Annals of Botany 108: 207 –214, 2011
doi:10.1093/aob/mcr109, available online at www.aob.oxfordjournals.org
Plants in a crowded stand regulate their height growth so as to maintain similar
heights to neighbours even when they have potential advantages in height
growth
Hisae Nagashima* and Kouki Hikosaka
Graduate School of Life Sciences, Tohoku University, Aoba, Sendai 980-8578, Japan
* For correspondence. E-mail [email protected]
Received: 5 January 2011 Returned for revision: 15 February 2011 Accepted: 23 March 2011 Published electronically: 11 May 2011
† Background and Aims Although being tall is advantageous in light competition, plant height growth is often
similar among dominant plants in crowded stands (height convergence). Previous theoretical studies have
suggested that plants should not overtop neighbours because greater allocation to supporting tissues is necessary
in taller plants, which in turn lowers leaf mass fraction and thus carbon gain. However, this model assumes that a
competitor has the same potential of height growth as their neighbours, which does not necessarily account for
the fact that height convergence occurs even among individuals with various biomass.
† Methods Stands of individually potted plants of Chenopodium album were established, where target plants were
lifted to overtop neighbours or lowered to be overtopped. Lifted plants were expected to keep overtopping
because they intercept more light without increased allocation to stems, or to regulate their height to similar
levels of neighbours, saving biomass allocation to the supporting organ. Lowered plants were expected to be suppressed due to the low light availability or to increase height growth so as to have similar height to the
neighbours.
† Key Results Lifted plants reduced height growth in spite of the fact that they received higher irradiance than
others. Lowered plants, on the other hand, increased the rate of stem elongation despite the reduced irradiance.
Consequently, lifted and lowered plants converged to the same height. In contrast to the expectation, lifted plants
did not increase allocation to leaf mass despite the decreased stem length. Rather, they allocated more biomass to
roots, which might contribute to improvement of mechanical stability or water status. It is suggested that
decreased leaf mass fraction is not the sole cost of overtopping neighbours. Wind blowing, which may
enhance transpiration and drag force, might constrain growth of overtopping plants.
† Conclusions The results show that plants in crowded stands regulate their height growth to maintain similar
height to neighbours even when they have potential advantages in height growth. This might contribute to avoidance of stresses caused by wind blowing.
Key words: Height growth, stem elongation, plasticity, light competition, neighbour effect, stem diameter
growth, biomass partitioning, Chenopodium album.
IN T RO DU C T IO N
Light competition is critical for survival, growth and reproduction of individuals in dense stands. Plants that could not
receive sufficient light stop their growth and often die
(Weiner et al., 1990; Nagashima et al., 1995; Matsumoto
et al., 2008). As light is a unidirectional resource, taller
plants intercept more irradiance and overshade shorter competitors (Schmitt et al., 1995; Dudley and Schmit, 1996; Huber
and Wiggermann, 1997; Anten and Hirose, 1998; Huber
et al., 1998). It is well known that many herbaceous plants
enhance elongation of stems when the stand density or the
leaf area index (LAI) is high (e.g. Ballaré et al., 1990;
Weiner et al., 1990; Weiner and Thomas, 1992; Weiner and
Fisherman, 1994; Nagashima, 1999; Nishimura et al., 2010).
This response has been regarded as shade avoidance (Smith,
1982).
Height growth is, however, not always competitive but often
apparently co-cperative. In many plant communities, height is
similar among plants that reached the top of the canopy (e.g.
Koyama and Kira, 1956; Kuroiwa, 1960; Ford, 1975;
Hutchings and Barkham, 1976; Weiner and Thomas, 1992;
Weiner and Fishman, 1994; Nagashima and Terashima,
1995; Nagashima et al., 1995; Vermeulen et al., 2008),
which is called height convergence (Nagashima and
Terashima, 1995). Since tall plants receive high light levels,
one may consider that being tall is advantageous in light competition. However, plants do not necessarily keep this advantage. Height convergence is often observed among upper
plants with different biomass, even though plants with larger
biomass may have higher potential for growth (Weiner and
Fishman, 1994; Nagashima and Terashima, 1995). Why do
such plants not keep overtopping others?
Although being tall is advantageous in light competition, it
entails costs for plants. As leaf height increases, plants need to
invest biomass more than proportionately in the stem to
support their own weight, which in turn reduces the fraction
of leaf mass in the plant (Givnish, 1982; Niklas, 1992).
