
Research Article


Population Structure and its Influence on SelfThinning of Melastoma malabathricum L.


M. Faravani
and
B.B. Baki


ABSTRACT

The effects of density on the growth rate and survival
of individual plants as well as changes in population structure and selfthinning
were experimentally evaluated in Melastoma malabathricum at five
densities (19098, 76394, 152788, 229183 and 458365 seeds m^{2}).
The biomass (dry weight) of root, stem and leaf was measured for seven
times after drying from the 18 to 162th days after planting. It was applied
at 20 day intervals. The relationship between the total dry matter weights
per plant and plant densities of survivors for populations of Melastoma
malabathricum showed that each population will start to thin along
a line of slope from 3.7 to 1.2 until it reaches the maximum standing
crop. Mortality during the phase of selfthinning is largely among individuals
suppressed by the ensuing growth of neighbours, resulting in increased
shading within the canopies of neighbouring plants. The total dry matter
(m^{2}) was constant over a wide range of densities because individual
plant displayed densitydependent reduction in growth rate and hence in
individual plant size, in particular, because the reductions in mean plant
weight compensated exactly for increase in density. 




INTRODUCTION
Thinning processes may occur in all crowded plant and animal populations, pure
or mixed and this may play important roles in the demography of populations
and community structure (Quinones et al., 2003).
Intraspecific competition is a particular form of competition in which members
of the same species vie for the same resource in an ecosystem (e.g., food, light,
nutrients and space). This can be contrasted with interspecific competition,
in which different species compete (Solomon et al.,
2002). In selfthinning of plant populations, size inequality decreases
as a result of the predominant mortality of the smallest size class (Weiner
et al., 2001; Rivera and Scrosati, 2008).
By understanding the factors limiting the growth of the individuals within
the population, the response of the population as a whole can be deduced. This
finding, termed the law of constant final yield (Polley et
al., 2008) and this has been shown to hold for a large number of species.
A widely accepted generalization about these paths is the selfthinning rule,
or Power Law of Selfthinning (White and Harper, 1970;
Lonsdale and Watkinson, 1982; Li,
2002; Simard and Zimonick, 2005), otherwise known
as Self Thinning Law or the 3/2 Power Law or Yoda Law (Hara
et al., 2006; Rivera and Scrosati, 2008; Wiegand
et al., 2008).
The selfthinning rule relates plant mass to plant density in crowded, by a
powerlaw equation with an exponent 3/2. It has been also called the 3/2 power
law or Yoda`s law (Li et al., 2000; Rivera
and Scrosati, 2008).
The model for self thinning was taken from Yoda et al.
(1963) cited by Hara et al. (2006):
Log w = Log Îš + β Log Ï? 
where, w is the mean biomass per plant, where Ï? is the number of surviving
plants, k and β are the selfthinning coefficient and exponent, respectively.
The exponent β has been claimed to take the value 3/2 approximately regardless
of species, age or site conditions and k varies with species and growth conditions
and it is constant. The rule has been hotly debated whether a true selfthinning
law exists in nearly pure stands of post fire chaparral and if so, is it a 3/2
or 4/3 law (Guo and Rundel, 1998; Zeide,
2001; Bi, 2004; McCarthy and Weetman,
2007). Lonsdale and Watkinson (1982) showed the 3/2
power law is a characteristic of shoots but not of whole plants. Recently, Chen
et al. (2008) argued that the traditional slope of the upper boundary
line, 3/2, has been challenged by 4/3 which is deduced from some new mechanical
theories, like the metabolic theory.
More experimental or field studies should be carried out to identify
the more accurate selfthinning exponent. In this study we wanted to check
if the evidence could support acceptance of selfthinning rule as a quantitative
biological law in Melastoma malabathricum. By using the slopes
and intercepts of sizedensity relationships as variables, the slopes
can be explained by simple geometric arguments. Here, we hypothesized
that the sensitivity of plant may affect the rate of selfthinning, hence,
in the plant community through resource capture and utilization.
MATERIALS AND METHODS
Plant Establishment
Seeds of M. malabathricum of the same cohorts were collected
in September 2006 from the campus of the University of Malaya, Kuala Lumpur
(3 Â° 8` N; 101 Â° 42` E) Malaysia. A synthetic community of M.
malabthricum was established by sowing seeds directly in 26 cm depthx14
