Analysis of root fractal character in the hinterland of

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1、免费查阅精品论文Analysis of root fractal character in the hinterland ofTaklimakan desert, ChinaYang Xiaolin a, b*，Zhang Ximinga，Li Yiling a,b，Xie Tingtinga,b，Wang Weihua a,b，Ma Jianbinga,baXinjiang Institute of Ecology and Geography，Chinese Academic of Science，Urumqi(830011)bGraduate University of the Chine

2、se Academy of Science，Beijing（100039)E-mail：xiaolin4577AbstractFractal geometry is a potential new approach to the analysis of root architecture which may offerimproved ways to quantify and summarize root system complexity as well as yield ecological and physiological insights into the functional re

3、levance of specific architectural patterns. Otherwise, fractal analysis is a sensitive measure of root branching intensity and fractal dimension expresses the space filling properties of a structure. The objective of this study was to find out the fractal characteristics of root system in the hinter

4、land of Taklimakan desert in China. The whole root system of two naturally species was excavated and exposed with shovels in 2007.These species includes: Tamarix taklamakanensis, alligonum roborovskii.A one-factorial ANOVA with species as factor showed a highly significant effect on fractal dimensio

5、n, the difference of fractal dimension indicates the otherness of root branching pattern.The regression between link diameter and q, a were not significant for either species .So the ratio of the sum of root cross-sectional areas after a bifurcation to the cross-sectional area before bifurcation, a

6、and the distribution of the cross-sectional areas after bifurcation ,q are the ubiquitous characters of root system. In this paper ,we find the significant linear relationships between the diameter after branching and root length, biomass respectively, because root branching is self-similar and bran

7、chingrules are the same for roots of all sizes, root lengths，root biomass for the root systems of whole treescan then be estimated by measuring the diameter of each root at the base of the trunk or diameter after branching. The study showed that diameter of each root at the base of the trunk or diam

8、eter after branching are effective indexes which can measured easily to estimate the root lengths, biomass and other parameters of root architecture.Keywords: Taklimakan desert，root system，root architecture，fractal dimension，root length，rootbiomassPlant root systems are a major carbon sink as uptake

9、 organs for water and nutrients, and the interface between plants and the soil system, roots govern many competitive interactions (Fitter, 1987, 1991; Casper and Jackson, 1997). At a larger scale, roots influence processes important at the ecosystem level, such as soil erosion and carbon cycling (An

10、drew D. Richardson and Heinrich Zu Dohna, 2003). The size, structure, and extent of root systems control many of these functions, so it became a hotspot in underground ecology research (J S Huo, 2004).However, root systems of plants in general and trees in particular are notoriously difficult to mea

11、sure because of the difficulty in excavating large volumes of soil (Bhm W., 1979). Estimation of root lengths and root biomass for tree root systems using conventional methods is invariably a difficult and laborious task (Smith, D.M., 2001). How to research the root architecture by relating easily m

12、easurable parameters were attended in recent literatures (Andrew D. Richardson, 2003; Armin L. Oppelt, 2001; Eduardo Salas, 2004)The root architecture reflects the plants adaptive ability to make best use of unevenly distributed soil resources (Fitter, 1994). There are various means for determining

13、the size of root systems (A. Eshel,1998; Box, 1996) and the principles of fractal geometry seem appropriate for the description of rootsystems because the repetitive branching of roots leads to a certain degree of self-symmetry. Such*Corresponding author: Xinjiang Institute of Ecology and Geography,

14、 Chinese Academy of Sciences, No. 40-3South Beijing Road, Urumqi 830011, China.- 9 -self-similarity is a fundamental characteristic of fractal objects (A. Eshel, 1998).The self-similarity principle defines an object that maintains similar form over a range of scales. This principle applied to a tree

15、 root system predicts that roots follow the same bifurcation pattern from proximal roots to the smallest transport roots. The basic parameters of fractal root models describe the ratio of the sum of root cross-sectional areas after a bifurcation to the cross-sectional area before bifurcation, , and

16、the distribution of the cross-sectional areas after bifurcation, q (Van Noordwijk et al., 1994; Louise Y. Spek, 1994).Fractal dimension is an important parameter which reflects the difference of root branching status and extension of root system. P L Yang (1994) proposed that the fractal dimension c