Givnish (1982) proposed a game-theoretic model of plant
height growth. He assumed that overtopping the other plants
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208
Nagashima & Hikosaka — Height growth regulation in a crowded stand
is advantageous in light capture and thus leads to a higher production rate per unit leaf mass, but the leaf mass fraction in
shoot decreases with increasing plant height. His model predicted existence of the evolutionarily stable height (ESH) in
a stand at a given density: no other height (neither taller nor
shorter) is advantageous in biomass production in the stand
in which plants have the ESH. His model also predicted that
the ESH increases with increasing canopy cover. This was
well supported by forest forbs (Givnish, 1982). Enhancement
of height growth in response to crowding seems to be consistent with the prediction. Height convergence may be a result of
evolutionary stable growth of competing plants.
Although the model of Givnish (1982) can provide important insights into plant growth under competition, it is still
questionable whether his model fully accounts for the height
convergence observed in plant communities. First, his model
assumed that competing plants have equal biomass to each
other, which is not the same as field situations where plants
with different biomass have similar height (Weiner and
Fishman, 1994; Nagashima and Terashima, 1995). Secondly,
it is unknown whether the constraints assumed in the model
are appropriate to explain the plastic height growth of plants
found in open habitat. The model assumed that plants have
constant mechanical stability and accordingly the biomass
allocation to leaves depends only on plant height. There may
be, however, another disadvantage in being tall. When plants
overtop the neighbouring plants, they may be exposed to stronger wind than the neighbours, which might entail negative
effects on plant growth due to excessive transpiration and
mechanical stress (Drake et al., 1970; Grace, 1974; Putz
et al., 1983). If this is the case, being tall may be more disadvantageous than that considered in Givnish (1982).
In the present study, an experiment was designed to examine
whether plants avoid overtopping and whether the behaviour is
according to the Givnish model. A stand of potted plants was
made and the height of the pot (above or lower than neighbouring pots) was manipulated. The lifting treatment will
benefit plants in light capture without any reduction in leaf
mass fraction. This is in contrast to the situation of overtopping
plants in the Givnish model, where overtopping plants increase
light interception but reduce biomass allocation to leaves. The
lowering treatment will decrease light availability of the plant
despite the same leaf mass fraction as the neighbours. We postulated two hypotheses for response to the treatments. (1)
Lifted plants will keep themselves overtopping their neighbours because there is no disadvantage in overtopping.
Lowered plants may be suppressed due to the low light availability. (2) Treated plants may regulate their height growth so
that their height becomes similar to the neighbours. Lifted
plants will decrease the height growth and consequently be
caught up by the neighbours. Lowered plants may increase
height growth so as to have similar height to the neighbours.
Biomass allocation changes caused by the treatments were
also investigated. First it is expected, as has been assumed
by Givnish (1982), that biomass allocation to leaves depends
on stem length irrespective of treatments. If relationship
between allocation to leaves and stem length is affected by
the treatment, constraints other than that assumed in Givnish
(1982) are suggested in the competing plants. The
experimental results were also compared with the theoretical
prediction using the model of Givnish (1982).
M AT E R I A L S A N D M E T H O D S
The experiment was conducted with Chenopodium album, a
broad-leaved summer annual, in an experimental garden of
Tohoku University, Sendai, Japan (38825′ N, 140883’E).
Monthly mean air temperatures during the experiment were
18.0, 22.5 and 22.9 8C in June, July and August, respectively.
Seeds of C. album were obtained from plants in a natural population in 1995. Three hundred and twelve plastic pots, each
12.5 cm in diameter and 20 cm high, filled with a mixture of
7 : 3 vermiculite and Akadama (granular loamy soil 0.5 –
1 cm in diameter), were tightly arranged on a bench 0.9 m
wide, 5.4 m long and 0.5 m high and placed outdoors. On 5
June 1996, about five seeds of C. album were sown in each
pot. Pots were watered at 0700– 0715 h and 1600 –1615 h
every day by an automatic watering system. After emergence,
each pot was fertilized with 100 mL of nutrient solution of
0.01 : 0.02 : 0.01 NPK every week (10 mg N, 20 mg P and
10 mg K week21 per pot) from 26 June until 24 July, and
from 31 July with 100 mL of nutrient solution of 0.02 : 0.04
: 0.02 NPK (20 mg N, 40 mg P and 20 mg K week21 per
pot). Seedlings were thinned to leave one per pot by 16 July:
the plant density was 77 plants m22. On 2 August, the stand
was surrounded by 80 % shade cloth to the height of the top
of the plants to reduce edge effects. The height of the shade
cloth was changed according to the growth of the plants. On
3 August, the length and basal diameter of the stems of all
plants were measured. The stem length was measured
from the base to the terminal shoot apex to the nearest
1 mm, and the basal diameter was measured to the nearest
0.1 mm in the middle of the first internode. Care was taken
to allot plants of similar size for 21 target and 126 neighbouring plants. Pots were arranged to have a target plant surrounded by six neighbouring plants as shown in Fig. 1B.
