Crop Science Journal of Natural Resources and Life Sciences Education
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published in Crop Sci 39:1784-1791 (1999)
© 1999 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (10)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.
Agricola
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.
Crop Science 39:1784-1791 (1999)
© 1999 Crop Science Society of America

CROP PHYSIOLOGY & METABOLISM

Soybean Canopy Development as Affected by Population Density and Intercropping with Corn

Fractal Analysis in Comparison with Other Quantitative Approaches

Kayhan Foroutan-poura, Pierre Dutilleula and Donald L. Smitha

a Dep. of Plant Science, McGill Univ., 21111 Lakeshore Road, Ste-Anne-de-Bellevue, QC H9X 3V9, Canada

cydp{at}musica.mcgill.ca


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 
To better understand how crops intercept light, the complexity of plant structure needs to be characterized. Fractal analysis provides a novel approach for quantifying the geometric structure of individual plants. The objectives of this study were to determine (i) an appropriate methodology for estimating fractal dimension (FD) two-dimensionally for complex three-dimensional structures of plants such as soybean [Glycine max (L.) Merr.]; (ii) whether the temporal pattern of FD for soybean structure is altered by population density or intercropping with corn (Zea mays L.); and (iii) how the FD for soybean structure compares with other quantitative measures of shoot development. Soybean plants were randomly sampled in monocropped soybean and intercropped corn-soybean plots grown at the same site in three successive years. Sampled plants were cut at the stem base, and leaf blades were immediately detached. Leafless plant structure was photographed from the side which allowed maximum appearance of branches and petioles. The FD was estimated two-dimensionally from the scanned and processed images. Fractal dimension of soybean leafless structure increased with time for all treatments, coincident with the increasing complexity of structure as shoots developed. The rate of linear increase of FD with time varied among treatments. Leaf area per plant, plant height, and number of leaves per plant increased with time for all treatments, indicating a positive correlation with FD. In contrast, light penetration decreased during canopy development, and was negatively correlated with FD. Whereas leaf area evaluates the surface available for light interception, FD characterizes its geometric distribution in space.

Abbreviations: FD, fractal dimension • LA, leaf area • LAI, leaf area index • PPD, plant population density


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 
MANY VEGETATION

and yield variables are potentially influenced by the competition of the plant with a second crop in an intercrop system and by competition with other plants of the same species in monocrop systems, and this influence may be affected by changes in plant population density (PPD) (Fortin et al., 1994). The structure of plant vegetation and its geometric elements combined with the total amount of leaf area determine the distribution of light within the canopy.

In monocrop systems, soybean plants are more sparsely branched at greater densities than at lower densities (Weber et al., 1966). Soybean height increases with increasing PPD (Boquet, 1990), whereas leaf area index (LAI) and light interception increase with increasing PPD per unit land area (Parvez et al., 1989).

Intercropping is the practice of growing two or more crops simultaneously on the same field, to maximize total production per unit area. Although this is an ancient practice, it is still relatively uninvestigated. The most important advantage of intercropping systems comprised of both tall and short plants is the potential complementarity in sunlight utilization for crop production (Iragavarapu and Randall, 1996).

Among the different possible crop combinations, corn-soybean intercropping has received significant research attention (Martin et al., 1989). Intercropping systems can be organized in a range of patterns; for instance, growing the two crops in the same row or alternating or a given number of rows of each crop (West and Griffith, 1992). The latter is often referred to as strip cropping. Although yield variability in corn-soybean intercrop systems has been the focus of much research work, there is little information available regarding vegetation structure of soybean in intercropping with corn.