17、hanges with age and environment condition, and fractal dimension increased with development degree, Reversely, simpler the root branching, lower the fractal dimension. D.M. Smith (2001) concludes that the obvious relationship between fractal dimension and root length indicated the significant correl

18、ation between fractal dimension and the ability of exploration in the soil (Thomas C. Walk, 2004).The application of fractal dimension exist some shortcomings because its calculation need the whole root system excavation, an alternative method is needed, therefore, to enable routine estimation of th

19、e size of tree root systems. Based on the hypothesis of self-similarity, Van Noordwijk et al. (1994; 1995) attempted to overcome the previous constraint by relating easily measurable parameters for instance, trunk diameters and diameters of proximal roots to predict the whole structure of the root s

20、ystem. Linked with the pipe model theory (Mkel, 1986), Spek and Van Noordwijk (1994) hypothesized that this approach may be well suited to predict the distribution of dry matter, and total root length within a tree root system.If this can be established, the length and biomass of a root can be estim

21、ated from easily-determined information the initial diameter of the root. Root lengths and total biomass for the root systems of whole trees can then be estimated by measuring the diameter of each root at the base of the trunk and estimation for each root by each root collar diameter.The objective o

22、f our work is to research the application of fractal theory and the fractal root model as formulated by Van Noordwijk et al. (1994; 1995) for predicting root biomass and length. We applied the model to two desert trees in the hinterland of Taklimakan desert in Xinjiang: Tamarixtaklamakanensis, Calli

23、gonum roborovskii. The objective of this work was () to find the relationshipbetween fractal dimension and branching pattern, root length respectively () to test the assumption of self-similarity () to test the suitability of self-similarity and pipe model assumptions for the prediction of root biom

24、ass, root length.1. MATERIALS AND METHODS1.1. Study area and test sitesThe Taklimakan desert is in the Northwest of China and the location of the study area is in the hinterland of desert which is closed to Tazhong desert arboretum, E8339，N3857 (Figure 1), Thenatural plant community structure is sim

25、ple in study area and the natural plants include: Phragmites australis, Apocynum venetum,Cistanche tubulosa, Hexinia polydichotoma, Tamarix.taklamakanensis, Calligonum roborovskii. Because of restriction of the features of environment and water-salt conditions in desert, vegetation type is simple an

26、d vegetative coverness is low. According to the data from Tazhong Meteorological Station and the Auto-Meteorological Station, the annual average temperatureis 12.4. The recorded highest temperature is 45.6 and the lowest temperature on record is 22.2.The mean annual precipitation is 36.6 mm. The pot

27、ential evapotranspiration rate is 3638.6mm. The wind speed there is 2.5 m/s on average and the highest instantaneous speed is 24.0 m/s. The salinity content is 1.26-1.63 g/kg. The ground water is about 1.2 m.Fig.1 The location of study area in the hinterland of Taklimakan desert1.2 The fractal root

28、modelsThe box-counting method (Y Q Wang, 1999) was applied to determine the fractal dimension, and then based on fractal dimension to analysis the difference of root branching pattern and the relationship between root length and fractal dimension. The specific methods are as follow: the top view ima

29、ges of root system were first covered with a frame (34cm34cm). The frame was divided into a grid in five steps, each box having a side length r=34/2n (n=0-5). The numbers of intersected boxes N(r), found in the root images at each scale were counted. Plotting number of boxes N(r) against side length

30、 (r) on a loglog scale gave a straight line. Their linear regression equation is: logNr=-FDlogr+logK (FD is fractal dimension and logK is has been associated with fractal abundance)Van Noordwijk et al. (1994) proposed that fractal geometry combined with parameter estimation based on the pipe model t

31、heory (MacDonald. N., 1983) could be applied for describing tree root architecture. The basic parameters of fractal root models describe the ratio of the sum of root cross-sectional areas after a bifurcation to the cross-sectional area before bifurcation, a , and thedistribution of the cross-section

32、al areas after bifurcation , q .The equations as follow: = D 2beforeD 2 afterq = max(D 2before )D 2 after（ Dbeforeis diameter before bifurcation， Dafteris diameter after bifurcation）1.3 The method of root excavationFrom August to September in 2007, five plants of Tamarix.taklamakanensis,Calligonumro