cm diameter in black plastic pots, 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 Î¼mole photon m^{2}
sec^{1} outdoor and inside in insectproof house, respectively)
and mean ambient temperatures of 33 Â± 2 Â°C (day) and 25 Â±
2 Â°C (night) at Rimba Ilmu, University of Malaya, Kuala Lumpur. The
plants were watered once daily, in the morning from above with a fine
rose. A seed germination test experiment was conducted to check seed vigour,
seed viability and seed germination in advance, prior to experimentation.
Five sowing densities viz. 19098, 76394, 152788, 229183 and 458365 seeds
m^{2}, equal to 0.01, 0.040, 0.080, 0.12 and 0.240 g were applied
in area each measuring 0.0154 m^{2} and each density was accorded
ten replicates.
Recording of Density and Individual Weight of Melastoma malabathricum
A circular quadrate was sampled in the center of each pot (using PVC
pipe, internal diameter 3.0 cm) in the 40th (t_{1}), 60th (t_{2}),
80th (t_{3}), 100th (t_{4}) , 120th (t_{5}),140th (t_{6})
and 160th (t_{7}) Days After Planting (DAP). The small quadrate (7.1
cm^{2}) was used in the populations of M. malabathricum with
high density and the large quadrate (1.8 cm^{2}) in the populations
with low density. The total No. of plants in the quadrate was recorded as number
per m^{2}. Samples were taken seven times on 18th to 162 days after
planting (DAP) every 20 day intervals. All fresh plants were killed by liquid
N_{2} to stop their metabolism. They were separated into stem, leaf
and root before being dried for 48 h at 70 Â°C. After two weeks, the seed
germination was considered as the initial densities in this study. Densities
at this first observation were checked if they were less than the numbers we
had expected to germinate, based on the weighed seed lots for each pot and on
estimates of seeds pot^{1} (Table 1). Therefore failures
to germinate and mortality before emergence were not negligible. The mean seed
germination rate at 25 Â°C was 40 in the laboratory tests. We have used principal
component analysis with logarithmicized data to calculate the slope of the thinning
lines shown in this study (Mohler et al., 1978).
RESULTS AND DISCUSSION
Mean density of established plants of M. malabathricum during
the first measurement after germination was extremely lower than the initial
sowing density in all density treatments. Substantial declines in density
were observed with time by the first and ensuing harvests at the five
density treatment over period of 160 days after sowing, the declines were
densitydependent.
There was a strong, negatively densitydependent relationship with a
linear relation y = 29.27 3.56x, R^{2} = 0.94, p<0.05 for
inhibition of germination by increasing sowing density (Fig.
1).
This negative relationship has been already reported in other plants by Lonsdale
and Watkinson (1982). In these experiments, population numbers declined
from the initial sowing densities not only as a result of selfthinning but
also as a result of negatively densitydependent seed germination. At a sowing
density of 458,365 seeds m^{2}, only 14% of the seeds germinated, in
comparison with 30% at 19098 seeds m^{2}. There are, however, a number
of reports of in most of these experiments, where overall density was held constant
while seeds were aggregated in clumps of varying sizes. The CO_{2} produced
by the roots might be acting as an inhibitor and also competition for resources
between seeds and seedlings might be implicated (Inouye,
1980; Lonsdale and Watkinson, 1982).
As individuals grow in a competing population of plants, their mean biomass
increases and their number decrease. Plotting mean plant biomass (dry weight,
calculated by dividing total plant weight per pot by the number of survivors)
(log) against the five density of survivors (plant m^{2}) in the populations
with time of sowing showed that total plant weight decreased (Fig.
2, 3), starting in the lower right corner with a large
number of plants of small size and moving up and to the left as the number of
plants decline and the plants grow as a result of self thinning (Adler,
1996).
The relationship of the plant biomass and the plant density regimes were significant,
in the regression models for self thinning (Table 1). It indicates
the slope values and 95% confidence limits of slopes. The obtained slope value
(1.2) match well with findings based on a much longer observation period on
stands of shrub species in a different area (Schlesinger
and Gill, 1980). The selfthinning slope is more widely accepted, on theoretical
grounds, as being 1/2 (or 3/2), as originally suggested by Yoda
et al. (1963) and subsequent researchers, the regression slopes based
on the data of this study are much closer to  4/3 (based on mean biomass as
shown in Fig. 2).

