INTRODUCTION
Melastoma malabathricum L., otherwise known locally as the Straits Rhododenron,
Indian Rhododenron or Singaporean Rhododenron, is a common pioneer shrub species
in arable lands, abandoned farmlands, secondary forest openings and derelict
areas in Malaysia and elsewhere, especially in tropical and subtropical forests
of India, Southeast Asia and Australia (Meyer, 2001;
Baki, 2004). The species is a common scourge in young
rubber, oil palm, coconut plantations and fruit orchards and open places in
Malaysia.
Spatial analysis of tree trunks and development of biological branching structures
has become an established method to infer tree population dynamics such as selfthinning
or gap recruitment in forest communities (Caplat et al.,
2008; Getzin and Wiegand, 2007). Inter and intraplant
competition models illustrating densitymediated effects on yield and biomass
in plants have been the subject of vigorous academic pursuits by several workers
(Kropff and Struik, 2002; Cornelissen
and Stiling, 2008). Surveys on asymmetric growth are very useful in plant
competition and are essential in practical management for improving timber quality
and stand leaf area index or wind resistance of stands (Rudnicki
et al., 2001; Rock et al., 2004;
Getzin and Wiegand, 2007). Under field conditions without water stress,
branches do not converge into a universal movement to a favoured mature azimuth.
On the contrary, there is a trend toward azimuthal dispersion. Azimuthal movement
of branches is sensitive to initial clumping of foliage, being triggered initially
and more importantly, when the initial clumping is strong (Chelle,
2006; Saudreau et al., 2007). Some plant species
have a random distribution of horizontal rotation angle φ of leaf, independent
of planting pattern while other plant species can modify leaf orientation according
to the conditions. Plant canopy behaviour has a significant effect on light
interception (Maddonnia et al., 2001).
Drouet and Moulia (1997) reported that uniform distribution of leaf azimuth
was effected by light interception and crop architecture. Each leaf was characterized
by three parameters: leaf horizontal rotation angle, leaf vertical rotation
angle and leaf height (translation). The horizontal rotation angle has received
much less attention.
Studies on the leaf angle (θ, φ) have shown that the effects of initial
plant orientation on θ of leaf and height were less spectacular. Initial
plant orientation and density had a small effect on leaf vertical rotation angle.
An effect of density was observed only on leaf translation, but no intercalation
of leaves between adjacent plants was noticed in development of maize (Girardin
and Tollenaar, 1994; Maddonnia et al., 2001).
There is a remarkable correlation between plant architecture and the biogeographic
distribution of species in different places and this correlation can be used
to assess plant distribution in ecological science. Other reports indicated
that a species may show different orientations according to the environment
in which it grows and its behaviour is relatively fixed at the species level
(Ezcurra et al., 1991).
In this study, the system of primary and secondary branches of M.
malabathricum as a function of translation (plant height), their horizontal
rotation angles, vertical rotation angle and translation of branches over
different densities were checked for possible adaptive repositioning
of successive branches during 161 days of their growth from the transplanting
date. The spatial scales for branching patterns were analyzed along plant
height, as well as the directional preferences of growing branches in
relation to different plant densities and light regimes at the stand level.
The hypothesis was that branch orientation is a selected trait that permits
changes in the vertical and horizontal angle to achieve adequate light
interception.
MATERIALS AND METHODS
One hundred young uniform seedlings of M. malabathricum of the
same cohorts were collected in May 2006 from the campus of the University
of Malaya, Kuala Lumpur (3° 8’ N; 101° 42’ E) Malaysia
and raised in wooden boxes previously filled with garden soil of Malacca
series in an insectproof house with 12 h of natural sunlight (mean midday
radiation of 622 and 125 μmole photon/m^{2}/sec outdoor and
inside in insectproof house respectively) and mean ambient temperatures
of 33 ± 2 °C (day) and 25 ± 2 °C (night) at Rimba
Ilmu, University of Malaya. The most uniform plants were selected randomly
and transplanted into wooden boxes, each measuring 72x72x30 cm at the
density of 1(D1), 2(D2) and 3(D3) plants box^{1}, each with 3
replications The plants were transplanted into the centre of the box for
the single plants, while for 2 or 3 plants per box the plants were spaced
equidistant at 10 cm from each other. The plants were watered once daily,
in the morning from above with a fine rose. The boxes were arranged in
a completely randomized design.
For the branching pattern studies, each plant was progressively divided into
50 cm heights from the soil surface and denoted accordingly. A circle of transparent
plastic sheet divided into 8 sections, each with a 45° degree angle, was
prepared (Girardin and Tollenaar, 1994; Drouet
and Moulia, 1997). Overlays were prepared to assess branching patterns of
M. malabathricum with this plastic sheet. The direction and branch angles
(primary branches with respect to the mother plant) in each section were recorded
with the aid of a compass oriented clockwise. The vertical rotation angles were
measured with a clinometer.
A botanical numbering system were applied to plant branches, counting the branch
order(s) outward from the main stem (Borchert and Slade,
1981).The mean angles of orientation of primary branches with respect to
the main stem and other branches were measured, so were the angles of secondary
branches with respect to primaries (Fig. 1), viz. the horizontal
rotation angle (φ), the vertical rotation angle (θ), translation (H)
for each 50 cm throughout the plant height, based on the main stem for each
translation of 50, 100, 150, 200 and 250 cm (hereinafter referred as translation
1, 2, 3, 4 and 5, respectively). The horizontal rotation angle of the branch
was measured within sections the 45 degree, using a homemade circular protractor,
with clockwise orientation from the north direction (0°).

