more than 90 percent.
Fractal dimensions of F .Rhynchophylla and A .Mono are 1.1099 and 1.0630 , which indi-
cates their spatial occupation capaci ties are w eak and are suppressed strongly by some effects of
the masked of Q.Liaotunggensis.The fractal dimension of Q .Liaotunggensis decreases ,
reaching 1.3907 and creating bet ter condit ion for F.Rhynchophyl la population w hich invades
arbor layer at alti tude 1245m.Because of the co-mask action of Q .Liaotunggensis and F .
Rhynchophyl la , f ractal dimensions of A .mono and A.bi f lora populations decrease drastical-
ly while spatial dist ribution of L .Bicolor and R .micranthum which appear in quantity at al-
titude 1245m is depressed to a large ex tent.At altitude 1280m , Q.Liaotunggensis and F .
Rhynchophyl la populations still exit in the arbo r layer , but the spatial occupation capaci ty of
F .Rhynchophylla population declines in a w ide range w ith ef fect of Q.Liaotunggensis popu-
lation(its f ractal dimension is maximum).Although fractal dimension of A.mono increases a
116 植　　物　　研　　究　　　　　　　　　　　　　　　20 卷
lit tle , its capacity of spatial occupation is still weak and it dist ributes under arbor layer.There
is no distribution of A .bif lora population.The fractal dimension of L .Bicolor populat ion de-
motes to the least point of 0.2585.Because the microenvi ronment changes such as small air hu-
midity , dry and meager soil and some naked rock , the spat ial distribut ion of plant population
appeares some variation at the top (at altitude 1315m).The fractal dimension of F .Rhyn-
chophyl la is 1.7953 , exceeds Q.Liaotunggensis and become dominant species again.The
fractal dimension of Q.Liaotunggensis population is 1.3874 , the individual s plant height is
no less than 6m , it s crow n breadth is no less than 7m and has severe insect pest phenomenon.
Although there may have a lo t of reasons to result in descending of spatial occupation capacity of
Q.Liaotunggensis , the strong competition between F .Rhynchophyl la and Q.Liao-
tunggensis , pejorative circumstance and insect pest are the impo rtant reasons.The fractal di-
mension of A.mono descends to its least point of 0.1170.A.mono population is almost de-
prived of spatial occupation capacity under the poor habi tat environment and interacting among
F .Rhynchophy lla , Q.Liaotunggensis and dense brush.Fractal dimensions of L .Bicolor
and R .micranthum populat ion are almost the same , they are 1.2364 and 1.2264 , which
means thei r spatial occupation capacitys are almost the same , too.The height of brush can
reach to 3m;all of the brush populations almost f ill up gaps under arborous layer.
3.3　Comparison of fractal dimension implication of arbor population and shrub population
The plant community is an entirety.There exists interrelation among dif ferent popula-
tions.Fractal analysis of simulation crow n breadth reveals capacity of spatial occupation of dif-
ferent populations.In quadrat 5 , a great number of individuals of L .Bicolor population dis-
tribute out of crow n breadth of Q .Liaotunggensis (see Fig.1(b)and (d)).Also there are
lots of overlapping parts between tw o species , the mo re overlap , the more competi tion of inter-
species.The degree of the interaction betw een arbor and shrub is different.Arbo r layer popula-
tion play s a leading role because its crow n breadth is bigger.The spatial distribution of shrub
population is rest ricted by arbor populat ion.The fractal dimension of L .Bicolor and that of
Q.Liaotunggensis are similar to a great extent in quadrat 5(see Fig.2 c and d), which seems
to indicate that their spatial occupation capacities may be approximate , but the implications of
both f ractal dimensions are different.By the same fractal dimension , the Q.Liaotunggensis is
in possession of bigger crow n breadth but a few of individual quantity , and the spatial occupa-
tion capacity is litt le affected by shrub population.It is distinct that the individuals of L .Bi-
color population dist ribute dispersively w ith g reat effects of arbor layer.
3.4　The fractal analysis of distribution dynamic of dif ferent populations at altitudes
The condition of circumstance changes gradually f rom bo ttom to top.F.Rhynchophylla
population may be more adaptive to deteriorat ive circumstance than Q .Liaotunggensis with
increasing f ractal dimensions at alti tudes (see Fig.3).The dominant position of Q .liao-
tunggensis will be substituted by the o ther populations , F .rhynchophylla w ill increase g radu-
ally w hile the spatial occupat ion capacity of A .mono becomes weak successively.
