Effects of Ultraviolet-B Irradiance on Intraspecific Competition and Facilitation of Plants: Self-Thinning, Size Inequality, and Phenotypic Plasticity
and Phenotypic Plasticity. PLoS ONE 7(11): e50822. doi:10.1371/journal.pone.0050822
Effects of Ultraviolet-B Irradiance on Intraspecific Competition and Facilitation of Plants: Self-Thinning, Size Inequality, and Phenotypic Plasticity
Rui-Chang Zhang 0
Yue Lin 0
Ming Yue 0
Qian Li 0
Xiao-Fei Zhang 0
Xiao Liu 0
Hong Chi 0
Yong- Fu Chai 0
Mao Wang 0
Lam-Son Phan Tran, RIKEN Plant Science Center, Japan
0 1 Key Laboratory of Resource Biology and Biotechnology in Western China (Northwest University), Ministry of Education , Xi'an, China , 2 Institute of Forest Growth and Computer Science, Dresden University of Technology , Tharandt, Germany , 3 Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling , Leipzig , Germany
(1) The effects of facilitation on the structure and dynamics of plant populations have not been studied so widely as competition. The UV-B radiation, as a typical environmental factor causing stress, may result in direct stress and facilitation. (2) The effects of UV-B radiation on intraspecific competition and facilitation were investigated based on the following three predictions on self-thinning, size inequality, and phenotypic plasticity: i) Self-thinning is the reduction in density that results from the increase in the mean biomass of individuals in crowded populations, and is driven by competition. In this study, the mortality rate of the population is predicted to decrease from UV-B irradiance. ii) The size inequality of a population increases with competition intensity because larger individuals receive a disproportionate share of resources, thereby leaving limited resources for smaller individuals. The second hypothesis assumes that direct stress decreases the size inequality of the population. iii) Phenotypic plasticity is the ability to alter one's morphology in response to environmental changes. The third hypothesis assumes that certain morphological indices can change among the trade-offs between competition, facilitation, and stress. These predictions were tested by conducting a field pot experiment using mung beans, and were supported by the following results: (3) UV-B radiation increased the survival rate of the population at the end of self-thinning. However, this result was mainly due to direct stress rather than facilitation. (4) Just as competitor, facilitation was also asymmetric. It increased the size inequality of populations during self-thinning, whereas stress decreased the size inequality. (5) Direct stress and facilitation influence plants differently on various scales. Stress inhibited plant growth, whereas facilitation showed the opposite on an individual scale. Stress increased survival rate, whereas facilitation increased individual variability on the population scale. (6) Trade-offs between competitions, facilitation, and direct stress varied in different growing stages.
Funding: Research was supported by grants from the National Science Foundation of China (30670366, 31070362) and Special Foundation of Key Laboratory of
Resource Biology and Biotechnology in Western China, Ministry of Education (2010JS100). The funders had no role in study design, data collection and analysis,
decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
The ultraviolet irradiance (280 nm to 320 nm) reaching the
Earths surface has significantly increased since 1979 due to the
unprecedented destruction of the ozone layer. Recent studies
predict further increase of ultraviolet irradiance in the future [1,2].
Several studies relative to the impact of enhanced UV-B radiation
on plant physiology, morphology, growth, and development have
been conducted [3,4,5,6,7,8]. The immediate effects of increased
UV-B in biotic interactions among plant individuals have great
potential consequences [9,10]. Studies showed that enhanced
UVB radiation, as an abiotic stress factor, alter the competitive
interactions among plants both at intra- and interspecific levels
[3,11,12,13]. Thus, UV-B radiation greatly affects the plant
population and community structure [14,15]. Nevertheless, the
potential role of positive interaction among plants under the stress
of enhanced UV-B radiation, have not been investigated.
Negative interactions, such as competitions, are dominant biotic
factors that shape plant populations and communities . The
important role of positive interactions (facilitation) in the structure
of plant system has been proven by several studies [17,18,19].