Fig. 1: 
The three parameters of the horizontal rotation angle
φ, the vertical rotation angle θ and translation (H) measured
from the north direction during plant growth to describe the development
of the aerial structure of Melastoma malabathricum L. 
The branchbase height above the soil was measured using a rule tape.
Growth parameters, viz., plant height; lengths of primary and secondary
branches and reproductive traits (time and duration of flowering, number
of flowers branch^{1} or flowers plant^{1}) were recorded.
Data Analysis
Directional data commonly occur in environmental studies when measurements
are taken from an orientation or cyclical timing application. The mean
direction is denoted by mean vector values, defined as follows: Let θ_{1}
... θ_{n} be the angular observations expressed in the form
of radians [0, 2θ]. Then, the mean direction, 6, is defined by:
where, i is the imaginary unit, i.e., i^{2} = 1
Two frequentlyused families of distributions for circular data include the
von Mises and the Uniform distribution (Fisher, 1993; Gatto
and Jammalamadaka, 2007).
The sample mean direction is a common choice for moderately large samples,
because when combined with a measure of sample dispersion, it acts as a summary
of the data suitable for comparison and amalgamation with other such information.
The sample mean is obtained by treating the data as vectors of length as one
unit and using the direction of their resultant vector r that it lies in the
range (0, 1). Resultant vector r is a measure of concentrations 1r is a measure
of dispersion. Lack of dispersion 1r = 0 and maximum dispersion is 1r = 0.
The angular variance is defined as s^{2} = 2(1r). Note that r = 0 does
not necessarily indicate a uniform distribution (Zar, 1998).
The Rayleigh’s test is used to test whether the population from which the
sample is drawn differs significantly from randomness (Fisher,
1993; Zar, 1998; Mardia and Jupp,
2000). In order to compare and test whether the mean directions of two or
more samples will differ significantly from each other, a widely used statistical
test is the WatsonWilliams test or approximate Analysis of Variance (ANOVA)
(Batschelet, 1981; Mardia and Jupp, 2000;
Jammalamadaka and Sengupta, 2001).
The hypothesis was that there is a correlation between a circular variable
(horizontal or vertical rotation angle) and linear variable (branch length or
translation). The hypothesis entailed the calculation of the circularlinear
correlation coefficient (Fisher, 1993; Zar,
1998; Mardia and Jupp, 2000; Jammalamadaka
and Sengupta, 2001). This correlation coefficient r ranges from 0 to 1.
Suppose that a linearcircular correlation (Mardia and Jupp,
2000), which is a measure of correlation between a linear variable x and
an angular variable θ, is defined by:
Where:
r_{xc} 
= 
Corr (x, cosθ) 
r_{xs} 
= 
Corr (x, sinθ) 
r_{cs} 
= 
Corr (cosθ, sinθ) 
The hypothesis of no circularlinear association is rejected if r^{2}
is too large. The data were processed and displayed with the software
ORIANA and the R Project for statistical computing of the circular data,
median, circular mean and concentration parameter.
RESULTS AND DISCUSSION
Melastoma malabathricum has terminal branch flowers and after flowering,
commonly old branches at the base and inside of canopy die. This plant displays
both terminal and axillaryflowers. The branching pattern of M. malabathricum
illustrates that of Leeuwenberg’s model. This model consists of equivalent
orthotropic modules, each of which is determined in its growth by virtue of
ultimate production of a terminal inflorescence. Branching is threedimensional,
producing the several equivalent modules and is correlated with flowering except
in a few examples with branched sterile juvenile axes (Halle
et al., 1978; Judd, 1986).
Horizontal Rotation of Plant Branches
The Rayleigh’s test showed the distribution of φ was centrally
symmetrical in different plant populations and the computed lengths of
mean vector (r) were 0.032, 0.047 and 0.014 for the density regimes of
D1, D2 and D3, respectively (Table 1). Figure
2 shows boxplots of (φ) for each density of the branches.
Such association is also given in Table 1, which is
a summary of the horizontal rotation angle for each of the plant densities.
The angular observations were calculated by Eq. 1. Figure
2 seems to imply that (φ) values are not dependent on, or influenced
by, the density of branches. In this regard, we applied the circular ANOVA
to test if density influences the mean direction of (φ).
Table 1: 
Directions of symmetric growth for the horizontal rotation
angle of Melastoma malabathricum as analyzed by descriptive
statistics 