Plant vegetation architecture can be quantified by a range of methods (Lang, 1990; Sinoquet et al., 1991; Moulia and Sinoquet, 1993). However, there are problems in developing reliable models for plant geometric structure, especially for plants with complex vegetation arrays, such as soybean. First, difficulties may arise in the characterization of some structural parameters (Sinoquet and Andrieu, 1993). Second, when the number of input components in the model for canopy characterization increases, the reliability of the output decreases and the computation time increases (Andrieu and Baret, 1993). Third, many assumptions must be made regarding structural parameters, when using simulation methods to incorporate a geometric model for soybean structure (Hommertzheim, 1979). There exists no mathematical procedure to describe plant vegetation architecture completely, and improved methods are needed.

Fractal analysis has provided a novel approach for quantifying the geometry of complex or noisy shapes and objects (Mandelbrot, 1983). Contrary to regular shapes with integer dimensions in classical geometry, fractals are not regular and may have an integer or non-integer dimension (Mandelbrot, 1983). Fractals occur in the processes of developing, fragmenting, and branching in biological; ecological; and other systems (Frontier, 1987; West and Goldberger, 1987; Otto, 1996). Fractal geometry has been applied to describe various aspects of soil (Baveye et al., 1998), spatio-temporal variability (He et al., 1994; Eghball and Power, 1995), plant-insect interactions (Morse et al., 1985), the morphology of fungal colonies (Mihail et al., 1994) and crop root systems (Eghball et al., 1993; Lynch et al., 1993; Nielsen et al., 1997), and the form complexity in plants (algae: Corbit and Garbary, 1995; ferns: Kübler and Dudgeon, 1996; weeds: Critten, 1997). Thus, fractal geometry has the potential to quantify the structural complexity of crop shoots which develop their canopies as complex geometric forms.

The structure of a developing shoot is determined by its size and its quality. Its size may be characterized by the amount of leaf area, plant height, and number of leaves per plant, among other measures. To characterize quality, one focuses on variables related to the spatial arrangement of the vegetation such as the vertical and horizontal profiles of leaf area, leaf inclination, leaf azimuth, and leaf dispersion (Pearce et al., 1967; Blad and Baker, 1972; Sinoquet and Andrieu, 1993). Fractal analysis, through the measure of complexity it provides with the fractal dimension (FD), will characterize the quality of structure of developing shoots further.

Plants grow three-dimensionally in space, but three-dimensional estimation of fractal dimension is not easily accessible, especially for field experiments. For this reason, we developed first an appropriate two-dimensional method of FD estimation for the complex three-dimensional vegetation structure of a crop such as soybean. Accordingly, the objectives of this study were to determine (i) an appropriate methodology for estimating FD two-dimensionally for a complex three-dimensional plant structure; (ii) whether the temporal pattern of FD for soybean structure is altered by various PPDs and corn-soybean intercropping; and (iii) how changes in the FD for soybean structure are related to changes in other quantitative measures of shoot development. In this work, the corn-soybean intercropping experiments were conducted by alternating single rows of each crop. Possible uses of FD in plant canopy modeling for a better understanding of how crops intercept light are explored.


   Materials and methods
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
Results and discussion
 Conclusions
 REFERENCES
 
Field Experimentation
Three experiments were carried out at the Emile A. Lods Agronomy Research Centre, Macdonald Campus of McGill University, Ste-Anne-de-Bellevue, QC, Canada. Each experiment was arranged as a randomized complete block design with four blocks and temporal repeated measures. The experiments were conducted on Endoaquept soil. The corn hybrid was `Pioneer 3921', and the soybean cultivar was Maple Glen. Both genotypes are commonly produced in eastern Canada. Soybean seeds were inoculated with Bradyrhizobium japonicum prior to seeding. In the years preceding the experiments, the sites had been used to produce corn. The soybean monocrop and corn-soybean intercrop were planted in plots measuring 2.3 by 5 m (6 rows spaced 37.5 cm apart) and 4.5 by 5 m (6 rows of corn 75 cm apart with one row of soybean midway between each pair of corn rows), respectively. The crops were planted on 22 May 1995, 20 May 1996, and 15 May 1997. Plots were over seeded and then thinned to the desired PPD at the seedling stage. The final PPDs were the normal population density for soybean (450 000 plants ha-1) and two additional densities equal to 0.5 and 1.5 times the normal density. For corn-soybean intercropping, the normal density of corn based on 72 000 plants ha-1 and half the normal density of soybean were used (Martin et al., 1989). To avoid border effects, two rows with the same PPD as the plants of the plot were seeded on either side of the plot and, additionally, a 3 m spacing was left between adjacent plots. The plants received only rainwater, and were fertilized as recommended (CPVQ, 1994), with 20 and 90 kg ha-1 of N for soybean monocrop and corn-soybean intercrop, respectively. Additionally, plants received 32 kg ha-1 of P and 62 kg ha-1 of K during field preparation, as recommended by a soil test.