The height differences between the target and neighbouring
plants were created on 4 August, 60 d after sowing, when the
mean plant height was 37 cm and LAI was 2.3. Seven targetplant pots were lifted by 7 cm (lifted plants), another six
target-plant pots were lowered by 7 cm (lowered plants), and
the other six target-plant pots were kept at the same level as
the neighbouring pot (control; Fig. 1A). The height and diameter of target plants were measured in the same way as above.
The height of six neighbouring plants was also measured for
each target plant. Photosynthetically active radiation (PAR)
was measured with quantum sensors (LI-190SA, LI-COR
Inc., Nebraska, Lincoln, USA) at the top of the plant and
outside the stand. For each plant, PAR was averaged from
three measurements.
One and two weeks after the treatment, the height and diameter of target plants and the height of the neighbouring plants
were measured. In the experimental period two neighbours
were replaced with marginal plants to make the neighbourhood
condition of target plants even. After measurements, target
plants were harvested and separated into organs (leaf, stem and
root), and dried at 80 8C for 3 d and weighed. LAI increased to
2.9 and 4.5 in 1 and 2 weeks after treatments, respectively.
Nagashima & Hikosaka — Height growth regulation in a crowded stand
where Pmax and Pmin are the photosynthetic rate per unit leaf
mass of unshaded and shaded leaves, respectively; o is the
probability of horizontal overlap of leaves; leaves are distributed on stems randomly within the range of hi (1 + s). When an
invader is shorter than the neighbours (h1 , h2),
[h1 (1 + s) − h2 (1 − s)]2
g(h1 , h2 ) = Pmin +
4h1 h2 s
o
(2)
× 1 − × (Pmax − Pmin )
2
A Pot-height treatment
Control
(C)
For an explanation of how the equations are derived see
Givnish (1982), but note that eqn 2 is in a different form
from the equation given in that paper. Leaf mass fraction,
f(s), is given as a function of stem length (s), where a and b
are a constant.
Lifted
(Li)
Lowered
(Lo)
f (s) = a − bs
B Pot arrangement
C
209
Li
Lo
Lo
C
C
Li
F I G . 1. Experimental design: treatment of height difference (A) and arrangement of pots (B). Target plants were lifted, lowered, or remained the same
level as surrounding plants, as indicated.
Effects of the treatment on plant growth were analysed by
the generalized linear model with a normal error distribution
and identity link (JMP statistical software; SAS Institute
Inc., Cary, NC, USA). Tukey – Kramer honestly significant
difference test was used for post-hoc pairwise comparisons.
In simulations, 0.374 and 0.043 mmol CO2 g21 leaf dry mass s21
were adopted for Pmax and Pmin, respectively, which were calculated from the top (1.68 g N m22) and bottom leaves (0.44 g N
m22) of dominant individuals in a monospecific stand of
Chenopodium album established in the same experimental
garden in 1999 (for details, see Hikosaka et al., 2003). Values
of a and b were 0.73 and 0.0031, respectively, which were
obtained from control plants in the present study (r 2 ¼ 0.97),
s is 0.48 from the average of control plants, and o was regarded
as one as the LAI exceeded one. Simulations were conducted in
the case of an invader 7 cm higher or lower than neighbours
(simulation A); and an invader whose pot is lifted or lowered
by 7 cm (simulation B). In simulation A, height (h) and stem
length (s) of an invader are identical values, while in simulation
B, h and s are different values from each other. The evolutionarily stable height (h*), which is defined as the height of a stand
where no invader with any other height has higher photosynthetic productivity (g × f ), is given as follows (Givnish, 1982):
h∗ =
Simulation
Optimal leaf height of lifted or lowered plants was simulated
according to the model of Givnish (1982). The model assumed
single-leaf plants but the model can be extended to multi-leaf
plants like C. album. Here photosynthetic production of an
invader plant that competes with neighbours for light is considered. Plant photosynthetic production is obtained by photosynthetic production per unit leaf mass (g) multiplied by
allocation of shoot mass to leaves [ f(s)], where s is stem
length, g is a function of the mean height of the leaves of
target (h1) and neighbouring (h2) plants. When an invader is
taller than the neighbours (h1 . h2)
[h2 (1 + s) − h1 (1 − s)]2
o
×
g(h1 , h2 ) =Pmax −
2
4h1 h2 s
2
(1)
× (Pmax − Pmin )
(3)
(a/b) × o × [1 − (Pmin /Pmax )]
2s + (1 − s) × o × [1 − (Pmin /Pmax )]
(4)
In simulation B, an optimal height maximizing their photosynthetic production was numerically found out for lifted or
lowered invaders.