Plant facilitation is defined as the beneficial effects of neighbors
through the amelioration of habitat (e.g. moderation of stress),
which is particularly important when considering the performance
of plants under environmental severity (i.e. abiotic stress) . The
stress-gradient hypothesis (SGH)  predicts the a shift from
competition to facilitation along environment gradients, wherein
facilitation should be dominant over competition in the
development of population and community structure under high-stress
conditions [22,23,24]. This theory was supported by several
studies [25,26,27,28] and these studies also proposed an idea that
can expand the conceptual framework in ways of explicitly
considering the type of stress gradient and the characteristics of
life-history strategy . In connection with intraspecific
competition, the categories of stress have become more important
because individuals of certain species have the same life-history
strategy of CSR [30,31]. Although SGH was originally formulated
at the interspecific level, its validity at the intraspecific level was
The effects of enhanced UV-B radiation on plants would have
two aspects if facilitation appears. Direct stress inhibits plant
growth and facilitation, which is beneficial to individuals in the
population. However, as a non-resource-related abiotic stress,
enhanced UV-B radiation is different from resource-related stress,
such as water, light, and nutrients. The facilitation introduced by
UV-B radiation mainly reduces the damage from UV-B irradiance
rather than improve the utilization of resources. If facilitation does
exist in the context of UV-B radiation, this study proposes three
predictions about size inequality, self-thinning, and phenotypic
plasticity. These predictions will be verified by applying the SGH
theory in a field pot experiment.
The mortality rate of plants in a population increases as the
population density increases, which is known as density-dependent
mortality or self-thinning. Self-thinning is caused by competition.
Self-thinning occurs when crowding is severe, is concentrated
among the smallest individuals, and accordingly alter the size
distribution . Nonetheless, plants growing with supplementary
UV-B radiation may have a different mortality rate. The first
prediction describes that mortality rate is decreased by UV-B
radiation. This prediction is based on facilitation and direct stress.
First, plants receive more benefits from their neighbors as the
intensity of UV-B radiation increase in light of stress-gradient
hypothesis. Furthermore, neighboring plants protect individuals
from UV-B radiation damages because of facilitation. Hence, the
survival rate of population under high UV-B irradiance level is
higher than those under low UV-B irradiance level. This
explanation implies that the enhanced UV-B radiation, and not
self-thinning, was the primary cause of death in individuals.
Second, direct stress delays self-thinning and reduces the mortality
rate of the population by reducing the growth rates of individuals.
Hence, the survival rate of plants was higher under enhanced
UVB radiation compared with the ambient group. The second reason
is based on the premise that self-thinning was the main reason for
Competition among individuals usually increases size
variation within plant populations. Previous studies concluded that
the major factor that generates size variation in crowded plant
populations is size-asymmetric competition (i.e. larger plants
have more advantages due to their relative size in competition
compared with smaller ones). Larger individuals with more
advantages become gradually dominant in the population.
Accordingly, size inequality increases with density. The observed
increase in size inequality of populations supports the hypothesis
of size-asymmetric competition [32,33]. The effects of
selfthinning should also not be neglected because size inequality
keeps increasing until the onset of self-thinning as a crowded
population develops. However, this situation may change if the
population is placed under enhanced UV-B radiation. The
second prediction describes that direct UV-B stress decreases
the size inequality of the population because abiotic stress
decreases the growth rate of all the individuals, but not a part
of them. Nevertheless, the effects of facilitation on size
inequality are undetermined. There are two possibilities
regarding this condition. Larger individuals are more damaged
from UV-B stress than the smaller individuals. Consequently,
facilitation decreases the size inequality. In the second case,
larger individuals have more benefit from their neighbors
because they have more interactive area than smaller ones.
Therefore, size inequality of the population is increased by
facilitation, indicating that facilitation is unsymmetrical.
The third prediction describes that plant phenotypic plasticity
changes in different stages under enhanced UV-B radiation. Plant
phenotypic plasticity is caused by the changes in the allocation of
resources in the plasticity of plant size and morphology [34,35].