33、borovskii respectively were selected for the architectural description of root systems in the hinterland of Taklimakan desert. All the root systems were excavated by hand. In this study, we take more attention with coarse root. Coarse roots were defined as roots that exceed a threshold diameter of3

34、mm. A reconstruction of root architecture below that value was not possible (Armin L.Oppelta, 2000, 2005). To maintain the spatial orientation and position of root as sufficient as possible. The root location of each exposed root was determined by 50 cm 50cm Grid and we accurately mapped the top vie

35、w designs in the 3525cm paper in accordance with the ratio of 1:50.Fig.2 Schematic representation of root branching. The dbefore is diameter before bifurcation; d1 and d2 are diameters after bifurcation1.4 The measurement of root parameterThe variables measured in exposed root systems were similar f

36、or Tamarix taklamakanensis,alligonum roborovskii( ) root diameters before bifurcation and after bifurcation (see Figure 2); ()the root diameter at the point of bifurcation (see figure 3); () the root length and dry matter forwhole root system and some main root segments (such as segment 1and segment

37、 2 in figure 3); () to draw top view design of root system.2 RESULTS2.1 Fractal dimension and root lengthTable 1 shows the results of the calculation of FD forTamarix.taklamakanensis,Calligonum roborovskii, it ranged from 1.1449 to 1.3679 and the average FD of Tamarix.taklamakanensis, Calligonumrobo

38、rovskiiis1.31260.049,1.21720.0583respectively.Aone-factorial ANOVA with species as factor showed a highly significant effect on FD (F=7.835, P=0.0230.05). Thereby, FD is closely correlated with species. It was found that there is remarkable exponential correlation relationship between FD and the roo

39、tFig.3 Schematic representation of the fractal model was presented by Van Noordwijk et al. (1994). Base on this hypothesis, root lengths and dry matters could be estimated by using basal diameter or the diameter after bifurcation, so we can estimated the whole root length and dry matter by basal dia

40、meter (Db) and forecastedthe root length and biomass for root segments of S1 andS2 by the diameters after bifurcation DS1 and DS2respectively.180length (see Figure 4): L=0.0097e7.061D, (R2=0.9596,root length(cm)L is root length, D is FD). This is closed to the result proposed by P L Yang (1994) for

41、the relationship between root length and fractal dimension: with the root length increasing or decreasing, the FD was increased or decreased. But also the minimal difference of FD will lead to160140120100806040200y = 0.0097e7.061xR2 = 0.9596maximal difference of root length and rootbranching pattern

42、.1.1 1.21.31.4 fractal dimensionFig.4 The relationship between fractal dimensions and root lengthTab.1.The fractal dimensions of two difference speciesTamarixFDRootCalligonumFDRoot0011.34241230011.306785.20021.289980.030021.210347.660031.3679162.130031.223549.60041.2414680041.200845.50051.3213130.32

43、0051.144934.8Mean1.31256108.696Mean1.2172452.5522.2 Root diameter and root length, root dry matterFractal geometry combined with parameter180root length L(cm)160140120100806040200y = 28.694x - 22.093R2 = 0.97240 2 4 68 root diameter d(cm)estimation based on the pipe model theory (Van Noordwijk et al

44、., 1994; MacDonald.N., 1983) could be applied for describing tree root architecture. Linked with the pipe model theory (Mkel, 1986), and using a recursive model, Spek and Van Noordwijk (1994) hypothesized that this approach may be well suited to predict the distribution of dry matter, root length wi

45、thin a tree root system by relating easily measured1800root biomass B(g)160014001200100080060040020002.52lg(L)1.510.50-0.5y = 280.64x - 229.5R2 = 0.94070 2 4 68 root diameter d(cm)y = 1.9235x + 0.8123R2 = 0.9595parameters. The obvious linear relationshipbetween basal diameter or the diameter after b

46、ifurcationandrootlength,drymatter respectively are showed in Figure 5 for Tamarix. taklamakanensis, Calligonum roborovskii. The linear relationship can be reflected by the regression equation as follow: L= 28.694d -22.903(R2 = 0.9724, L is root length, d is basaldiameter or the diameter after bifurc

47、ation), B=280.64d- 229.5(R2 = 0.9407, B is dry matter, d is basal diameter or the diameter after bifurcation). West, et al. (1997) claimed to have found “a general model for the origin of allometric scaling laws in biology,” and the allometric exponent is closed 2 for the relationship between base d