Fig. 1: 
Seed germination as influenced by sowing density of
Melastoma malabathricum 

Fig. 2: 
The relationship between the total dry matter weights
per plant and plant densities of survivors for populations of Melastoma
malabathricum sown at five densities (15) with the lines joint
populations of the five sowing densities harvested on seven successive
occasions indicating the trajectories, over time (40160 DAP) and
these population would have followed. Arrows indicate the directions
of the trajectories, or the direction of selfthinning. At low densities
especially, growth and hence mean dry weight is roughly independent
of density but with ensuing plant growth over time, densitydependent
reduction in growth compensation is denoted by variations in density,
leading to achievement of fairly constant dry matter and slope of
1.17 
Table 1: 
Gradient and intercept values for the thinning lines
of populations of Melastoma malabathricum grown under various
plant densities regimes and plant biomass (mg), calculated by principal
components analysis 

**, *Mean the relationship between two variables in
the regression model is significant at p<0.01 or p<0.05. The
equation of the lines is log w = log k + β log Ï? where,
w is plant biomass (mg), Ï? is the density of survivors and k
and β are constants 
The slope of 1/3 (or 4/3) have also been reported more frequently in recent
empirical studies (Bi, 2004; McCarthy
and Weetman, 2007). The relation of the mean plant biomass and the survivors
conforms to the power law with an ideal slope value is within the 95% confidence
limits of the slopes of the significant models at p<0.05 (Table
1). The same results depicting the similar slope structure(s) have been
already reported by Kays and Harper (1974), Westoby
and Howell (1986) and Zhang et al. (2005).
The slope line is close to 1 but not exactly 1 and the relationship between
dependent variable (w) and an independent or explanatory variable (p) is ultimately
allometric (Marquet et al., 2005). In intraspecific
competition, the resultant populations based on differential birth rates and
death rates of plant (whether as genet or ramet entities), or number leaves
or branches per plant, (as ramet entities), can regulate individual plant production
or population at stable density from a very wide range of initial densities,
bringing them to a narrow range of final densities and production per unit area
and it therefore trends to keep density within certain limits (Fig.
2).
Figure 2 shows the fluctuations within plant biomass
in single plant or per unit in populations of M. malabathricum whereas
plant density decreases leads to parallel decrease in plant biomass. It
is a schematic representation of the effects selfthinning on the numbers
and individual plant weights with time in Melastoma malabathricum
populations. It is envisaged that each population will start to thin along
a line of slope from 3.7 to 1.2 until it reaches the maximum standing
crop. Mortality during the phase of selfthinning is largely among individuals
suppressed by the ensuing growth of neighbours, resulting in increased
shading within the canopies of neighbouring plants. It also depicts the
likely patterns by which populations of M. malabathricum might
increase from an initially very small size of aboveground biomass (when
the plant colonizes a previously unoccupied area) only to reach the asymptote
as time progresses. If a succession of time intervals is taken singly,
then each final density can be treated as the initial density for the
next timeinterval.
Oneway ANOVA and Tukey`s Post Hoc Test (data not shown) indicate the
mean plant was significantly (p<0.05) higher at low densities (Fig.
2). This phenomenon maybe caused by more photosynthetic activity among
leaves because of leaf size as mean weight of leaves per plant was more
at low density regimes. The total dry matter (m^{2}) was constant
over a wide range of densities because individual plant displayed densitydependent
reduction in growth rate and hence in individual plant size, in particular,
because the reductions in mean plant weight compensated exactly for increase
in density.
The relationship between mean shoot weight per plant (calculated by dividing
total shoot weight per sample by the number of survivors) and the density
of survivors in the populations conforms with the power law; thinning
occurred along a line with a slope of 1.10 (R^{2} = 0.63, p<0.05)
and 95% confidence limits to slope 2.07 (or 0.12) an intercept, log
k, of 8.59 and then deflect from it as dead genets accumulate within the
population (Fig. 3, Table 2).
Under the environmental regime of the present experiment, being conducted in
the insectproof house with mean midday radiation of 622 and 125 Î¼mole photon
m^{2} sec^{1} outdoor and inside in insectproof house , respectively,
therefore, with reduce light intensities, maximum yield is reduced; and the
slope is not exactly 1 but it is close to 1 or  4/3 (Table
1). In practice thought ,few selfthinning populations reach these maximum
yields; and selfthinning populations with the slope of exactly 1 are rare
(Begon et al., 1990; Guo and
Rundel, 1998). Table 1 show all lines have a slope of
approximating to 3/2 within the 95% confidence limits. The mean line slopes
were less than 3/2 because of M. malabathricum is perennial shrub and
the experiment conducted for a short period of 6 months.
The regression slopes, however, could change dramatically and if this happens,
it reflects the integrated effects of all external influences like as disturbances,
grazing, disease, drought, or other stressinducing factors (Guo
and Rundel, 1998). Different regression algorithms will produce different
slope estimates, depending on the error structure of the data and the correlation
between the bivariate data (Hamilton et al., 1995;
Bi, 2004; Zhang et al., 2005).