Phenotypic plasticity enables plants to adapt to different
environments. Plant height can be special in all the morphological indices
because of the important trade-off between obtaining light
resources and avoiding damages for plants growing under
enhanced UV-B radiation. Plants are apt to be taller to struggle
for light resources at higher densities, whereas they tend to be
shorter to avoid the damages of supplementary UV-B radiation
. Moreover, we speculate that the strategy for resources and
stress should be changed in different growth periods because the
impact of competition and UV-B radiation is not alterable under
different growing stages.
The current study aims to test the three hypotheses on plant
population and address the following problems: (1) Identify the
main factor that decreases the mortality rate of the population
during self-thinning, direct stress, or positive interactions; (2)
Determine whether facilitation increases or decreases size
inequality of population; and (3) Distinguish the mechanism in
the shift in strategy on obtaining light resources and avoiding stress
under different growth periods.
The biomass of plants in the isolated group declined with
UV-B radiation (Figure 1A), indicating that direct stress
decreases the biomass. Strong self-thinning was observed in
stage 3 (Figure 2). Meanwhile, the mean biomass declined with
UV-B radiation (Figure 1B), implying that the biomass of plants
was decreased by the net effects of stress and facilitation in stage
3. However, both total biomass of the population and the mean
biomass per plant increased with UV-B radiation at high
density in stage 2 (Figure 1C), suggesting that facilitation took
place in stage 2. Therefore, facilitation increased individual
biomass. The results in stage 2 show that the total biomass of
the population under the ambient UV-B radiation was still
lower than the low-enhanced radiation and high-enhanced
UVB radiation groups although the effects of UV-B stress were
higher than the facilitation in stage 3 (Figure 1B). This
condition was due to the least number of survival rates among
individuals under ambient UV-B.
Populations that experienced UV-B stress and facilitation had
higher survival rates than those under normal circumstance
(Figure 2). However, no statistical difference was observed between
populations under low- enhanced UV-B radiation and those under
high-enhanced UV-B radiation.
The Gini Coefficient in isolation was not calculated because
there was only one individual in one pot. Table S1 shows that in
the three stages, the Gini Coefficient of these plants were all
significantly affected by the UV-B treatments, density levels, and
two-way interaction between UV-B6Den (density) (P,0.001).
The conduction of multiple comparisons was difficult and
unpractical in the two-way ANOVA because of the interactions
between UV-B radiation and density. Thus, in this experiment,
one factor had to be fixed before the multiple comparisons. Results
showed that there was no consistent trend in the Gini Coefficient
of each plant part (root, stem, leaf, and fruit) during the three
stages (Figure 3). However, coincidental patterns at different
radiation and density levels were observed upon focusing on the
total plant biomass.
The enhanced UV-B radiation, which represented both UV-B
stress and facilitation, strongly influenced the size inequality of the
population with competition. The competition increased the size
inequality (Figure 4), regardless of whether there was UV-B stress
and facilitation. Furthermore, the minimum Gini coefficient was
observed at low density and the maximum Gini coefficient was
found at high-density in the field pot experiment (Figure 3).
The impacts of enhanced UV-B radiation on size inequality
were not as simple as competition; they were related to the
growing stage of the plant populations (Figure 4). The population
had lower size inequality under normal environmental condition
than that under both low-enhanced and high-enhanced UV-B
radiation in all three stages. However, the high-enhanced group
had the highest size inequality in stage 2 when the density was low.
Moreover, size inequality of the populations under low-enhanced
UV-B radiation was higher than that under high-enhanced UV-B
radiation stage 1. However, it was the lowest in the last two stages
Except for branch number and plant height, all morphological
indices (leaf number, crown width, and leaf area per plant)
decreased with the increase in density and UV-B radiation
(Figure 5). The branch number increased as UV-B radiation
increased in isolation. Plant height increased with density under
ambient condition, whereas plant height decreased with density
under both low- and high- enhanced UV-B radiations.
Plant height showed different trends in different stages. UV-B
radiation decreased plant height, but was increased with density
under ambient condition in all three stages. In stage 1, the height
increased with density under low- and high-enhanced UV-B
radiation; however, the result was totally opposite in the last stage.