48、iameter and total length (Van Noordwijk, et al.1994). In our study for the root system ofTamarixtaklamakanensis,Calligonum roborovskii, the linear regression of log d-0.500.51lg(d)Fig.5 The relationship between root diameter and root biomass, root length respectively.(independent variable) versus lo

49、g L (dependent)yielded a slope of 1.924 (intercept 0.8123, R2 =0.9595; see Figure 5). This is close to the allometric exponent 1.95 proposed by Van Noordwijk et al. (1994) for the relationship between base diameter and total length.2.3 The scaling factor a and allocation factor q for two species1.41

50、.2Scaling factor10.80.60.40.20Tamarix taklamakanensis0.9545 0.11960 2 46 root diameter(cm)1.210.80.60.4allocation factor0.20Tamarix taklamakanensis0.68400.12840 1 2 3 45 root diameter(cm)scaling factor2.521.510.50Calligonum roborovskii1.06220.27570 2 4 68 root diameter(cm)1.61.41.210.80.6allocation

51、factor0.40.20Calligonum roborovskii0.70740.21550 2 4 6 8 root diameter(cm)Fig.6 The scaling coefficient of a , q with two difference speciesThe self-similarity principle (Mandelbrot, 1983) defines an object that maintains similar form over a range of scales. This is the foundation of fractal models

52、and the basic parameters of fractal root models describe the ratio of the sum of root cross-sectional areas after a bifurcation to the cross-sectional area before bifurcation, a , and the distribution of the cross-sectional areas after bifurcation, q (Van Noordwijk M., Spek L.Y., 1994).The figure 6

53、showed the scaling coefficients a and q .The parameter a for Tamarix taklamakanensis, Calligonum roborovskii are 0.95450.1196, 1.06220.2757respectively and the coefficient q are 0.68400.1284，0.70740.2155 for two species. This is closed tothe coefficients( a are 1.15and 1.14，q are 0.72 and 0.77) prop

54、osed by Eduardo Salas (2004) for E. lanceolata and G. sepium. We study the relationship between root diameter and the scaling parameters a , q by a recursive model. The results indicated that there are no obvious correlations between root diameter and the scaling parameters a , q, so we proposed tha

55、t the fractal parameters a , q are the ecumenical features of root architecture , they were invariable with the change of root diameters.3. DISCUSSION3.1 The fractal dimension and root lengthThe habits of root branching pattern and development status form a non-periodic complex system. It has always

56、 been considered a disordered branching structure in Euclidean Space and it is difficult to measure quantitatively.The repetitive branching of roots leads to a certain degree of self-symmetry. Such self-similarity is a fundamental characteristic of fractal objects (A. Eshel, 1998). Therefore, the fr

57、actal theory is a efficient method to study quantitatively size ,branching pattern of root system , it also can analysis the degree of complexity of branching, density and ability of exploration of root system. Nielsen (1999) found that there is a significant correlation between fractal dimension an

58、d the space extension of root system, and FD is associated with branching pattern of root system (Thomas C. Walk,2004). In our study we found that the FD is ranged from 1.1449 to 1.3679 for two different species. A one-factorial ANOVA with species as factor showed a highly significant difference on

59、FD for Tamarix.taklamakanensis, Calligonum roborovskii. The difference of FD indicated the otherness of branching pattern. Because of fractal dimension indicated the degree of development directly, higher fractal dimension, more complicated root branching (P L Yang, 1999). So fractal dimensions of t

60、wo different species indicated that high complexity of root branching of Tamarix.taklamakanensis, reversely the branching of Calligonum roborovskii is simple, number of branching is low.This is in accordance with the exponential relationship proposed by P L Yang (1999) for the relationship between F

61、D and root length. In this study, evidence is presented that the synchronous changing relationships between FD and total root length, the fractal dimension was changed with theincreasing or decreasing of root length and the minimal change of FD will lead to maximal difference of root branching patte

62、rn. Because of total root length is likely to be a sufficient estimate of depletion and competition in soil, so the difference of FD reflects the otherness of ability of exploration and fertilizer absorptive capacity of root system in soil.3.2 Root diameter and dry matter, root lengthThe root length and biomass are important aspects of root architecture which reflect root size and ability of exploration in soil. The feature analysis of root length and biomass is helpful to understand the adaptability of root system in special environment. But of ro