Fig. 3: 
Selfthinning in Melastoma malabathricum populations
sown at five densities (15) against mean shoot biomass (mg plant^{1})
with the lines joint populations of the five sowing densities harvested
on seven successive occasions. They therefore indicate the trajectories
, over time (40160 DAP), that these populations would have followed.
The arrow indicates the directions of the trajectories, i.e., the
direction of selfthinning. The gradient of the thinning slope was
1.10 
Table 2: 
Gradient and slope intercept values for the thinning
lines within populations of Melastoma malabathricum grown under
various plant densities regimes and mean shoot biomass (mg plant^{1})
, calculated by principal components analysis 

^{+}Intercept (k), slope (β), R^{2}
correlation coefficient and thinning populations by the reduced major
axis using the equation Log w = log k β log p, where, w is mean
shoot dry weight per plant, Ï? is the density of survivors 
The slope value for selfthinning has been argued that the 3/2 power rule
should be the 4/3 law (Ogawa, 2001; Niklas,
2003; Niklas and Spatz, 2006) based on the metabolic
theory (West et al., 1997). Other researchers
(Adler, 1996; Chen et al.,
2008) also provided a range of slope to describe the selfthinning rule.
Table 3: 
Allometric relationships between mean leaf mass (mg
plant^{1}) and mean root for Melastoma malabathricum
grown at five plant densities 