Moreover, plant height decreased with density under
highenhanced UV-B radiation, but remained stable under
lowenhanced UV-B radiation in stage 2.
In this study, the effects of direct stress and facilitation on
populations with and without mortality were investigated. In the
field pot experiment, the effects of direct stress and facilitation
were too difficult to separate due to the close link between abiotic
Figure 2. Survival rate and mean biomass under different levels of UV-B radiation in the last stage. The high-density group under
different UV-B radiation levels (ambient, low-enhanced and high-enhanced) showed the relationships between the survival rate (bar) of mung bean
population and the mean biomass of individuals of the population (solid line) in the last month during self-thinning. The bars surmounted by
different letters are significantly different (P , 0.05) according to Duncans test and data are means 6 SD (there are 9 pots and n = 157 plants).
stress and positive interactions. Therefore, the following
assumptions were made:
(1) Facilitation only takes place when stress is present.
Facilitation increases with abiotic stress based on the current
study on facilitation. Positive interactions help individuals to
ameliorate the undesirable conditions caused by stress. Positive
interaction also protect plants from the damages of stress and
accelerates the growth of individuals in the population (2) Every
individual obtains resources from an area around them, whereas
neighboring plants assist and compete with each other where their
areas overlap . However, the overlapping area is relatively
small in the early phases of growing season. Hence, the
interactions, such as competition and facilitation among
individuals, were assumed to have minor effects in the first stage; (3) Dead
plants were assumed to neither facilitate nor compete with other
individuals. Thus, dead plant should be excluded from the analysis
for the simplicity in interpreting and analyzing the results .
Our results from the field pot experiment supported the
previous prediction that enhanced UV-B radiation can reduce
the mortality rate of individuals during self -thinning.
First, competition decreased the mean biomass of plants
(Figure 1A and Figure 1B). Second, direct stress decreased the
mean biomass. However, facilitation increased the individual
biomass. Furthermore, survival rate decreased rather than
increased with mean biomass of individuals. Based on these
results, we can conclude that stress, instead of positive interactions,
increased the survival rate of population. The balance of
competition, stress without facilitation (both decreasing mean
biomass), and positive interactions (increasing mean biomass)
determined the mean biomass per plant. In terms of the whole
growing season, the effects of UV-B stress and competition on
mean biomass were more than the positive interactions (Figure 1B).
Based on density-dependent mortality, direct stress postponed
the inception and lessened the rate of plant growth by reducing
growth rates. Thus, the number of survivors at the end of the
growing season was lower under stressful environment than that
under normal environment. This finding was consistent with
previous results from various studies, such as the field pot
experiment on Triticum aestivum under drought stress  and
the zone-of-influence  based on the WBE model . These
studies demonstrated that mortality rate is interrelated with the
rate of growth in self-thinning.
Interestingly, stress influences plants differently on various
scales. On the individual scale, the direct effects of stress on plants,
which inhibit plant growth, is negative for isolated individuals.
However, it can also increase the survival rate of plants on the
population scale, which is positive for a group of individuals.
The enhanced UV-B radiation decreased the size inequality of
the population in all growing stages. However, the trend was not
simply monotonic, except for stage 1. Size inequality initially
decreased, and then increased with UV-B radiation in stages 2 and
3. However, size inequality decreased monotonically with stress in
stage 1. The death of plants in stage 3 complicated the analysis of
plant size inequality because it decreased the size inequality of
survivals during self-thinning and these survivors were quite equal
in size after the extensive mortality [32,40]. Still, a non-monotonic
decrease in the relationship of size inequality and UV-B irradiance
was observed in the last stage. Nonetheless, plant populations
under ambient condition showed less survival rates than
populations under low- and high-enhanced UV-B radiation.
Consequently, according to assumption (2), direct stress
decreases the size inequality of populations simultaneously when
facilitation increases size inequality. Otherwise, we are unable to
interpret the monotonic decrease in the relationship of size
inequality and UV-B irradiance in the early stage and the
nonmonotonic decrease in the relationship during the last two stages.