Measurements
In each of the 3 yr, we measured LAI, canopy light penetration, plant height, and number of leaves per plant weekly at 48, 55, 62, 69, and 76 d after planting. The LAI and canopy light penetration (µmol s-1 m-2) were measured with an LAI-2000 Plant Canopy Analyzer (LI-COR Inc., Lincoln, NE) and a Line Quantum Sensor (LI-COR Inc.), respectively. Light penetration (%) of plant canopy was calculated as I/I0 x 100, where I0 is the irradiance above plant canopy and I is the irradiance under plant canopy. Values of LAI and canopy light penetration were not calculated for intercropped soybean because of difficulties in calculating the respective contribution of corn and soybean crops. To have all measurements on an individual plant basis, leaf area (LA) per plant and light penetration (% per plant) were calculated using the PPD of the treatment in question.

Photography, Scanning and Image Processing
In the 3 yr, photographs of soybean plants were taken at the times of measurement, to estimate FD. At each time of measurement, a soybean plant was randomly sampled in each monocrop and intercrop plot in each experiment, and was cut at the base of the stem. The leaf blades were detached from the petioles immediately, and the structure of the leafless plant was photographed with an ISO 25 Kodachrome black and white slide film (Eastman Kodak Co., Rochester, NY). The plant was photographed from the side which allowed the maximum appearance of branches and petioles. This side might change depending on the soybean treatment; only for the greatest plant population density was it systematically parallel to the row. In order to improve contrast, a white 2- by 2-m styrofoam sheet was held behind each plant at the time it was photographed.

The developed images were scanned at a resolution of 72 dpi (required by the Fractal Dimension Calculator software described below) with a Nikon AX-1200 scanner for PowerPC Macintosh (Nikon Scantouch Corporation, Tokyo, Japan). The scanned images were saved as 8-bit grayscale PICT files (graphics format for Apple Macintosh computers).

Image processing was performed with NIH version 1.60, an image processing software operating on Apple Macintosh computers and written by Wayne Rasband of the National Institutes of Health, Bethesda, Maryland. The software is in the public domain through internet (http://rsb.info.nih.gov/nih-image/; verified 20 May 1999). Each PICT file was converted to 1-bit black and white with the threshold command. This was followed by a "cropping" operation, including the removal of unwanted parts of the background that the NIH software found sufficiently dark to assign the black color. After conversion to black and white and cropping, skeletal images of leafless plants were taken using the skeleton command and were saved as PICT files, as required by the Fractal Dimension Calculator software. These skeletal images of leafless soybean shoots collected during five weeks represent the development of their branching pattern.

Estimation of the Fractal Dimension of Soybean Structure
Although plants grow three-dimensionally in space, we used photographs of soybean shoots placed on a plane, and constrained our investigation to two dimensions in this study. Contrary to methods designed for two-dimensional estimation of fractal dimension, methods for three-dimensional fractal dimension estimation for objects with three-dimensional physical structure are not well defined, easily applicable, or accessible for applied research. For these reasons, a method defined for two-dimensional FD estimation which provides acceptable information about the geometrical complexity of plant structure will be used more often in applied research.