Fig. 2: 
Boxplots of the horizontal rotation angles of branches
(φ) as a function of planting density in Melastoma malabathricum 
Table 2: 
Approximate ANOVA values for testing the influence of
plant density of Melastoma malabathricum on horizontal rotation
angle of branches (φ) and the hypothesis: (H0: v_{1}
= v_{2} = v_{3} against H_{1}: v_{1}≠
v_{2} or v_{1} ≠ v_{3} or v_{2}
≠ v_{3}) 

^{ns}: No significant difference at p < 0.0.5 
The results of the circular ANOVA test applied to the horizontal rotation
angles are shown in Table 2. With Fvalue of 0.0203
and because p (F>0.0203) ≈ 0.980>0.05, the null hypothesis
is accepted. This implies that the mean directions for all three densities
are not different from each other for each planting density of M. malabathricum.
Similar patterns of symmetrical distributions were registered in the
different translations, irrespective of density regimes to which the plants
of M. malabathricum were subjected. The registered horizontal rotation
angle (mean direction) for the translations 15 were 249.292°, 175.935°,
230.576°, 75.832° and 90°, respectively. The means of algebraic
values of the horizontal rotation angles between two successive branches
were not significantly different, irrespective of the plant density, with
a mean vector of μ_{φ} = 212.89^{0} after 161
days of growth from seedling time to the successive date of measurement.
In addition, the observations do not seem to follow the unimodal distribution
(Fig. 3). Therefore, any given one branch had an equal probability
of the alternate position (Drouet and Moulia, 1997).
Similar observations were recorded for Larrea ameghinoi (Ezcurra
et al., 1991):
Influence of Plant Density on the Vertical Rotation Angle
It is too natural that the vertical rotation angle in the range from
0 to 180 degrees and it was also observed in the Rayleigh’s uniformity
test that the vertical rotation angles were not distributed uniformly
in the different plant densities (Table 3). The ANOVA
applied to assess the effects of density on the length of branches of
M. malabathricum. Since P (F>12.702) = 5.80x10^{5}
< 0.05, the hypothesis was rejected that the mean directions for all
densities are considered the same (Table 4). Given these
results, a natural question is: “AWhen subjected to plant density,
which mean direction of the branches will take a different value from
the others θ. Here, the comparisons for three pairs of densities
were made, viz., Densities 1 and 2, Densities 1 and 3 and Densities
2 and 3. Table 5 shows approximate ANOVA table values
for Densities 1 and 2, Densities 1 and 3 and Densities 2 and 3. From Table
5, it can be seen that the Fvalue is 3.68 in Densities 1 and 2 and
here, the null hypothesis was accepted, i.e., μ_{1} = μ_{2},
since P (F>3.68) ≈ 0.058 > 0.05. On the other hand, Fvalues
are 26.97 and 10.12 Table 5 in Densities 1 and 3 and
Denesties 2 and 3; because of this, the null hypotheses can be rejected,
μ_{1} = μ_{3} and μ_{2} = μ_{3},
respectively. The mean direction is defined in the same manner, as shown
in Equation 1. Invariably, there is a tendency that the
angles for Density 3 generally take smaller values than those for Densities
1 and 2. As for the comparison between Density 1 and 2, it seems that
Fig. 4 and Table 3 show that distributions
of the angles for Density 1 and 2 are similar. However, from Table
5, the mean direction of the angles for Density 2 is less than that