^{+}Intercept (k), slope (β), R^{2}
correlation coefficient and thinning populations by the reduced major
axis using the equation Log w = log kβ log p 
If succession of time intervals is taken singly, then each final density can
be treated as the initial density for the next time interval. Thereafter, the
biomass increased less and less with each time intervals until the population
reached its carrying capacity (resources of the environment that can just maintain
the population size in without a tendency to either increase or decrease (Begon
et al., 1990).The biomass might therefore be expected to follow a
sigmoidal curve due to ensuing competition vis à vis the onset of
competition between survivors in high densities than low densities. This is
a consequence of the hump in its recruitment rate curve, which is itself a consequence
of intraspecific competition. When the log of average leaf weight per plant
was plotted against the log of density of survivors for a crowded evenaged
plant population, in such a way that the population`s trajectory was held under
a line of slope 1.12 (R^{2 }= 0.58, p<0.05) and 95% confidence limits
to slope 2.23 (or 0.01) with an intercept, log k, of 8.69 (Table
3).
The results of this experiment suggests that there are limited resources
available for M. malabathricum plant growth and that at high densities
these are shared among the bigger number of competing individuals. If
this would be the case, it is expected that provision of extra resources
would allow greater growth of individuals` plants and greater yield per
unit area. We have seen that intraspecific competition of M. malabathricum
can, over a period of time, could influence the number of deaths, the
number of births, among genets or ramets, or both, the amount of growth
and the distribution of biomass within the population. With progressing
the time, the individuals grow in size, their requirements increase and
they therefore compete at an increasingly greater intensity. This, in
turn, tends to gradually increase their risk of dying. Thus, the number
that survived and the growth rate of the survivors are simultaneously
influenced by density.
A slope of 3/2 indicates that in a growing, selfthinning population,
mean plant weight increases faster than the decreases in density. A population
following a 3/2 thinning line will therefore steadily increase its total
weight (or yield). Eventually, of course, this increase will cease as
yield cannot increase indefinitely. Instead, the thinning line might be
expected to change from slope of 3/2 to a slope of 1, in such a way
that the increase in mean plant weight is likely compensated by as the
decrease in density.
A slope of 1 indicates that the further growth of survivors is exactly balanced
by the deaths of other individuals. Upon reaching the asymptote with the maximum
total yield possible, no further increase is possible for the said species in
question in that environment (Begon et al., 1990)
.
The mean weight of leaves per plant was influenced by the plant density treatments
and the highest leaves weight per plant was recorded in the lowest plant density.
As the surviving leaves in the canopy grow old, their photosynthetic activity
falls below that required balancing respiratory load so that leaves, branch
and eventually whole genets begin to die. Consequently, the number of live plants
and the proportion of live matter within the population decreases (Donohue
and Schmitt, 1999). Further statistical analysis using logarithmic regression
on the relationship between plant height (cm) and log density of survivors as
a function of time confirmed that the power law prevailed whereby thinning occurred
along a line with a slope of 1.42 (R^{2 }= 0.71, p<0.05) and within
the 95% confidence limits to slope 2.46 (or 0.38), with an intercept, log
k, of 10.36 (Table 4).
Table 4: 
Gradient and slope intercept values for the thinning
lines of populations of Melastoma malabathricum grown under
various plant densities regimes and plant height (cm), calculated
by principal components analysis 

^{+}Intercept (k), slope (β), R^{2}
correlation coefficient and thinning populations by the reduced major
axis using the equation Log w = log k β log p, where, w is plant
height, Ï? is the density of survivors 
Table 5: 
Gradient and intercept for the thinning lines of populations
of Melastoma malabathricum grown under various plant densities
regimes and mean root biomass (mg plant^{1}), calculated
by principal components analysis 

^{+}Intercept (k), slope (β), R^{2}
correlation coefficient and thinning populations by the reduced major
axis using the equation Log w = log k β log p 
Plant responses to crowding may be mediated by resource availability and/or
by a specific environmental cue, with the ratio of red:far red wavelengths (R:FR)
perceived by phytochrome (Donohue and Schmitt, 1999).
Root biomass was significantly (p<0.05) affected by density, being
greater at low density than at high density (data not shown). Root biomass
decreased with increasing plant density in all harvests, indicating that
root growth was negatively related with plant density. The logarithmic
models between different plant survivors at different densities and dry
weight of root conforms to the power law; whereby thinning occurred along
a line with a slope of 1.23 (R^{2 }= 0.62, p<0.05) and within
the 95% confidence limits with slope values registering 2.34 (or 0.13)
and an intercept, log k, of 9.69. It showed that increased root competition
could lower the slope and/or intercept of the selfthinning line transverse
by plant populations (Table 5).
As root: shoot ratios were remarkably constant over the broad range of
plant size achieved in the five densities. Thus, these plants do not exhibit
above versus belowground biomass tradeoffs in their ability to compete
for light versus belowground resources.
Plasticity in biomass allocation, root morphology and root distribution pattern
has been found to be an important adaptive mechanism to acquire nutrient resources
(Xie et al., 2001, 2007). As with shoot biomass,
root biomass increased in low density levels. The rate of increase slowed or
became negative with increasing the population density. The value of the selfthinning
exponent was 1.23 at the final phase, 160 days after transplanting of stand
development.
In summary, present results support the concept of competitionmediated
selfthinning rule. The different selfthinning power is a plant response
to the resource utilization and sensitivity to stress. Because regression
slopes are affected by multiple factors, they can vary greatly among species
and habitats. Regression analysis could be very helpful in identifying
the presence of other factors that affect the development of ecological
communities. More wellcontrolled experiments should be carried out in
order to identify which is more accurate values between 3/2 and 4/3
or 1.
By considering all morphological attributes of the different growth forms suggests
that growth form differentiation may be a plastic response to increasing levels
of density stress. For example, increased density in plant populations commonly
resulted in decrease in plant size as a result of increasing competition for
limited resources (Harper, 1977). Likewise, the decreased
allocation of resources to sexual reproduction is a common response to high
levels of intraspecific competition (Harper, 1977).
ACKNOWLEDGMENT
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.