The vegetative structure of soybean is geometrically complex because plants establish a branching pattern around a main stem which includes the true branches, in the botanical sense, and the petioles which support trifoliolate leaves in a non-planar manner with considerable overlapping. The architecture of the vegetation is determined by this branching pattern in which the leaves are arrayed in space by the petioles, which has a large impact on the efficiency with which they carry out light interception. While leaves intercept sunlight, they are not a major determinant of the geometric form of soybean; leaf positions are determined by the petioles and the branches that support them. Thus, the leafless branching pattern, including the petioles, is of interest in soybean. From a geometric point of view, the FD of the leafless branching pattern measures the complexity of the vegetative structure of soybean. Therefore, all the estimates of FD in this study were obtained from images of leafless soybean shoots (Fig. 1) .



View larger version (29K):
[in this window]
[in a new window]
  		Fig. 1 Changes in the leafless structure of soybean shoots during development in the different treatments. The fractal dimension value for each image is reported beneath the image

 
Structural parameters affecting the FD of leafless branching pattern are the degree of the ramifying process of soybean branches and their tortuosity, extension and arrangement in three-dimensional space. Although branch intersections may occur in the image of a leafless plant, these obscure very little of the overall branching pattern. By using images of leafless soybean shoots to estimate FD, essentially all the structural parameters affecting the value of FD are captured. Use of this type of image for fractal dimension estimation is consistent with the procedures followed for fractal analysis of crop root systems (Eghball et al., 1993; Lynch et al., 1993; Nielsen et al., 1997) and form complexity of plants other than crops (Corbit and Garbary, 1995).

Procedure of Fractal Dimension Estimation
Mandelbrot (1983) discussed a number of techniques that can be used to estimate the fractal dimension. One of these techniques is the box-counting method which is appropriate for estimating FD from two-dimensional images (Foroutan-pour et al., 1999). In this method, each image is covered by a sequence of grids made of squares of descending sizes and for each grid, two values are recorded: the number of squares intersected by the image, N(s), and the side length of squares, s. The regression slope (D) of the straight line formed by plotting log[N(s)] against log(1/s) indicates the degree of complexity, or FD, which ranges between 1 and 2 (1 <= D <= 2) (Mandelbrot, 1983). An image having an FD of 1 or 2 will be considered as completely differentiable or very rough and irregular, respectively. The linear regression equation used to estimate FD is

where K is a constant and N(s) is proportional to (1/s)D (Mandelbrot, 1983).

The box-counting method of FD estimation was implemented using the Fractal Dimension Calculator software for the Apple Macintosh computer, written by Paul Bourke of the School of Architecture, University of Auckland, New Zealand (available at paul@bourke.gen.nz.). By default, this software uses 12 box sizes. Two important user options are the range of box sizes and the number of grid offsets to be used (Soddell and Seviour, 1994; Foroutan-pour et al., 1999). Obviously, both the maximum and the minimum box size depend on the resolution of the scanned image, including its size and its structure. The definition of the range of box sizes is a common problem for any discrete image processing. In this study, the best range of box sizes was determined for each image, following Foroutan-pour et al. (1999).

Line and curve thickness of more than one pixel (i.e., the smallest possible box size in the box-counting method) and non-uniform thickness may cause problems in FD estimation. To prevent this type of problem, we used skeletons of the scanned and processed images for box-counting analysis, following Foroutan-pour et al. (1999).