for Density 1.

Fig. 3: 
The mean vector (μ = 212.89°) of the horizontal
rotation angle φ irrespective of plant density in the single
plant spacing of Melastoma malabathricum 
Table 3: 
Descriptive statistics of the vertical angle θ
of branches in Melastoma malabathricum 

*Significant difference at p < 0.05 
Table 4: 
Approximate ANOVA table for testing the influence of
density on the rotation angle of branches of Melastoma malabathricum 

*Significant difference at p < 0.05 
When plants of M. malabathricum were subjected to density stress,
the ensuing competition between branches led them to be more erect in
stature as in D3, with measurably smaller vertical rotation angle θ
values.
The same result was observed in that the branches of densitystressed plants
had an inward curving of the branch planes (Ezcurra et
al., 1991). When plant population increased, branches became progressively
more erect with the mean angles decreasing from 52.27° to 47.8° and
41.81° (Table 4). Results were in agreement with other
reports citing significantly smaller θ angles at higher densities.

Fig. 4: 
Boxplots of the vertical rotation angle of the branches
for each plant density of Melastoma malabathricum 
Table 5: 
Approximate ANOVA for (a) Densities 1 and 2, (b) Densities
1 and 3 and (c) Densities 2 and 3 of Melastoma malabathricum 

**Significantly difference at p < 0.01; ns, not significantly
difference at p < 0.05 
Relationship among Vertical Rotation Angles and Translations
Statistical analysis of the circular data indicated that the lengths
of mean vector increased throughout the translation from the base to the
top of plant height in other words ,branches were more erect in the top
of the plant canopy, arguably for optimization of light interception (Table
6).
The WatsonWilliams test with multiple comparison showed there were significant
differences in F = 50.157, (p < 0.01) for the vertical rotation angle in
different translations. When WatsonWilliams tests for paired comparisons of
the vertical rotation angles for branches at different heights were done, results
indicated that θ values decreased with increasing translations from 0 cm
to 150 cm, with nonsignificant differences for ensuing translations beyond
150 cm (Table 6). However, if the angles were greater than
50°, it was apparent that branch lengths decrease slightly as the angle
increased. These results are consistent with those obtained by others (Drouet
and Moulia, 1997; Maddonnia et al., 2001),
who studied the effect on developmental plasticity in crown asymmetry both by
the directionality of solar radiation geometry and by local competition between
individual plants and their modules (Ezcurra et al.,
1991).
One report showed that the vertical and horizontal rotation of foliage clusters
are nonrandom as are secondary leaf and branch orientations, which allow branches
and leaves to intercept light without interfering with each other (Neufeld
et al., 1988).
The difference in vertical rotation angles at different translations
can easily be compared by plotting the lengths and translations of multiple
boxplots. Figure 5 clearly shows the prevailing inverse
relationship between translation and θ values in M. malabathricum
in which the vertical rotation angle decreases when plant height increases.
This conclusion is strengthened by the WatsonWilliams Ftests for vertical
rotation angles in different translations of M. malabathricum (Table
7).