REFERENCES 
Adler, F.R., 1996. A model of selfthinning through local competition. Proc. Nat. Acad. Sci. USA., 93: 99809984. Direct Link 
Begon, M., J.L. Harper and C.R. Townsend, 1990. Ecology, Individual, Population and Communities. 2nd Edn., Blackwell Scientific Publications, London, ISBN: QH541.B415.
Bi, H., 2004. Stochastic frontier analysis of a classic selfthinning experiment. Aust. Ecol., 29: 408417. CrossRef  Direct Link 
Chen, K., H.M. Kang, J. Bai, X.W. Fang and G. Wang, 2008. Relationship between the virtual dynamic thinning line and the selfthinning boundary line in simulated plant populations. J. Integr. Plant Biol., 50: 280290. CrossRef  ASCI 
Donohue, K. and J. Schmitt, 1999. The genetic architecture of plasticity to density in impatiens capensis. Evolution, 53: 13771386. Direct Link 
Guo, Q. and P.W. Rundel, 1998. Selfthinning in early postfire chaparral succession: Mechanisms, implications and a combined approach. J. Ecol., 79: 579586. CrossRef 
Hamilton, N.R.S., C. Matthew and G. Lemaire, 1995. In defence of the3/2 boundary rule: A reevaluation of selfthinning concepts and status. Ann. Bot., 76: 569577. CrossRef 
Hara, T., F. Koike and K. Matsui, 2006. Crowding effect in marine macrophytic algae populations. J. Plant Res., 99: 319321. CrossRef  Direct Link 
Harper, J.L., 1977. Population Biology of Plants. 1st Edn., Academy Press, London.
Inouye, R.S., 1980. Densitydependent germination response by seeds of desert annuals. Oecologia, 46: 235238. CrossRef 
Kays, S. and J.L. Harper, 1974. The regulation of plant and tiller density in a grass sward. J. Ecol., 62: 97105. Direct Link 
Li, B.L., H. Wu and G. Zou, 2000. Selfthinning rule: A causal interpretation from ecological field theory. Ecol. Model., 132: 167167. Direct Link 
Li, X.L., 2002. Competitiondensity effect in plant populations. J. Forest. Res., 13: 4850. CrossRef  Direct Link 
Lonsdale, W.M. and A.R. Watkinson, 1982. Light and selfthinning. New Phytol., 90: 431445. Direct Link 
Marquet, P.A., R.A. Quiñones, S. Abades, F. Labra and M. Tognelli et al., 2005. Review scaling and powerlaws in ecological systems. J. Exp. Biol., 208: 17491769. CrossRef  Direct Link 
McCarthy, J.W. and G. Weetman, 2007. Selfthinning dynamics in a balsam fir (Abies balsamea (L.) Mill.) Insectmediated boreal forest chronosequence. For. Ecol. Manage., 241: 295309. Direct Link 
Mohler, C.L., P.L. Marks and D.G. Sprugel, 1978. Stand structure and allometry of trees during selfthinning of pure stands. J. Ecol., 66: 599614. Direct Link 
Niklas, K.J. and H.C. Spatz, 2006. Allometric theory and the mechanical stability of large trees: Proof and conjecture. Am. J. Bot., 93: 824828. Direct Link 
Niklas, K.J., 2003. Reexamination of a canonical model for plant organ biomass partitioning. Am. J. Bot., 90: 250254. Direct Link 
Ogawa, K., 2001. Time trajectories of mass and density in a chamaecyparis obtusa seedling population. For. Ecol. Manage., 142: 291296. CrossRef 