TA B L E 1. Photosynthetically active radiation (PAR) at the top of
the plant relative to outside of stand just after the height
difference treatment (for control, lifted and lowered plants, see
Fig. 1)
Relative PAR at the top (%)
Control
Lifted
Lowered
88.9 + 1.0a
88.9 + 1.4a
85.4 + 4.3b
Different superscript letters indicate significant difference (P , 0.05)
assessed by Tukey–Kramer test (n ¼ 7 in each group).
210
Nagashima & Hikosaka — Height growth regulation in a crowded stand
RES ULT S
The PAR at the top of the plants was significantly lower in
lowered plants, though the difference was small (P ¼ 0.03,
ANOVA). No significant difference was found between lifted
and control plants (Table 1). In lifted plants, however, about
nine expanded leaves were positioned higher than the
canopy surface, while in control plants only three expanded
leaves were exposed to the top of the canopy. Thus light interception was increased by the lifting treatment.
Control plants exhibited the height growth rate of 23 cm per
week during the experiment. Lifted plants slowed stem
elongation (Table 2 and Fig. 2A). Two weeks after the onset
of the treatment, the difference in apparent height from neighbouring plants became 1 cm (not significantly different from
zero) in lifted plants (Fig. 2B). Lowered plants accelerated
stem elongation (Table 2 and Fig. 2A), and the difference in
apparent height from neighbours was reduced from 7 to
3.5 cm during the experiment (Fig. 2B). However, their
height was still lower than that of their neighbours (Fig. 2B).
Total biomass was significantly different among treatments
(Table 2). However, the biomass of lifted plants was not
greater than that of control plants (Table 2), even though
lifted plants might have received greater irradiance. Lowered
plants had smaller biomass than the other two (Table 2).
There was no significant effect of the treatment on leaf mass
and leaf mass fraction (leaf/total mass) despite the differing
stem lengths among the treatments (Table 2). The treatment
significantly affected the root mass and root mass fraction
(Table 2). Stem mass and the stem mass fraction showed a
marginally significant difference (Table 2). These results
suggest that there were changes in allocation between roots
and stems across the treatments: lifted and lowered plants
tended to invest more biomass in roots and stems, respectively.
Specific leaf area (SLA) increased more in lowered plants than
in the others, resulting in a greater leaf area ratio (LAR) in
lowered plants (Table 2). Lifted plants slowed stem elongation
but increased stem thickness enlargement, while lowered
plants accelerated elongation but tended to reduce diameter
growth (Table 2).
Table 3 summarizes the simulation results. Here it is
assumed that neighbours have an evolutionarily stable height
(h*) (eqn 4). When a stand is composed of pots at the same
height level (simulation A; no lifting or lowering), a plant
taller or shorter than h* has lower photosynthetic production
than the neighbours with h*. This is because, for example,
in a higher plant the positive effect by the increase in g was
smaller than the negative effect by the decrease in f. In simulation B, on the other hand, a lifted or lowered plant has the
same stem length as neighbours, but is 7 cm taller or shorter,
respectively, than the neighbours. A lifted plant has greater
photosynthetic production than the neighbours because they
increase g without a decrease in f. If the lifted plants decrease
their stem length and increase f, photosynthetic production
further increases. Photosynthetic production of the lifted
plants is maximized when they are 2 cm higher than the neighbours, suggesting that keeping 2 cm taller than neighbours is
advantageous for a lifted plant. A lowered plant in simulation
B produces less photosynthetically than the neighbours irrespective of stem length. Photosynthetic production of the
lower plant is maximized when the height is 4 cm lower
than the neighbours.