Statistical Analyses
The variables analyzed were fractal dimension of individual plant, leaf area per plant, light penetration (% per plant), plant height, and number of leaves per plant. To meet the assumption of normal distribution of the data in the repeated measures ANOVA, light penetration (percentage data) and number of leaves (count data) were transformed to square root of the variable plus 0.5 and square root of the variable, respectively. For each variable, the hypotheses of homogeneity of the variances and of the means over the 3 yr were tested and accepted using Bartlett's test (Steel and Torrie, 1980) and the classical F test, respectively. Means were then calculated over the 3 yr, per time of measurement, treatment and block, and a repeated measures ANOVA was performed on these means for each variable, following Moser and Saxton (1990), Potvin et al. (1990), and Dutilleul (1998). In the univariate procedure of repeated measures ANOVA, the tested effects are classified as between-subject effects, which are the treatment and block main effects since the plant is the subject, and within-subject effects, which are the time of measurement and its interactions with treatment and block. The statistical analysis of the repeated measures design resembles that of the split-plot design because of two error terms (one for the between-subject effects and one for the within-subject effects), but conceptual differences exist between them (Yates, 1982). Correlation analysis based on Pearson's r statistic was carried out to describe the relationships among variables.

The univariate procedure of repeated measures ANOVA was carried out by the GLM procedure of SAS version 6, statement REPEATED (SAS Institute Inc., 1989). Simple linear regression and correlation analyses were performed with SAS procedures REG and CORR (SAS Institute Inc., 1989, 1990).


   Results and discussion
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
Conclusions
 REFERENCES
 
Analysis of Fractal Dimension of Individual Plant
The repeated measures ANOVA indicated that fractal dimension of individual plant changed with time (P < 0.001) as the soybean shoots developed (Table 1) . Thus, the branching pattern of soybean had different levels of irregularity or complexity at different stages of growth. Figure 2 (a) shows the temporal pattern of FD of individual plant for each of the soybean treatments during shoot development. Clearly, FD of individual plant increased steadily with time for all treatments.


View this table:
[in this window]
[in a new window]
  		Table 1 Summary of results of the univariate procedure of repeated measures analysis of variance{dagger} for each variable

 


View larger version (18K):
[in this window]
[in a new window]
  		Fig. 2 Changes in (a) fractal dimension of leafless structure of individual plant, (b) leaf area per plant, and (c) light penetration (% per plant) during soybean shoot development as affected by treatments. Each data point represents a mean across 3 yr and four blocks per year

 
The rate of linear increase of FD with time varied among treatments (P < 0.001), as indicated by the test of differences among treatments on the linear contrast of time for FD of individual plant in Table 2 . This means that the complexity of soybean structure increased with time at different rates for some of the treatments. Based on the slope estimates in time plots, soybean treatments were ranked as normal PPD {approx} intercrop {approx} low PPD > high PPD (Table 3) . The approximate equality among normal PPD, intercrop, and low PPD treatments indicates that differences in FD that were established among these three treatments at the first time of measurement persisted during the following weeks. In contrast, the lower slope estimate for high PPD, combined with a lower FD at the first time of measurement, means that soybean shoots at high PPD had a less complex structure during their development, as illustrated in Fig. 2 (a). Because the time x treatment interaction of which a 1 df component is discussed above in terms of differences among treatments in the rate of linear increase of FD with time, we do not discuss the treatment main effects (P < 0.001) (Table 1).


View this table:
[in this window]
[in a new window]
  		Table 2 Differences among treatments{dagger}, as tested on polynomial contrasts over the five times of measurement in the repeated measures analysis of variance{ddagger} for each variable

 

View this table:
[in this window]
[in a new window]
  		Table 3 Values of slope estimate{dagger} in the time plot of each variable per treatment

 
In the plots planted with low PPD, there is more space for individual plants to develop, and less competition among individual plants for space and light. In contrast, plants in monoculture at high PPD and plants in intercrop culture compete strongly for resources, especially light (Brown, 1984). Soybean plants at low PPD are full and bushy in shape. In contrast, the structure of plants at high PPD is more narrow and linear. Competition at high soybean PPD is lower between rows than within rows. For this reason, we found that soybean shoots at high PPD developed in a plane perpendicular to the rows. This is consistent with Weber et al. (1966) who found that soybean plants are sparsely branched at high densities. Although the PPD of soybean in monocrop plots of low PPD and in intercrop plots were the same, FD of individual plant was greater for the soybean monocrop of low PPD than for the intercrop culture. Corn is taller and competes more effectively for light than soybean (West and Griffith, 1992; Fortin and Pierce, 1996). Thus, in the intercrop culture of corn and soybean with greater PPD for corn, corn is the "dominant" component and soybean, the "dominated" one, so that the actual competition experienced by soybean in intercrop is greater than in monocrop culture at the same PPD.