Fig. 5: 
Boxplots of the vertical rotation angles (degree) for
Melastoma malabathricum against the different translations:
1, 050 cm; 2, 50100 cm; 3, 50100 cm; 4, 150200 cm; 5, 200250
cm 
Table 6: 
Summary of vertical rotation angles and branch length
at different translations of Melastoma malabathricum 

*1, 050 cm; 2, 50100 cm; 3, 100150 cm; 4, 150200
cm; 5, 200250 cm 
Table 7: 
Pairwise comparison of vertical rotation angles at
different translations of Melastoma malabathricum by WatsonWilliams
Ftests, where F and P are Fisher’s variance ratio and the probability
associated with the null hypothesis, respectively that (H0: v_{1}
= v_{2} against H_{1}: v_{1}θ v_{2}) 

There is no comparison for translation 5 because this
included less than 5 observations 
Table 8: 
Summary of the Scheffe’s test on length of branches
for each density of Melastoma malabathricum* 

*Values with the same letter(s) have no significant
difference at α = 0.05 
This is a suitable strategy for plants of M. malabathricum to
achieve enough light for ensuring growth of leaves growing down inside
the canopy, where selfshading leads to lower light availability than
at the top of the plant canopy.
Table 6 Shows the relationship between translation and length
of branches, this reveals that, as the height of branches increases, branch
length decreases, with the exception that the median of translation 2 (50100
cm) is slightly greater than that of translation 1 (050 cm). Formal comparisons
with Scheffe’s test indicated that the lengths decreased significantly
which had F = 44.43 and α < 0.01 from 41 to 8 cm at translations 1 and
4 respectively, but the difference in branch lengths between the translations
1 and 2 was not significant at α < 0.05 and no comparison was made for
translation 5 because it included less than 5 observations for Scheffe’s
test (Table 8). Table 8 summarizes branch
lengths at each translation. The boxplots listed in Fig. 6
show that branch lengths of M. malabathricum have an inverse relationship
with the plant translation. Branches in the top of the canopy were more erect
than their counterparts at lower heights, arguably for optimization of light
interception. Such orientation and distribution of branches allow the gradual
warming of leaf surfaces during the morning, with maximum light interception
(Ezcurra et al., 1991).
Evaluating the Influence of Plant Density on Branch Length
ANOVA for singlefactor plant density regimes on the branch lengths
indicated that with increasing plant density, branch length significantly
decreased (p < 0.05) from D1: 40.4 cm, D2: 30.3 to D3:28.6, although
there was no significant difference between the length of branches in
D2 and D3. The lengths of branches for each density, explicitly showing
that the higher the planting density, the shorter was the length of branches
of M. malabathricum. It is possible to confirm this interpretation
based on Scheffe’s test on length of branches for each density of
Melastoma malabathricum (Table 8).
CircularLinear Correlation among Branch Lengths with Vertical Rotation
Angle
A natural question to address is whether there is a definite relationship
between the lengths and vertical rotation angles of branches. Table
8 shows a plot of the vertical rotation angles θ and lengths
of branches. Possible relationships between vertical rotation angle, circular
variable and branch length and linear variable in M. malabathricum,
as influenced by plant density regimes were attempted by using equation
2. The linearcircular correlation between the lengths and θ
angles is given by r^{2} = 3.0x10^{3}. The highest circularlinear
correlation (r = 0.594, p < 0.01) between the vertical rotation angle
values and the lengths of branches in different plant densities was observed
in the translations exceeding 150 cm of the plant height.
All measures in this study were taken during a growth period of 161 days
from seedling to flowerdisplaying growth stages and the results showed
that the vertical rotation angles of the branches bear an inverse relationship