The spatial dist ribution of shrub populations changed widely in all of the quadrats.The
1171 期　　　　　　　　祖元刚等:北京东灵山地区辽东栎林种群空间分布分形分析
　　Fig.3　Variation of fractal dimensions of simulation
crow n breadth of different populations in Q .
L iaotunggensis forests along altitudes.
　　—◎— Q.Liaotunggensis
—◆— Fraxinus rhynchophyl la
—■— Acer mono
— — A belia bi f lora
—+— Rhododend ron micranth um
—★— Lespedeza bicolor
variabili ty of A .bif lora population is big
and i t has w ider spatial dist ribution under
dense arbo r layer at low altitude.The R .
micranthum population is apt to adapt to
dry ci rcumstances and it substi tutes fo r
A.bif lora w ith high capacity of spatial
occupation at high altitude.The impo r-
tant reasons of decreasing of A .bi f lora
are st rong spatial dist ribution capacity of
Q .Liaotunggensis and the interspecies
competi tio n betw een Q.Liaotunggensis
and F .Rhynchophyl la at middle alti-
tude.The spatial dist ribution of arbor lay-
er is almost of no large change because the
interspecies competi tion betw een Q.
Liaotunggensis and F .Rhynchophylla
f rom 1245m to 1315m.Therefo re , the
spatial dist ribution of R .micranthum is
stable.
4.Conclusion
The results of f ractal analy sis by us-
ing coordinates and simulation crow n breadth indicate the method of f ractal analysis of simula-
tion crow n breadth is the bet ter tools to describe some characters of spatial distribution pat tern.
And i t adapts to study the spatial distribut ion pat tern of plant population w ith dif ferent and
complex crow n breadth.In addition , in order to study the spatial heterogenei ty and spatial oc-
cupation capacity , we may adopt the f ractal analysis method by using coordinate point to calcu-
late f ractal dimension.Usually i ts conclusion is dependable.Especially some herbaceous mono-
co tyledon plants w ith small crow n breadth w hich can be ignored such as sedge family ,
g ramineae may be studied as well by this method.
The capacities of spatial occupation of dif ferent populations vary at altitudes.Fractal di-
mensions of plant populations in arbor layer o r that in shrub layer may be compared in o rder to
explain thei r capacit ies of spatial occupation.For arbo r and shrub populations , the f ractal di-
mensions of arbor layer can not be compared direct ly with that of shrub layer , the same fractal
dimension represents dif ferent characters of spatial dist ribution.
The capacity of spatial occupation of plant species varies as the changing of environment
condition.Fractal dimensions of plant populations are determined by the biological characters
and envi ronments , etc.The capacity of spatial occupation of shrub populations is affected
strongly by arbor populations.
118 植　　物　　研　　究　　　　　　　　　　　　　　　20 卷
Reference
1.Morse , D.R., Law ton , J.H., Dodson , M.M.&Williamson M .H.Fractal dimension of vegetat ion and the dist ribut ion
of arthropod body lengths.Nature , 1985 , 314:731～ 733
2.Zeide , B.Primary unit of the t ree crown.Ecology , 1993 , 74(5):1598～ 1602
3.Zu Yuangang , Ma Keming &Zhang Xijun.A fractal method for analysi s spatial heterogeneity of vegetat ion.Acta Ecologica
Sinica , 1997 , 17(3):333～ 337
4.Ma Keming , YeWanhui and Sang Weiguo et al.Study on plant communi ty diversity in Donglingshan mountain , Beijing Chi-
na(X):β-diversity and f ractal analysis on t ransect on dif ferent scales.Acta Ecologica S inica , 1997 , 17(6):626～ 634
5.Ma Keming &Zu Yuangang.The descript ion of vegetative dist ribut ion at mini-scale by f ractal theory.In:Li C hongjing &
Wang Meixing et al.(Edi tors).The f ractal theory and application.Yunnan Univercity Press , Kunming , 1996 , 112～ 113
6.Ma Keping , Chen Lingzhi and Yu Shunli et al.The major community types in Dongling mountain region.In:Chen Lingzhi
&Huang Jianhui(Edi tors), The study of st ructure and function of ecosystem in the w arm temperate zone of Northern Chi-
na.Science Press , Beijing , 1997 , 56～ 72
1191 期　　　　　　　　祖元刚等:北京东灵山地区辽东栎林种群空间分布分形分析