D IS C US S IO N
The present study showed that plants in crowded stands regulate their height growth so as to maintain similar height to
neighbours: plants whose top had been lowered relative to
their neighbours accelerated the elongation rate while plants
whose top had been lifted higher than the neighbours
reduced the elongation rate (Fig. 2).
Lifted plants did not keep themselves overtopping neighbours, even though they had two advantages at the onset of
TA B L E 2. Stem dimensions, plant dry mass, dry mass partitioning, leaf area, growth parameters of target plants 2 weeks after
treatments (see Fig. 1)
Stem length (m)
Height increment (m)
Diameter (mm)
Diameter increment (mm)
Length/diameter (m m21)
Total mass (g)
Root mass (g)
Stem mass (g)
Leaf mass (g)
Root/total mass (g g21)
Stem/total mass (g g21)
Leaf/total mass (g g21)
Lamina area (cm2)
SLA (m2 kg21)
LAR (m2 kg21)
Control
Lifted
Lowered
P-value
0.835 + 0.007b
0.459 + 0.008b
4.31 + 0.06
0.49 + 0.03b
194 + 3b
6.68 + 0.24
1.71 + 0.10ab
2.65 + 0.10
2.33 + 0.07
0.255 + 0.007ab
0.396 + 0.006
0.349 + 0.003
602 + 26
28.9 + 0.7b
9.01 + 0.22b
0.775 + 0.006c
0.400 + 0.006c
4.40 + 0.08
0.66 + 0.04a
176 + 3c
6.50 + 0.14
1.76 + 0.06a
2.50 + 0.06
2.24 + 0.06
0.271 + 0.006a
0.385 + 0.007
0.344 + 0.003
566 + 14
28.4 + 0.7b
8.70 + 0.15b
0.870 + 0.008a
0.496 + 0.007a
4.21 + 0.07
0.47 + 0.04b
207 + 3a
5.99 + 0.19
1.44 + 0.10b
2.42 + 0.06
2.13 + 0.07
0.240 + 0.010b
0.405 + 0.006
0.355 + 0.008
613 + 23
32.4 + 0.8a
10.25 + 0.20a
<0.0001
<0.0001
0.161
0.0015
<0.0001
0.0348
0.0210
0.0815
0.107
0.0265
0.0964
0.232
0.231
<0.0001
<0.0001
Values are means + s.e. Different superscript letters indicate significant differences (P , 0.05) among treatments according to Tukey –Kramer test (n ¼ 7 in
each group).
P-values are the result of generalized linear model analyses (d.f. ¼ 2). Significnat values (P , 0.05) are highlighted in bold.
SLA, specific leaf area (lamina area/lamina mass); LAR, leaf area ratio (lamina area/total mass).
Nagashima & Hikosaka — Height growth regulation in a crowded stand
TA B L E 3. Simulation results
0·9
a
b
A
0·8
Stem length (m)
c
0·7
a
b
0·6
c
0·5
Control
Lifted
Lowered
0·4
0·3
0·10
B
Apparent height difference
from neighbouring plants (m)
a
0·05
a
b
0
b
a
a
c
b
–0·05
c
–0·10
211
0
1
Height of invader plant
(cm)
Simulation A
Unchanged pot height
h*
h* + 7
h* – 7
Simulation B
7 cm lifted
h*
h* + 7
h* + 2 (optimal)
7 cm lowered
h*
h* – 7
h* – 4 (optimal)
Photosynthetic production (mmol CO2 g21
d21)
2.333
2.307
2.317
2.532
2.521
2.533
2.135
2.136
2.140
Photosynthetic production per above-ground biomass is calculated as the
product of photosynthetic production per leaf mass (g) and leaf mass fraction
( f ). In every simulation, height of neighbouring plants is an evolutionarily
stable one (h* ¼ 153 cm). In simulation A, the height of an invader plant is
altered from the neighbours with an identical pot height to the neighbours.
‘h* + 7′ means that the height of an invader is 7 cm higher/lower than h*. In
simulation B, the pot height of an invader plant is lifted up or lowered by
7 cm compared with neighbours. ‘h* + 7′ in ‘7 cm lifted’ in simulation B
means that the height of an invader is 7 cm higher than h* due to pot
elevation but the stem length is the same as the neighbours. ‘h* + 2′ means
that height and stem length are 2 cm higher and 5 cm lower than the
neighbours and the invader that has this height has a higher photosynthetic
production than those at other heights. Similarly, ‘7 cm lowered’ means that
the pot height of an invader is 7 cm lower than the neighbours.