Polley, H.W., B.J. Wilsey and J.D. Derner, 2008. Do species evenness and plant density influence the magnitude of selection and complementarity effects in annual plant species mixtures? Ecol. Lett., 6: 248256. CrossRef 
Quinones, R.A., T. Platt and J. Rodriguez, 2003. Patterns of biomasssize spectra from oligotrophic waters of the Northwest Atlantic. Prog. Oceanogr., 57: 405427. CrossRef 
Rivera, M. and R. Scrosati, 2008. Selfthinning and sizeinequality dynamics in a clonal seaweed (Sargassum lapazanum, Phaeophyeae). J. Phycol., 44: 4549. CrossRef  Direct Link 
Schlesinger, W.H. and D.S. Gill, 1980. Biomass, production and changes in the availability of light, water and nutrients during the development of the chaparral shrub, Ceanothus megacarpus after fire. J. Ecol., 61: 781789. CrossRef 
Simard, S.W. and B.J. Zimonick, 2005. Neighborhood size effects on mortality, growth and crown morphology of paper birch. For. Ecol. Manage., 214: 251265. Direct Link 
Solomon, E.P., L.R. Berg and D.W. Martin, 2002. Biology. 6th Edn., Brooks Cole, Pacific Grove, Calif., London, ISBN 10: 0030335035.
Weiner, J., P. Stoll, H. MullerLandau and A. Jasentuliyana, 2001. The effects of density, spatial pattern and competitive symmetry on size variation in simulated plant populations. Am. Nat., 158: 438450. Direct Link 
West, G.B., J.H. Brown and B.J. Enquist, 1997. A General model for the origin of allometric scaling laws in biology. Science, 276: 122126. CrossRef 
Westoby, M. and J. Howell, 1986. Influence of population structure on selfthinning of plant populations. J. Ecol., 2: 343359. Direct Link 
White, J. and J.L. Harper, 1970. Correlated changes in plant size and number in plant populations. J. Ecol., 58: 467485. Direct Link 
Wiegand, K., D. Saltz, D. Ward and S.A. Levin, 2008. The role of size inequality in selfthinning: A patternoriented simulation model for arid savannas. Ecol. Model., 210: 431445. Direct Link 
Xie, Y., S. An, B. Wu and W. Wang, 2006. Densitydependent root morphology and root distribution in the submerged plant vallisneria natans. Environ. Exp. Bot., 57: 195200. Direct Link 
Xie, Z.M., Z.H. Ye and M.H. Wong, 2001. Distribution characteristics of fluoride and aluminum in soil profiles of an abandoned tea plantation and their uptake by six woody species. Environ. Exp. Bot., 26: 341346. Direct Link 
Yoda, K., T. Kira, H. Ogawa and K. Hozumi, 1963. Selfthinning in overcrowded pure stands under cultivated and natural conditions. J. Inst. Polytech. Osaka City Univ., 14: 106129. Direct Link 
Zeide, B., 2001. Natural thining and environmental change: An ecological process model. For. Ecol. Manage., 154: 165177. Direct Link 
Zhang, H., G.X. Wang, Z.O. Liu, Z.X. Sheen and X.Z. Zhao, 2005. Sensitivity of response to abscisic acid affects the power of selfthinning in Arabidopsis thaliana. Bot. Bull. Acad. Sinica, 46: 347353. Direct Link 