In addition, the balance among positive interactions (increasing
variation), stress, and mortality driven by competition (both
decreasing variation) determined the size inequality of the
As a result, the second explanation is more reasonable. Early in
the stand development, the spatial pattern was more important
than the symmetry of competition within the population.
However, the size asymmetry of competition became more
important after the plants grew and the competition intensified
. In the beginning of the field pot experiment, individuals grow
Figure 4. Trends of Gini Coefficient under different UV-B and density levels in the whole growing season. The Gini Coefficient of the
individual total biomass of low- and high- density groups under ambient conditions (-%-), low-enhanced UV-B radiation (-#-), and high-enhanced
UV-B radiation (-g-) was calculated respectively in each month after the plants were sampled. Bootstrapping determined the confidence intervals
(95%). Each data point represents the result calculated from 5000 samples based on bootstrapping. Otherwise, as for Figure 3.
in a uniform spatial pattern. However, soil conditions and other
factors are not exactly the same for each individual, thereby
resulting in size variation. Larger individuals tend to share more
damage from supplementary UV-B radiation than the smaller
ones because of their larger size. However, larger individuals also
benefit from positive interactions more greatly than smaller ones
because of their larger overlapping area. Some individuals are
facilitated by neighbors, whereas some are even not. Nevertheless,
larger individuals obtain more benefits than damages. Thus, the
overall inequality of size in the population increased at the end.
This result was supported by the experiments in this study
Therefore, just as kin recognition [41,42], positive interactions
are also sometimes linked to altruism. Nonetheless, the trade-off
between competition and facilitation may not be purely altruistic
for whole individuals. Positive interactions are also asymmetric
exactly as competition in the population due to the more reward
than expense for larger ones.
Furthermore, the influence of facilitation on different scales also
differs. Facilitation increases the biomass of individuals on
individual scale positively, whereas the individual variability is
increased by facilitation on population scale. On the contrary,
direct stress affects plants negatively on the individual scale, but it
decreases size inequality on population scale.
In addition to positive interactions and competition, trade-off
between light resources and damages from UV-B radiation are
also important in the development of plants. UV-B radiation
decreased the leaf numbers, crown width, leaf area, and height of
plants. However, UV-B radiation slightly increased the branch
number at lower density [4,43,44]. Nonetheless, every
morphological index was decreased with density, except for plant height
under normal condition. Our field pot experiment results were
also consistent with our previous prediction.
In terms of morphology, a trade-off has to be made between
gaining light resources and averting the damage from the radiation
as far as a sole individual is concerned because of the characteristic
of UV-B irradiation. The trade-off was more complicated when an
individual has a neighbor because of the additional trade-off
between competition and positive interactions. This study focused
on the four factors and two trade-offs. The competition and the
Figure 5. Morphological indices at different levels of density and UV-B radiation in last stage. Isolated and low-density groups under
each UV-B radiation level measured the five morphological indices of mung beans in every month before biomass was measured. The morphological
indices were branch number, plant height, leaf number, crown width, leaf area per plant. This figure only shows the results in the last month. The
three symbols represent ambient conditions (-%-), low-enhanced UV-B radiation (-#-), and high-enhanced UV-B radiation (-g-). The number next to
each point indicates the SD. In the last month, the morphology of eleven plants (low-density group) was destroyed. Thus, there were n = 52 plants for
the low-density group and n = 9 plants for the isolated group.
desire for light resources resulted in plants choosing to enhance the
height. However, the result of stress was actually the opposite.
Trade-offs are also related to positive interactions because larger
individuals obtain light resources more easily and also benefit from
neighbors more greatly than smaller ones. Plants changed their
strategy during various growing stages because of these trade-offs.
The interactions among plants were not significant during the
early development. Individuals tend to grow taller to obtain light
and benefit under enhanced UV-B radiation. This condition was
primarily because the desire for resources was more urgent for
individuals in the early stage (Figure 6). However, the effects of
stress exceed the influence of interactions and the desire for
resources. Plant height then decreases with UV-B radiation in the
following stages (Figure 6).