2
Weeks after treatment
F I G . 2. Growth of stem length of target plants (A) and difference in height of
the top of plants between target and neighbouring plants that was obtained as
[height of a target plant (+7 cm, for lifted plants; – 7 cm, for lowered plants)]
– (mean height of six adjacent plants) (B), after pot-elevation treatment (see
Fig. 1). Different letters indicate significant differences (P , 0.05) among
treatments according to Tukey –Kramer test (n ¼ 7 in each group). Bars
represent + s.e.
experiment: increased light interception and less cost of tissues
to support leaves at higher positions. At the end of the experiment, the height difference between lifted and the neighbour
plants became 1 cm (Table 2). The value was similar to that
expected from simulation B (Table 3). However, growth was
quite different from that expected from the Givnish model.
First, fraction of leaves in the plant mass was not different
among the treatments despite the different stem lengths
(Table 2). This result suggests that the cost of competition
may not be fully accounted for by a reduction in leaf mass fraction with an increase of plant height (stem mass fraction).
Secondly, lifted plants did not increase growth, even though
they had received more light than their neighbours (Table 2).
This suggests that overtopping is not advantageous for photosynthetic rate per leaf mass. Some other costs or constraints
therefore need to be incorporated for understanding height
growth regulation in crowded stands.
What was the cost or constraint of overtopping, then?
Constraint of being tall has been considered mainly based on
safety against buckling: a stem bends due to its own and leaf
weight (e.g. McMahon, 1973; King, 1986; Niklas, 1993a, b,
1994a, b; Casal et al., 1994; King et al., 2009). However,
buckling safety does not necessarily guarantee safety against
breaking damage caused by wind blowing. Because wind
speeds increase dramatically above the boundary layer of the
canopy (Goudriaan, 1977; Speck, 2003), overtopped plants
may be exposed to stronger winds than the neighbours. As
wind speed increases, the risk of mechanical failure increases
(Niklas, 2000). During the present experiment, the maximum
instantaneous wind speed in the day was 7.3 – 25.4 m s21 in
Sendai (Japan Meteorological Agency). In a potted plant of
an erect annual, Xanthium canadense, wind speed of 20 m
s21 bent the stem by 50– 60 8 (H. Nagashima, Tohoku
University, Sendai, Japan, unpubl. res.). Thus lifted plants in
the present study might have suffered from wind blowing
and changed biomass allocation and morphology to avoid
mechanical failure. In fact, lifted plants reduced the height :
diameter ratio of the stem and increased the root mass fraction
(Table 2), both of which might have contributed to mechanical
stability (Niklas, 1992; Henry and Thomas, 2002; Anten et al.,
2005, 2006, 2009).
Another constraint may be transpiration. It is notable that
lifted plants did not have greater biomass than control plants
(Table 2), though the intercepted light might have been
greater. This suggests that light use efficiency in photosynthesis (carbon gain per unit absorbed light; Hikosaka et al.,
1999) was lower in lifted plants. Grace (1974) showed that
an increase in wind speed from 1 to 3.5 m s21 enhanced transpiration and reduced water content of leaves in Festuca
212
Nagashima & Hikosaka — Height growth regulation in a crowded stand
arudinacea. It is probable that wind induced stomatal closure
to prevent water loss (Drake et al., 1970), leading to a
reduction in photosynthesis rates. Lifted plants increased the
root mass fraction (Table 2), which is also in accord with
general responses to water stress (Watts et al., 1981).
Lowered plants, on the other hand, accelerated height
growth, nearly reaching the canopy top (Fig. 2). The height
difference was – 3.5 cm, which was close to the prediction
by the Givnish model (Table 3). Enhanced height growth
was realized at the expense of stem diameter growth, leading
to a higher height : diameter ratio of the stems (Table 2).
This change in stem morphology is in accord with the previous
studies in which subordinate plants were more slender than
dominant and solitary plants (Weiner et al., 1990; Weiner
and Thomas, 1992; Weiner and Fishman, 1994; Nagashima
and Terashima, 1995). Biomass allocation was also changed
(Table 2); lowered plants tended to increase stem mass at the
expense of root as compared with the other plants (Table 2).
This also agrees with previous observations that plants allocate
fewer resources to roots when they are shaded or in a dense
stand compared with plants that are exposed or solitary (e.g.