Leaf Area per Plant, Light Penetration (% per Plant), Plant Height and Number of Leaves per Plant
The time x treatment interaction was significant (P < 0.001) for the four variables which were to be compared with FD (Table 1). An increase of LA per plant, plant height, and number of leaves per plant was observed during soybean shoot development for all of the treatments, except the intercrop which was not measured for leaf area per plant [Fig. 2 (b) and 3]. In contrast, Fig. 2 (c) shows a decrease of light penetration (% per plant) with time in monocrop plots of low, normal and high PPD. The rate of linear increase or linear decrease with time of LA per plant, light penetration (% per plant), plant height, and number of leaves per plant, varied strongly among treatments, as did the quadratic and cubic contrasts of time for light penetration (% per plant) and plant height (Table 2). On the basis of slope estimates in time plots, soybean treatments are ranked as low PPD > normal PPD > high PPD for LA per plant and light penetration (% per plant), intercrop > high PPD > normal PPD > low PPD for plant height, and low PPD {approx} H normal PPD > intercrop > high PPD for number of leaves per plant (Table 3). Because of the time x treatment interaction, we do not discuss the treatment main effects (P < 0.001) (Table 1).

It is noteworthy that the height of soybean plants in the intercrop treatment showed a sharp increase after the fourth time of measurement (i.e., 69 d after planting) in our study. This may have been caused by the increase in competition of soybean with corn for light interception at a time when the corn plants were achieving their maximum height. In intercrop plots, light penetration into lower levels of the canopy decreased as the corn developed and there was less light available for the soybean plants. Soybean plants compensated by adjusting their structure, resulting in increased plant height with more leaves at the upper levels of the canopy. Similarly, Baker (1979) reported that in intercropped fields, the upper portion of the taller crop did not suffer from competition for light, when it was above the leaves of the lower crop.

Correlation Analysis
Leaf area per plant, plant height, and number of leaves per plant each showed a strong positive correlation with fractal dimension of individual plant (LA per plant: r = 0.995, P < 0.001; plant height: r = 0.976, P = 0.004; number of leaves per plant: r = 0.970, P = 0.006). As soybean shoots developed, FD of individual plant, LA per plant, plant height, and number of leaves per plant all increased (Fig. 2 and 3) . It is important to note that these correlations resulted from temporal changes. However, when correlations were analyzed on treatment sample means calculated across times of measurement, FD of individual plant and plant height were negatively correlated, as FD of individual plant was less for the high soybean PPD which corresponded to greater plant height, and was higher for the low soybean PPD which was characterized by smaller plant height.



View larger version (23K):
[in this window]
[in a new window]
  		Fig. 3 Changes in (a) plant height and (b) number of leaves per plant during soybean shoot development as affected by treatments. Each data point represents a mean across 3 yr and four blocks per year

 
Furthermore, FD of individual plant and light penetration (% per plant) were negatively correlated (r = -0.964, P = 0.008). This suggests that as soybean shoots developed, the complexity of their structure increased, while less light penetrated into the canopy. LA per plant and light penetration (% per plant) were also negatively correlated (r = -0.979, P = 0.004).