Trade-offs among stress, light resources, competition, and
facilitation may affect the allocation strategy of plants corporately.
Therefore, further research is needed in connection with these
The prediction that states the balance among stress,
competition, and positive interactions collectively affect the self-thinning,
size inequality, and phenotypic plasticity, is supported by the
experimental results. Facilitation influences the pattern of the size
structure of populations. More works in both mathematical and
conceptual field should be conducted because the effects of
facilitation and stress are difficult to separate in field experiment.
Facilitation should not be neglected in the allocation of resources
and self-thinning of individuals. Consequently, future studies
should integrate facilitation in the current allometric theory mainly
based upon competition. This integration would explicitly explain
the allometric relationship of plants within populations.
Materials and Methods
Mung beans (Vigna radiate) cultivar Qindou-20 was grown in the
biological garden of Northwest University (Xian, China, 34.3uN,
108.9uE; altitude 397 m). This species was chosen because of its
short growth period and large leaves, which can effectively reflect
the effects of radiation. The field pot experiment was designed to
contain the three graded levels of density and three graded levels
of supplemental UV-B radiation. Thus, there were a total of 363
treatments, with three replicates for each treatment. The growing
season of mung beans lasts three months from May to July in the
Xian region. Strong self-thinning was observed in the last month
according to our preliminary experiment in 2009. Therefore, each
month was chosen as a growing stage. We sampled 9
(treatments)63 (replicates) pots of plants for measurements at the
end of May, June, and July, respectively, so that 2763 pots were
prepared in the aggregate. The period of experiment followed the
local farming of mung beans, which started from April 29, 2010
and finished at the end of July (86 days).
Pots were filled with soils obtained from the biological garden.
Seeds of mung beans were then sown to the pots (diameter 25 cm,
height 35 cm) with the following three densities: isolated (1 plant
per pot), low-density (7 plants per pot), and high-density (37 plants
per pot). The effects of irregular germination on the experiment
were avoided by adding the prepared 27 pots of seedlings for the
transplantation. These seedlings were separate from the 81 pots of
mung beans. These 108 pots were then placed in the field. The
distance between each pot was about 0.5 m and the plants were all
under the same field management.
The mung bean seeds were sown in light of the hexagonal
patterns. In this method, plants can use the space (resources) in
an economical way; thus, different individuals can possess the
same effective area . Aside from the individuals on the edge
of a pot, every plant was surrounded by six equidistant
neighbors. Therefore, there were 7 individuals for the
lowdensity group and 37 individuals for the high-density group to
mimic the competition conditions and based on the
characteristics of the hexagon. The distances between the two
neighboring individuals were 1.5 cm and 3 cm for low- and
high-density. Furthermore, 1 plant per pot was also prepared in
the isolated group to distinguish the effects of UV-B radiation
and the interactions among plants.
The first true leaf of each seedling would spring after one week
or two. These mung beans seedlings were exposed to the following
UV-B treatments:?ambient (as control), low-enhanced, and
highenhanced. Lamps were suspended above and perpendicular to the
plants. The enhanced UV-B stress strength was expressed as the
distance between the lamps and the top of the plants. In the
lowenhanced and high-enhanced UV-B radiation groups, UV-B
radiation source consisted of Qin brand (Baoji Lamp Factory,
China) 40 W lamps. These lamps were filtered with one layer of
0.13 mm cellulose diacetate film that filters radiation below
280 nm [46,47]. Spectral irradiance levels were measured by a
UV radiometer (Instrument Company of Beijing Normal
University, Beijing, China).
The UV-BBE was estimated using the generalized plant response
action spectrum normalized to 300 nm . The daily enhanced
UV-B radiation was set for 8 h per day (9:00 to 17:00). The lamp
height above the plants was adjusted weekly to maintain a distance
of 0.6 and 0.4 m between the lamps and the top of the plants.
Supplemental irradiances of 3.60 and 5.62 kJ?m2 UV-BBE were
respectively provided. Based on calculation , these
supplemental UV-B radiation levels were equal and can be increased at
Xian, with 22% and 35% stratospheric ozone reductions during a
clear day at the summer solstice (8.05 kJ?m2 UV-BBE during clear
sky conditions at the summer solstice). In the control group, plants
only received ambient UV-B radiation. The UV-B lamps were
also suspended, but were not provided with electric power to
ensure that cultures can receive the same levels of sunlight with
low- and high- enhanced radiation. Pots were rotated every 3 days
or 4 days to minimize positional effects.
Measurements and Statistical Analysis
The number of living individuals, stem height, basal
diameter, crown width, and leaf areas were measured in the
isolated and low-density group. In the pre-experiment,
selfthinning occurred in the high-density group (only 10 to 20
survivals after self-thinning) instead of the low-density group
(initial distance was 3 cm). As a result, strong interactions
among plants in the high-density group were ensured by
counting the number of living individuals and randomly
selecting 10 individuals that own at least one neighbor not
more than 3 cm away from them in each pot for the biomass
measurements. Furthermore, only individuals in the middle
were selected and those on fringe of the pot were not chosen to
avoid the edge effect. Individuals under all treatments were then
harvested and dried at 80uC until constant weight was achieved
to collect stem, leaf, root, and fruit (pod) biomass of each plant.
Only the total biomass was measured for the rest of the
individuals in the high-density group (See Materials. S1).
Gaining light resources and avoiding UV-B stress is an
important trade-off for an individual. When plants have neighbors
there would be competition and positive interactions between
them. This study focused mainly on the four factors and two
tradeoffs. However, in addition to competition, facilitation, desire for
light resources, and stress, the high-density group introduced the
fifth factor (self-thinning). Self-thinning influenced the plant
morphology and provided difficulty in separating the effects of
all the factors in the field pot experiment. As a result, the
morphological indices of the high-density plots were ignored
temporarily. This difficulty was the reason why different
measurements were taken for the high-density treatment
compared with the low-density treatment and the control.
Biomass was used to study size inequality because it reflects the
sum of various effects on plants. The degree of size hierarchy for
each treatment was estimated by comparing the Gini coefficient
 and it is given by:
where n is the number of plants, x is the mean size, i = 1, n and
j = 1, n, and xi, xj are the sizes of ith and jth plants, respectively.
The Gini coefficient ranges from 0 (all individuals have equal size)
to a theoretical maximum of 1. The calculated G values were
multiplied by n/(n-1) to obtain the unbiased values (G) [50,51].
Ninety-five percent confidence intervals for G were determined
using the bootstrapping technique . The 5000 bootstrapping
samples were made in Matlab.
The Gini coefficient obtained from calculation utilized UV-B
radiation and density as two fixed factors. The obtained data were
evaluated statistically at the factorial level using two-way variance
analysis (Two-way ANOVA). The significance was calculated at
p,0.05 or p,0.001 level according to the Duncans multiple
range test. Furthermore, the n reflects the number of plants in
Table S1 F-values of two-way ANOVA for the effects of
density, radiation, and their interaction on the Gini
Coefficient of mung beans in every parameter
(***P,0.001). The overall effects of UV-B radiation, density,
and interactions (density6UV-B radiation) on the Gini Coefficient
of mung beans were determined by the two-way analysis of
variance (ANOVA). The significance was calculated at p,0.05
and at p,0.001 level based on Duncans multiple range test.
Materials S1 Supporting materials show data of each
biomass parameter (root, stem, leaves and fruit/pod
size) under each UV-B radiation and density condition.
We would like to acknowledge the editors and four anonymous referees for
extremely helpful comments. We thank Wen-Ting Tang and Qian-Cai
Meng for assistance with the garden, Wen-Wen Wang and Peng-Cheng
Wan for their helpful conversations.
Conceived and designed the experiments: RCZ YL MY. Performed the
experiments: RCZ QL XFZ XL. Analyzed the data: RCZ HC YFC MW.
Contributed reagents/materials/analysis tools: YL MY. Wrote the paper:
RCZ. Manuscript revision: MY.
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