Corré, 1983a, b; Maliakal et al., 1999; Nishimura et al.,
2010). These results imply that accelerating height growth is
costly: reduced diameter growth may increase a risk of mechanical failure of plants and reduced root mass fraction may be
disadvantageous for acquisition of below-ground resources as
well as lower mechanical stability. However, the elongation
may benefit the plants by carbon gain, since wind speed is
lower than it is on the outside of the canopy (Goudriaan,
1977; Speck, 2003).
In the model of Givnish (1982), total biomass of plants was
assumed to be identical among individuals for simplification.
The model showed that, if a stand consists of individuals
with evolutionarily stable height (ESH), plants at another
height cannot have higher biomass production rates.
However, this does not necessarily hold when the stand consists of individuals with different total biomass. If an individual has a greater biomass than neighbours, it can have a higher
production rate even though its height is greater or shorter than
the ESH of the neighbours (Table 3). In other words, the
Givnish model may not explain why height convergence is
often observed even among upper plants with different
biomass (Weiner and Fishman, 1994; Nagashima and
Terashima, 1995). The present results clearly suggest that overtopping others is not necessarily advantageous even when the
individual has a greater potential for height growth. Plants
keep their height similar to their neighbours to avoid constraints that arise by overtopping others.
Convergence of height growth leads to J-shaped or bimodal
frequency distribution of plant height (J-shaped: the population consists of many similarly tall plants with a smaller
number of shorter plants) (Koyama and Kira, 1956;
Kuroiwa, 1960; Ford, 1975; Hutchings and Barkham, 1976;
Weiner and Fishman, 1994; Nagashima and Terashima,
1995; Nagashima et al., 1995). Height convergence also
accounts for a non-linear relationship between log-transformed
height and diameter, which has commonly been observed in
various plant communities; height is positively correlated
with diameter among subordinate short plants, while height
is relatively similar in dominant tall plants irrespective of
diameter (Ogawa et al., 1965; Assmann, 1970; Kira, 1978;
Rai, 1979; Kohyama et al., 1990; Niklas, 1995; Aiba and
Kohyama, 1996; Thomas, 1996; Sterck and Bongers, 1998;
Weiner and Thomas, 1992; Weiner and Fishman, 1994;
Nagashima and Terashima, 1995). Subordinate individuals
tend to increase their height, while dominant plants suppress
their height growth to keep their height similar to their
neighbours even though they have a greater potential of
height growth. Such an apparently co-cperative growth
of height may make plant – plant interactions less competitive,
which allows coexistence of dominant plants. Nagashima et al.
(1995) earlier showed in C. album stands that the number of
upper plants that reach the canopy top was similar irrespective
of initial density, which may partly result from co-cperative
growth of the upper plants.
Several environmental cues have been suggested for the
regulation of height growth. In particular, the red : far-red
(R/FR) ratio in incident light affects stem elongation (for
review, see Ballaré, 1999, 2009; Smith, 2000). Height convergence was impeded by treatments to reduce the R/FR effect
(Ballaré et al. 1994; Aphalo and Rikala 2006). On the other
hand, mechanical stimuli such as swaying due to wind may
also affect stem growth (Biro et al., 1980; Telewski, 1990;
Jaffe and Forbes, 1993; Henry and Thomas, 2002; Anten
et al., 2005, 2006, 2009). Both factors can account for our
results: lifted plants might have received a higher R/FR ratio
in incident light and stronger winds than others, leading to a
suppression of stem growth. This will be analysed in a forthcoming paper.
In summary, it was found that plants in crowded stands
regulate their height growth to maintain a similar height to
their neighbours even when there are potential advantages to
height growth. Lifted plants increased neither biomass allocation to leaves nor biomass production, indicating that overtopping neighbours is not necessarily beneficial in competing
plants. There may be other constraints for overtopping. A
likely constraint is wind blowing, which may reduce mechanical stability and/or cause a deterioration in the water status of
the plants.
AC KN OW L E DG MEN T S
We thank two anonymous referees, and N. Osada, Y. Osone,
H. Taneda and M. Tateno for valuable comments and suggestions, and K. Satoh for the experimental set-up. This work was
supported by Research Fellowships of the Japan Society for
the Promotion of Science for Young Scientists (nos 3025
and 40172) to H.N. and by KAKENHI (nos 20677001 and
21114009) to K.H.
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