to the translations. Generally, the higher the translation of the canopy,
the shorter branches were in length. Vertical rotation angles were proportional
to branch lengths when the θ values did not exceed 50°. If θ
is in excess of 50°, the branch length decreases slightly as θ
increases. However, a circularlinear correlation coefficient shows that
there is no clear association between vertical rotation angle θ and
branch lengths. Plant density has a negative effect on the length of branches,
but horizontal rotation angles φ were dependent on density to which
the plants of M. malabathricum were subjected.
Light absorption by plants affects the development of a canopy directly, through
photobiological processes. Asymmetric tree growth is an adaptation to maximize
photosynthesis by growing in response to the presence of gaps and neighbours,
topographical site conditions or incoming solar radiation. High neighbourhood
densities may result in densitydependent mortality of individuals or modules,
or/and this may be compensated by shifting the crown centers away from the main
stem as the tree expands branches on the side of canopy gaps in the lower translations,
or closer or erect to the main stem in the higher translations. It follows that
with higher plant densities, or with the measurement extended for a longer period,
a longterm competitive effect among neighbouring plants may prevail. If this
happens, asymmetric distribution of the horizontal rotation angle to the gap
direction of the canopy as branch networks develop through plastic (Harper,
1977) response to a heterogeneous light environment because canopy structure
is mainly subjected to maximize photosynthesis. It is generally assumed that
trees optimize light harvest via more regular crown patterns; also, this is
important in natural systems because the range of influence of plants becomes
greater with size and age. Therefore, larger plants beyond immediate neighbours
often have the greatest influence on the growth of a focal plant (Muth
and Bazzaz, 2002; Getzin et al., 2006). Further
plant modules tend to expand their growth toward the gaps prevailing in the
canopy.
Results demonstrate that competitive interactions with neighbours affect the
spatial arrangement of branch systems in M. malabathricum. Branch systems
were more developed away from the maximum competitive pressure of neighbors,
as asymmetry was not observed in crown shape. Density of neighbors did not appear
to contribute significantly to the relation between branch system and pressure
from neighbors for 161 days after transplanting the seedling into wooden boxes.
The resulting spatial pattern tended to reduce the overlap between neighboring
branch systems. A plant with a close neighbor responds by investing in branch
growth away from the competitive pressure or simply into zones free of neighbors
(Brisson and Reynolds, 1994). Under this model, two plants
can be close to each other and not compete. Competition in the population is
for space and only occurs when a plant branch system is crowded on all sides.
It would be interesting to see the photosynthetic efficiency of branches
subjected to different light regimes within the translations and relate
branch growth and dispersion into the gaps or away from the competition
zones. It would be equally interesting to assess the azimuthal positioning
of branches in relation to their photosynthetic efficiency, or whether
uniformity in branch alignment and symmetry within a canopy are actually
translated into photosynthetic efficiency or biomass production among
competing plants.
ACKNOWLEDGMENTS
We acknowledge the financial assistance through Fundamental Grant No.
PS074/2007B given to the first author by the University of Malaya and
to the Institute of Biological Sciences, University of Malaya for providing
the facilities throughout this study. The authors appreciate the help
rendered by Prof. Dr. Bill Gregg of University of State Mississippi:,
USA and two other anonymous referees for their review and useful suggestions
on the manuscripts.