Novel Aspects of the Fractal Analysis Approach
Most biological systems and many physical ones are heterogeneous and irregular. The most readily apparent feature of many physiological systems is their structural complexity. Studying the physiological structure and function in a single model is one of the major challenges of modern biology. To understand the complex interrelationships among biological development, form and function, the structural complexity must be characterized. Higher plants, as important organisms in nature, develop their canopies in a complex and irregular manner. They must array their foliage in space to optimize light interception and gas exchange, and the geometric structure of the canopy can have a great impact on the ability of plants to intercept light. In this article, we have presented a new approach to the characterization of the geometric structure of individual plants: the fractal analysis. Characterizing the geometric structure of plant canopies with a single numeric value is now possible and provides a more complete description of the canopy structure. For instance, the relationship between LAI and light penetration has often been modeled with the Beer-Lambert equation (Maass et al., 1995; Vose et al., 1995), as follows:

where I is the irradiance under the crop canopy, I0 is the irradiance above the crop, and k is the extinction coefficient or fraction of light intercepted per leaf area unit. This equation describes the relationship between proportional light penetration and LAI. It suffers from the absence of a component characterizing the geometric distribution of leaf area, which is so important for light interception. Plants with the same leaf area may have different spatial foliage distributions and hence, different patterns of light interception. Therefore, combining LAI with a spatial description of the canopy based on FD might improve the description of light penetration into the canopy.


   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
REFERENCES
 
Our study shows that fractal geometry provides a useful tool for quantifying complex structures of plants such as soybean. In particular, fractal analysis can be used to measure complexity in the structural development of shoots and in the structural response of plants to cultural practices. Images of leafless soybean shoots provide an appropriate material for estimating the fractal dimension of individual plants two-dimensionally. In this study, changes of FD with time were characterized by a linear increase for all of the treatments. There was no significant difference among the rates of linear increase of the fractal dimension of soybean leafless structure in low and normal PPDs and when intercropped with corn. However, the rate of linear increase of FD at the high PPD was significantly less than in the other treatments. An increase of leaf area per plant, plant height, and number of leaves per plant was observed during shoot development for all of the treatments, with the exception of the intercrop which was not measured for leaf area per plant. In contrast, a decrease of light penetration (% per plant) with time was observed in monocrop plots of low, normal and high PPD. Accordingly, leaf area per plant, plant height, and number of leaves per plant showed a strong positive correlation with fractal dimension of individual plant over time, whereas light penetration (% per plant) was negatively correlated with fractal dimension of individual plant and leaf area per plant. As soybean shoots developed, the complexity of their structure increased, leaf area increased, and less light penetrated into the canopy. Whereas leaf area per plant provides a single value to measure the amount of surface available for light interception, FD provides a single value to characterize the branching pattern of the plant and hence, the geometric distribution of the leaf area in space. Combining the two measures helps us understand better how crops capture light and may have important practical implications for plant canopy modeling in future studies.


   ACKNOWLEDGMENTS
 
This study was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche (Fonds FCAR) through research grants to the second author, and by the Conseil des Recherches en Pêches et en Agroalimentaire du Québec (CORPAQ) through a research grant to the third author. We are grateful to four anonymous reviewers, the Technical Editor and the Associate Editor for comments on an earlier version of the paper.

Received for publication August 24, 1998.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 




This article has been cited by other articles:


Home page
 ANN BOT (LOND)Home page
P. Dutilleul, L. Han, and D. L. Smith
Plant Light Interception Can Be Explained via Computed Tomography Scanning: Demonstration with Pyramidal Cedar (Thuja occidentalis, Fastigiata)
Ann. Bot., January 1, 2008; 101(1): 19 - 23.
[Abstract] [Full Text] [PDF]

Home page
 Agron. J.Home page
K. Foroutan-pour, P. Dutilleul, and D. L. Smith
Inclusion of the Fractal Dimension of Leafless Plant Structure in the Beer-Lambert Law
Agron. J., March 1, 2001; 93(2): 333 - 338.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (10)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.
Agricola
Right arrow Articles by Foroutan-pour, K.
Right arrow Articles by Smith, D. L.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Vadose Zone Journal
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome