Annals of Botany 78 : 169–179, 1996
Mechanisms of Central Die-back of Reynoutria japonica in the Volcanic Desert on
Mt. Fuji. A Stochastic Model Analysis of Rhizome Growth
N A O K I A D A C HI*†, I C H I R O T E R A S H I MA‡ and M A S A Y U K I T A K A H A S HI*
* Department of Plant Sciences, Faculty of Science, The UniŠersity of Tokyo, Hongo, Bunkyo-ku, Tokyo 113
and ‡ Institute of Biological Sciences, UniŠersity of Tsukuba, Tsukuba, Ibaraki, 305 Japan.
Received : 11 October 1995
Accepted : 29 February 1996
Reynoutria japonica (Polygonaceae) is a pioneer clonal herb colonising the volcanic desert on Mt. Fuji (height
3776 m), central Japan ; establishment of secondary successional species occurs only in the central die-back parts of
the clonal stands of R. japonica. Clonal stands were excavated and the morphology and growth pattern of the
rhizomes were investigated with special reference to the mechanisms of central die-back. Four morphological
parameters, length of mother rhizomes, and number, branching positions and branching angle of daughter rhizomes
on respective mother rhizomes were measured or counted, and their roles in rhizome growth were examined
employing a stochastic computer simulation model of the whole stand development. The simulations clarified that,
of these four parameters, the branching angle was the most influential determinant of the whole pattern of shoot
distribution and that the central die-back was produced when the mean branching angle was 40° or smaller. These
results strongly infer that the onset of central die-back is caused intrinsically by R. japonica itself by having the mean
branching angle of 40°. The adaptive significance of the growth pattern is discussed in relation to resource acquiring
and habitat exploitation strategies of this species.
# 1996 Annals of Botany Company
Key words : Below-ground morphology, branching angle, central die-back, clonal plant, computer simulation,
Japanese knotweed, Reynoutria japonica Houttuyn, rhizome growth pattern.
INTRODUCTION
In the volcanic desert on Mt. Fuji (height 3776 m), central
Japan, an early stage of primary succession is underway.
Reynoutria japonica Houttuyn is the dominant coloniser,
forming circular monoclonal stands (patches) which sometimes exceed 50 m#. As a patch develops, shoot density of R.
japonica decreases in its centre. This phenomenon is referred
to as ‘ central die-back ’. Since later successional species are
seen only in the central die-back parts of R. japonica and not
on bare ground, central die-back is considered a key process
in the early stage of primary succession (Adachi, Terashima
and Takahashi, 1996). Aerial shoots of R. japonica within a
clonal patch are connected to each other by rhizomes
(Maruta, 1981 ; Hirose and Tateno, 1984) and the whole
patch develops outwards by sympodial branching of the
rhizome systems. We have shown that central die-back is
brought about neither by interspecific nor by intraspecific
competition of the aerial shoots, but by the systematic
growth pattern of the rhizomes (Adachi et al., 1996).
Plants are composed of repeating structural units
(modules) connected together, which are usually arranged
as branching structures (White, 1979 ; Harper, 1981, 1985 ;
Waller and Steingraeber, 1985 ; Waller, 1988). Tree branches, aerial shoots, and rhizomes are all considered as
modules. The architecture and growth pattern of some
plants have been analysed from this point of view. Honda
† Present address : Global Environment Division, National Institute for Environmental Studies, Tsukuba, Ibaraki, 305 Japan.
0305-7364}96}080169­11 $18.00}0
(1971) claimed that branching angle and, to a lesser extent,
module length are the primary factors determining the
whole structure of tree branches. The behaviour of
buds—whether they stay dormant or die—is also important
(Harper, 1981 ; Borchert and Honda, 1984 ; Borchert and
Tomlinson, 1984). This approach can be applied to the twodimensional structures of rhizomes or stolons as well as to
trees. For clonal plants, it has been shown that the
architecture and growth pattern of below-ground organs
largely define the structure and dynamics of the aerial
shoots (for reviews, see Bell, Roberts and Smith, 1979 ;
Waller and Steingraeber, 1985 ; Sutherland and Stillman,
1988, 1990). Bell et al. (1979) explained both the aerial and
subterranean structures of several clonal species, such as
Alpinia speciosa and Medeola Širginiana, using a graphic
simulation model of the subterranean structure. Taking a
rhizome branch as a basic module and applying simple
growth rules, they successfully reconstructed the whole
clone structure. Callaghan et al. (1990) further incorporated
the effects of rhizome age on growth traits of Lycopodium
annotinum and explained the growth pattern of the stands.
Cain (1990) applied a random-walk model, which had been
used frequently for animal movement models, to the growth
of Solidago altissima stands.
In clonal plants, the below-ground parts are important
for physiological functions as well as physical structure.
They provide paths for long distance transport of water,
nutrients and assimilates, and also places for reserves of
nutrients and assimilates. In some clonal species the whole
clone can act as one organism (for reviews, Pitelka and
# 1996 Annals of Botany Company
170
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
Ashmun, 1985 ; Marshall, 1990). Although connections
between ramets of some species last for only a short period
(up to 2 years), other clonal species possess rhizome or
stolon connections for longer periods (Eriksson and Jerling,
1990). In the latter species, ramets in habitats rich in
resources support the growth of ramets in less favourable
sites by transporting water, nutrients and assimilates.
Connected ramets exploit and utilize resources cooperatively and achieve efficient production as a whole. In
such species, the spatial arrangement of ramets is particularly important for both exploring and exploiting
resources efficiently. Thus, the architecture of the whole
clone and its adaptive significance cannot be understood
without knowing the characteristics of below-ground
organs. However, the growth pattern of the whole genet has
been studied for only a limited number of species (Watt,
1945, 1970 ; Kershaw, 1958, 1962 ; Edwards, 1984), and
quantitative approaches employing morphological measurement and simulation models are limited to such as Medeola
Širginiana (Bell, 1974), Alpinia speciosa (Bell, 1979), Carex
arenaria (Bell et al., 1979), Anemone nemorosa (Shirreffs and
Bell, 1984), Lycopodium annotinum (Callaghan et al., 1990),
Solidago altissima (Cain, Pacala and Silander, 1991), and
Trifolium repens (Cain et al., 1995).
The objectives of this study were : (1) to investigate
quantitatively the growth patterns of R. japonica rhizomes
in the volcanic desert on Mt. Fuji and thereby reconstruct
the clonal growth of the whole patch ; and (2) to identify the
key factors responsible for the central die-back observed on
Mt. Fuji. The adaptive significance of the architecture and
rhizome morphology of R. japonica is also discussed with
special reference to its habitat and role in primary succession.
MATERIALS AND METHODS
The field site is a volcanic desert (1500 m above sea level) on
the southeast slope of Mt. Fuji (height 3776 m). The last
eruption in 1707 destroyed the vegetation and the ground is
covered with a thick scoria layer (Tsuya, 1971). Discrete
monoclonal patches of R. japonica, the dominant pioneer,
show apparent central die-back. In small patches (approx.
1–10 m#), bare ground can be seen in their central parts and
in larger patches the areas of central die-back are frequently
replaced by later successional species. Both plant and field
site are described in more detail elsewhere (Adachi et al.,
1996).
The below-ground structure of R. japonica develops as
follows (Adachi et al., 1996). (1) A seedling develops several
rhizomes. (2) The apical bud of each rhizome develops into
an aerial shoot. (3) The aerial shoot is annual and produces
a few or more subterranean winter buds at its basal part by
the end of the growth period. (4) One or a few winter buds
at the aerial shoot base sprout in the following spring to
form new aerial shoots close to its mother shoot. Thus,
aerial shoots sprout at almost the same position for several
years, forming a small cluster of shoots (shoot clump). (5)
Since iterations of aerial shoot formation of the clump were
not observed to exceed six times, it is suggested that the
shoot clump has a definite life-span of approx. 5 years.
While the shoot clump keeps producing new aerial shoots,
1
2
α
n
l1
L
ri = li /L
F. 1. Morphological parameters of rhizomes of R. japonica. Branch
length (L), branching positions (l , l , …, ln), number of daughter
" #
branches (n), and branching angle (α). Relative branching position of
the ith daughter branch was calculated as ri ¯ li}L. A solid circle and
a dotted circle indicate a live and a dead shoot clump, respectively.
the lateral buds on the rhizome remain dormant. When the
shoot clump ceases to produce any new shoots and dies, a
few dormant buds sprout and begin to grow horizontally as
new rhizomes of the next order (called ‘ generation ’ here).
The fact that the branching is suppressed while shoot clump
is active suggests the involvement of apical dominance. The
new rhizomes branch off the mother rhizome with a certain
branching angle and extend fairly straight. The apex of the
new rhizome develops into a new aerial shoot and forms a
new shoot clump. The whole patch develops by iterating
these steps from (2) to (5).
Plant material
A quarter of a circular patch (diameters of 4±6 and 4±0 m
along and across the slope, respectively) was excavated at
the end of growth season (Nov. 1990) in an archaeological
manner. The excavated rhizomes and shoots were carried
back to the laboratory and the following parameters were
measured : length of a rhizome (L), relative position of the
branching of the daughter rhizome to the length of mother
rhizome (ri ¯ li}L ; r of ith daughter branch), number of
daughter rhizomes branched from a rhizome (n), branching
angle between a daughter rhizome and its mother rhizome
(α) (Fig. 1).
Although all the rhizome branches were used for the
measurements of α, some branches could not be used for the
determination of other parameters. For L and r, only intact
rhizome branch samples were used. Those with subterranean
terminal buds at their tips were excluded, because they were
still growing.
Relative frequency
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
A
L = 40.8
(±20.0)
n = 26
0.2
B
r = 0.76 (±0.18)
n = 54
0.2
0.1
0.1
20
0
Relative frequency
0.3
171
0.3
40
60
80
Length (cm)
100
0.4
C
n = 1.75 (±1.21)
n = 20
0.2
0.3
0 0.2 0.4 0.6 0.8 1
Relative branching position
D
α = 40.4 (±7.5)
n = 71
0.2
0.1
0
0
0.1
0
2
4
6
8
No. of branches
10
12 0
20
40
60
80
Branching angle (deg.)
100
F. 2. Frequency distributions of morphological parameters of rhizomes. A, Length (cm). B, Relative branching position. C, Number of
branches. D, Branching angle (°). The values are the means with standard deviations in parentheses. As for branching angle, the value is not
arithmetic mean with a standard deviation, but the mean angle with angular deviation in parentheses. n denotes number of samples. See Fig. 1
for the other abbreviations.
The model
A numerical model of rhizome growth was developed. It
was coded in Pascal language, and run on a personal
computer (PC-9801 Series, NEC, Tokyo, Japan). The
growth of rhizome systems was described using the following
morphological parameters : branch length (L), relative
branching position of rhizomes to the length of its mother
rhizome (r), number of daughter branches (n), branching
angle (α) (Fig. 1). The variations of these values are
expressed as probability distributions, shown in Fig. 2. The
parameter values were changed randomly and independently
of each other for each branch according to the probabilities
of their frequency distributions. The sign of α was changed
randomly. While the patch excavated had rhizomes as long
as 80 cm (Fig. 2A), younger and smaller patches had only
shorter rhizomes. Generally speaking, the length of a
rhizome cannot exceed the radius of the patch. Seedlings
which are 10–20 cm in diameter have rhizomes only as long
as 5–10 cm, respectively. Therefore, we assume that L
increases linearly with the generation (i) of rhizomes and
express as Li ¯ L ¬[1­er¬(i®1)] (Li : Length at ith
"
generation, er : extension rate). ‘ Generation ’ of rhizome is
defined as number of branching order from the initial
seedling to the rhizome under consideration.
An outline of the model is as follows. (1) The model
calculates the distribution of rhizome branches and shoot
clumps for each ‘ generation ’. Since clumps were found to
have a definite life-span, approx. 5 years (Adachi et al.,
1996), we assumed that the life-span of clumps is identical in
this model. Daughter rhizomes sprout on every rhizome
simultaneously when the existing clumps die. (2) The initial
seedling produces five rhizomes (first generation). Each of
these rhizomes forms daughter branches (second gener-
ation). The daughter rhizome branches from its mother
rhizome at relative branching position r (r ¯ l}L, 0% r % 1,
l : position of branching measured from the base of the
mother rhizome) and at branching angle α. The generation
of daughter branches belongs to the one next to the mother
branch, i.e. if a mother branch is at the Nth generation, its
daughter branches belong to the (N­1) th generation. (3)
The apex of each rhizome develops into an aerial shoot and
forms a shoot clump. When a shoot clump dies and is
unable to produce new aerial shoots, daughter rhizomes
branch off mother rhizomes and develop new shoot clumps
at their apices. These procedures are repeated to reproduce
the development of a patch.
Since aerial shoots are formed in clumps, the effects of
changes in parameter on the arrangement of shoot clumps
were examined. In practice, the positions of shoot clumps
on x–y coordinates were calculated for various conditions,
and the distributions of the clumps were analysed by
calculating statistics for the clump densities.
SensitiŠity analysis
To evaluate the effects of changes in each of these
morphological parameters, stochastic simulations based on
modified frequency distributions were run. The frequency
distribution of only one parameter was varied at a time,
with others being kept to the original frequency distributions. A feature of a stochastic model is that simulation
results differ from run to run. Therefore, simulations were
repeated 50 times under the same initial set of conditions
and the average clump densities were calculated along the
patch radius.
Deterministic simulations were also carried out, in which
every parameter followed the actual mean of the measured
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
values and only one was changed at a time, to evaluate the
effect of variance in the stochastic model.
RESULTS
Rhizome morphology
The morphological parameters of the rhizomes measured
are shown in Fig. 1. Their lengths (L) had a broad range,
from 11 to 74 cm (Fig. 2A). Some rhizomes were omitted
because they were still growing. Relative branching position
(r) was strongly skewed to the right (Fig. 2B). The number
of daughter branches (n) showed a distribution skewed to
the left (Fig. 2C). Since the distribution of branching angle
(α) was symmetrical around zero, the distribution of absolute
values is shown for α. α showed a distinctive unimodal
distribution with an average of 40±4° with angular deviation
of ³7±5° (see Batshelet, 1981 for the statistical calculations).
7th generation
1.0 m
F. 3. Examples of the results of stochastic simulations. Distribution
maps of shoot clumps at the seventh generation are shown. Each cross
shows the position of the seedling where the whole clone began to grow.
The morphological parameters were fixed to the actual distributions
shown in Fig. 2.
Clump density (m–2)
172
40
30
20
10
0
0.5
1.0
1.5
2.0
Distance (m)
2.5
3.0
F. 4. Changes in clump distribution pattern with the rhizome
generation. (—E—) Shows the mean clump densities in the seventh
generation and the changes in the densities in the fourth (+), sixth (*),
and eighth (D) generation, respectively.
Fifty-nine per cent occurred within the range from 30° to
50° (Fig. 2D).
Analysis with a simulation model
When the actual morphological parameters of rhizomes
were adopted, central die-back was reproduced in every
stochastic simulation. Some examples of simulated distribution pattern of shoot clumps are shown in Fig. 3.
The effects of the generation on the distribution of clumps
are presented in Fig. 4. The clump distribution is expressed
as the changes in clump density with distance from the
centre of the patch. The number of clumps in distance
classes every 25 cm from the centre was counted, and their
densities were calculated. The central die-back was apparent
at the fourth generation and was maintained to later
generations. Since shoot clumps usually have a life-span of
4–5 years, we may roughly estimate age of a patch by
multiplying the generation of the latest rhizome by 4 or 5.
Therefore, it is expected that the die-back first appears
approx. 20 years after the seedling emergence. At and after
the eighth generation, the density in the centre became
greater than that at the periphery. This is because some
rhizomes gradually begin to grow inwards after several
branchings and the number of such rhizomes increases with
the generation. However, in the field, once the central dieback areas are produced, they are invaded by successional
species (Adachi et al., 1996). Since the initial process of
central die-back is our present concern, the complication
brought about by the returning rhizome branches was
avoided and our analyses of the effects of changes in
morphological parameters were confined to the clump
distribution patterns in the seventh generation, which is
estimated to be approx. 30 years old.
The effect of branching angle (α) on clump distribution is
shown in Fig. 5. In each of these simulations, rhizomes
repeated branching six times from the seedling to the
seventh generation with an identical frequency distribution
of branching angle.
There was a small difference between the mean angle
(¯ 40±4°) calculated with the raw data (actual measured
angles) and the mean angle (¯ 43±8°) calculated with the
histograms of frequency distribution (Fig. 2), because
the histograms have only discrete values. However, since
the value calculated with the raw data is more accurate and
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
50
A
173
7th generation
100
B
30
80
20
10
0
0.5
1.0
1.5
2.0
50
2.5
C
Clump density (m–2)
40
Clump density (m–2)
Clump density (m–2)
40
60
40
30
20
20
10
0
0.5
1.0
1.5
2.0
2.5
Distance (m)
0
0.5
1.0
1.5
2.0
2.5
Distance (m)
F. 5. Effects of changes in mean branching angle on shoot clump distribution. Results are shown for the seventh generation. Only the mean
of the branching angle distribution was modified. The variance of branching angle and the frequency distributions of other morphological
parameters were fixed to those of actual distributions shown in Fig. 2. Symbols and vertical bars indicate the means and the 95 % confidence
intervals for the 50 simulations. (—E—) Mean clump densities calculated with the actual plant data set (see Fig. 2, calculated mean from this
frequency distribution was α- ¯ 40°). A, The frequency distribution in Fig. 2D was shifted by 20°. (D) and (– –*– –) indicate the densities for
decreased (by 50 %, α- ¯ 20°) and increased (by 50 %, α- ¯ 60°) branching angles, respectively. B, The frequency distribution in Fig. 2D was shifted
by 40°. (D) and (– –*– –) indicate the densities for α- ¯ 0° (decreased by 100 %) and α- ¯ 80° (increased by 100 %), respectively. C, (D), (+) and
(*) indicate the densities for α- ¯ 45° (increased by 5°), 50° (increased by 10°) and 60° (increased by 20°), respectively. Error bars were omitted
for simplicity.
realistic, the mean branching angle (α- ) is referred to simply
as the mean of raw data.
For the sensitivity analysis, the frequency distribution of
α was modified. The actual mean angle (α- ¯ 40°) was
increased or decreased by moving the actual frequency
distribution. Angular deviation was not altered in these
modifications. For other parameters, the actual frequency
distributions were used (see Fig. 2). When α- was 40°, many
clumps were found in the periphery, while some clumps
were found in the central area. Increasing α- to 60° (­50 %)
changed the distribution pattern of clumps greatly. The
clumps were distributed all over the patch from the centre to
the periphery, and the clump density was highest in the
central region, decreasing gradually toward the periphery
(Fig. 5A). When α- was reduced to 20° (®50 %), the clumps
shifted outwards and the clump density was highest near the
periphery (peak was approx 1±1 m from the centre) and
there were few clumps in the central area.
When α- was increased or decreased further, the above
tendencies were more obvious (Fig. 5B). When α- was 0°
(®100 %), the area of central die-back became greater and
the peak of the clump density moved outward (approx.
1±4 m from the centre). In contrast, when α- was further
increased to 80° (­100 %), the clumps were highly
concentrated in the central area and the size of the patch
greatly diminished (most clumps were distributed within
1 m from the centre).
Slighter modifications to the frequency distribution of the
branching angle revealed that, with increase of α- from 40°,
clump density decreased gradually in the periphery and
increased rapidly in the central area (Fig. 5C). The ratio of
the density at the centre to that at periphery was about onethird at α- ¯ 40°, but increased to half at α- ¯ 45°. When αwas 50°, the clumps were more crowded in the centre.
Figure 6 shows the effect of rhizome branch length (L) on
clump distribution. The extension rate (er) was increased or
decreased by 50 %, instead of L itself, to investigate the
effect of rhizome length to the whole clump distribution
pattern. In our model, initial mean rhizome length was set
to a quarter of the actual mean observed in a medium size
174
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
7th generation
100
B
50
Clump density (m–2)
80
A
Clump density (m–2)
40
60
40
30
20
20
10
0
0.5
1.0
1.5
Distance (m)
2.0
2.5
0
0.5
1.0
1.5
2.0
2.5
Distance (m)
F. 6. Effects of changes in extension rate of rhizome branches. (E) Show the mean clump densities for the standard er (¯ 0±25) (based on actual
plant data set). See the Fig. 5 legend for the other conditions. A, (D) and (*) indicate the densities for er ¯ 0±125 (decreased by 50 %) and
er ¯ 0±375 (increased by 50 %), respectively. B, (D) and (*) indicate the densities for er ¯ 0±0 (decreased by 100 %) and er ¯ 0±5 (increased by
100 %), respectively. (^) are for er ¯®0±05 (decreased by 120 %).
patch ; thus, when er ¯ 0±25, La at the seventh generation
coincided with the actual mean branch length. When er was
0±375 (­50 %), the clump density distribution moved
outwards without any large modification of its distribution
pattern and densities. When er was 0±125 (®50 %), the effect
was opposite : the patch size became smaller and clump
densities became greater (Fig. 6A). These distribution
patterns were unchanged with further increase or decrease
of er (Fig. 6B).
As er becomes larger, L- increases faster. Thus, the result
shown in Fig. 6 indicates that changes in L- affect both the
patch size and clump density. However, changes in La did
not alter the overall shape of the patches.
The effects of relative branching position (r) on the clump
distribution were similar to those of er and}or L (Fig. 7).
With the increase in r, patch size increased, though its effect
on the size was not so great as that of er. Since the range of
r is restricted from 0 to 1±0, some of the modified frequency
distributions skewed to either end. The results show that the
clump distribution pattern changed when ra was modified
greatly (e.g. increased by 0±4 or decreased by 0±6). However,
if ra was moved only within the range ³0±2, the distribution
pattern did not change greatly.
The results of the simulations with different numbers of
daughter branches per mother rhizome (n) are shown in Fig.
8. It is clear from this result that n changes the densities, but
not the distribution pattern of shoot clumps.
Though the life-span of shoot clumps is definite and was
estimated to be less than 5 years (Adachi et al., 1996), it can
be modified artificially in the simulation model and the
effects of definite life-span on the clump distribution can be
analysed. Figure 9 shows the clump densities along the
patch radius when the life-span of the clumps changed. As
the life-span becomes longer, the clump densities increased
and the peak of the densities moved towards the centre.
Therefore, if the life-spans of the clumps were longer, the
clump density in the central area would not decrease.
In Fig. 10 the results obtained with the deterministic
simulations of rhizome growth are shown as shoot clump
distribution maps viewed from the top. In each of these
simulations, all the morphological parameters were fixed to
their actual means except the number of branches (n) and
the branching angle (α). n was fixed to 2 for simplicity and
α was varied from 0° to 80° by 20° for sensitivity analysis.
Open circles represent shoot clumps. Some clumps overlapped other clumps. When the angle was 0°, all the clumps
in every direction occurred at one site (64 clumps overlapped
at each of the sites). When the angle was 20°, the clumps
were arranged like a very narrow ring, having a vacant area
inside. When the angle was 40°, the aerial shoot clumps
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
175
7th generation
100
B
Clump density (m–2)
80
50
A
Clump density (m–2)
40
60
40
30
20
20
10
0
0.5
1.0
1.5
Distance (m)
2.0
2.5
0
0.5
1.0
1.5
2.0
2.5
Distance (m)
F. 7. Effects of changes in relative branching position. (E) Show the mean clump densities for the actual mean r (¯ 0±77). In order to modify
the distribution, the frequency distribution in Fig. 2B was shifted by 0±2 or 0±4. When the shifted value exceeded 0 or 1, it was assumed to be
0 and 1, respectively. See the Fig. 5 legend for the other conditions. A, (D) and (*) indicate the densities for r ¯ 0±57 (decreased by 0±2) and
r ¯ 0±91 (increased by 0±2), respectively. B, (^), (D) and (*) indicate the densities for r ¯ 0±18 (decreased by 0±6), r ¯ 0±37 (decreased by 0±4)
and r ¯ 0±99 (increased by 0±4), respectively.
were arranged like actual patches with central die-back.
At a branching angle of 60°, clumps filled the ground
almost evenly. At 80°, the clumps gathered in the central
area and the density was less in the periphery than in the
centre.
DISCUSSION
In this study we have simulated the development of R.
japonica patches and succeeded in reproducing apparent
central die-back. In our simulations, with the mean number
of current aerial shoots of 1±43 (s.e. ¯³0±10, n ¯ 54, see
Fig. 11 in Adachi et al., 1996), calculated shoot densities for
the patches of the seventh generation with the actual data
set were a maximum of 36±8 m−# in the periphery and
10±9 m−# in the centre (Fig. 5). These values were somewhat
smaller than the actual numbers (Masuzawa and Suzuki,
1991 ; Adachi et al., 1996). The reasons for this are discussed
later. However, it is stressed here that the ratio of density at
the centre to that at the periphery predicted by the
simulation, which can be used as a measure of distribution
pattern of clumps, was 3±4 for the seventh generation. This
value agrees with the observed values in the patches with
central die-back (Fig. 3 in Adachi et al., 1996).
Model analysis
Sensitivity analyses of the present model showed that,
among the morphological parameters measured, the branching angle (α) was the most essential determinant of the
central die-back. When the mean angle (α- ) was 40° or
smaller, die-back was obvious in the centre of a patch, but
it was not seen when the angle was greater than 40°, even by
only 10° (Fig. 5C). When α- ¯ 20°, an obvious central dieback was reproduced with a substantial hollow area in the
centre. However, shoot clumps were arranged as a narrower
band than that at α- ¯ 40° (Fig. 5A).
The other three parameters are mainly engaged in
determining the absolute size of patches or clump density
rather than the pattern of clump distribution. Of these
three, the length of rhizomes can be regarded as the second
most influential factor, because it changed the patch size
greatly and, thereby, clump density. However, the rhizome
length did not change the distribution pattern of clumps ;
only clump density and patch size were changed (Fig. 6). In
our model, it was assumed that the length of rhizomes
increased linearly with the generation. When the length
increased exponentially, marked central die-back appeared
176
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
7th generation
400
B
80
A
Clump density (m–2)
300
Clump density (m–2)
60
40
200
100
20
0
0.5
1.0
1.5
Distance (m)
2.0
2.5
0
0.5
1.0
1.5
2.0
2.5
Distance (m)
F. 8. Effects of changes in number of daughter branches. (E) Show the mean clump densities for the actual mean n (¯ 1±75). When the shifted
value exceeded 0, it was assumed to be 0. See the Fig. 5 legend for the other conditions. A, (D) and (*) Indicate the densities for n ¯ 1±54
(decreased by 0±25) and n ¯ 2±0 (increased by 0±25), respectively. B, (*), (D) and (^) Indicate the densities for n ¯ 1±33 (decreased by 0±5), n ¯
2±25 (increased by 0±5) and n ¯ 2±75 (increased by 1±0), respectively. Note that the range of clump density differs greatly from the other figures.
at much earlier generations, but the clump distribution
showed a similar pattern (data not shown). Even if the
rhizome length was constant (er ¯ 0) throughout a simulation, it also reproduced the central die-back (Fig. 6B).
Since branching position concerns the distance, it also
changed both the size of a patch and clump density (Fig. 7).
However, the effect was not so conspicuous as that of
rhizome length, because the branching position affects only
the local relationships between rhizomes and clumps of
aerial shoots. While the rhizome length can vary independently, the branching position can vary only within the
range of the branch length. The number of daughter
branches per mother rhizome only affected the clump
density, it did not affect the shape of the whole clone (Fig.
8).
These results strongly indicate that the central die-back of
a patch results from the conservation of rhizome growth
pattern, which supports our previous prediction that central
die-back is caused endogenously by R. japonica itself rather
than by interspecific and}or intraspecific competition
(Adachi et al., 1996). For clonal stands of R. japonica in the
volcanic desert on Mt. Fuji, it was observed that the shoot
clump has a definite life-span, approx. 5 years, and that,
while the clump is active, the sprouting of the daughter
branches is suppressed probably by apical dominance
(Adachi et al., 1996). It is obvious that the definite life-span
of shoot clumps and suppression of development of daughter
branches are also important factors responsible for the
central die-back in R. japonica patches. We incorporated
these attributes of the clump in the present model. If the lifespan of shoot clumps were indefinite (Fig. 9) and}or
branching of daughter rhizomes occurred free from apical
dominance (data not shown), clump density would continue
to increase in the central area, the older part within a patch.
The morphology and growth patterns of plants are
primarily determined ontogenetically, but they also exhibit
plasticity—responding to the environment and surrounding
organisms. Therefore, it may be necessary to take account
of density regulation in response to the environment. For
some clonal plants, changes in their growth patterns depend
on environmental conditions such as nutrients and light (for
reviews, see Waller and Steingraeber, 1985 ; De Kroon and
Schieving, 1990 ; De Kroon and Hutchings, 1994). Even
when the environment is stable, plants are known to
regulate branching intrinsically to maintain proper branch
density (Borchert and Slade, 1981). As for R. japonica on
Mt. Fuji, the aerial shoot density, which is almost
proportional to the clump density (for example, 1±43 shoots
per clump, Adachi et al., 1996), was usually below 200
shoots m−# (Masuzawa and Suzuki, 1991 ; Adachi et al.,
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
80
177
7th generation
70
α = 0°
α = 20
α = 40°
α = 60
Clump density (m–2)
60
50
40
30
20
10
0
0.5
1.0
1.5
Distance (m)
2.0
2.5
F. 9. Effects of changes in life-span of shoot clumps. (E) Show the
mean clump densities for the actual life-span, for one generation. (D),
(+) and (*) Indicate the mean clump densities when the life-spans were
changed to three, five and seven generations. All the results show the
density distributions at the seventh generation after the seedling. See
the Fig. 5 legend for the other conditions.
1996), so the number of daughter branches in R. japonica
may be regulated to avoid competition among ramets.
However, such regulation maintaining moderate shoot
densities would not cause die-back in the centre.
Significance of the clonal architecture
The convergence of branching angle and long persistence
of the rhizome systems seem to be important features of the
rhizome growth pattern and clonal architecture of R.
japonica on Mt. Fuji. Central die-backs of aerial shoot
populations that are apparently similar to the present
phenomenon have been reported for several clonal species.
However, they are brought about by different mechanisms.
Populations of aerial shoots of a common woodland
perennial Anemone nemorosa, for example, also grow
radially and develop a hollow centre. Examination of
below-ground organs and a computer simulation model
revealed that the rhizome segments were alive for only 7
years at the longest and that a circular population consisted
of an intermixture of different clones (Shirreffs and Bell,
1984). Solidago altissima is another perennial known to
show a circular distribution of aerial shoots. In this species,
rhizome connections persist for up to 5–6 years and, thus,
separate clonal segments are formed (Cain, 1990). When the
observed data were incorporated in a simulation model, the
‘ fairy rings ’ of this species could not be reproduced (Cain et
al., 1991). Cain et al. (1991) argued that it was a consequence
of the fact that branching angles of S. altissima were highly
variable including values which represented growth backward toward the parent ramet. They stated that fairy rings
were not a simple consequence of rhizome growth patterns,
α = 80°
1.0 [m]
F. 10. Distribution maps of shoot clumps at the seventh generation
calculated with deterministic simulations. The morphological parameters adopted are as follows. Number of daughter branches (n) and
relative branching position (r) were to 2 and 0±8, respectively. The
rhizome length was assumed to extend linearly (er ¯ 0±25) according to
the generation, as in the stochastic simulations. The initial number of
branches was 5.
but that other environmental and biological factors were
important to bring them about.
On the other hand, as shown in our analysis, branching
angle is particularly important for the formation of central
die-back of R. japonica on Mt. Fuji. This implies that there
may be some adaptive significance of the branching angle
and the architecture produced thereby. As for clonal plants
with regular branching angles, adaptive significance of
specific branching angles has been argued (for a review, see
Bell and Tomlinson, 1980). For example, a branching angle
of 60°, seen in Solidago canadensis (Smith and Palmer, 1976)
and Alpinia speciosa (Bell, 1979), leads to a hexagonal arrangement of the rhizomes, which is suggested as one of the
most efficient morphologies to pack a plane densely. Closely
packed aerial shoots and rhizomes are thought to be
favourable for monopolizing soil resources and to prevent
other species or competitive clones from invading the
habitat. It is therefore advantageous to have 60° for utilizing
a good habitat and to increase the stability of the population,
178
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
though it is unfavourable for exploring new habitats
extensively. It may increase the possibility of intraclonal
competition. The plants with a branching angle close to 0°
showed linear development of rhizome systems going away
from the initial site most rapidly and expanded their
habitats far away if other conditions concerning the rhizome
growth were the same (Bell and Tomlinson, 1980 ; Callaghan
et al., 1990). Thus it is thought to be a favourable way to
explore new habitats in spatially heterogeneous environments, where resources are found only in patchy microsites.
However, simple adaptational interpretations of the
architecture of modular organisms based on the mean
values have been severely criticised, because such a simple
approach fails to explain the real arrangements of rhizomes
for species such as Medeola Širginiana (Cook, 1985, 1988 ;
Cain and Cook, 1988) and Solidago altissima (Cain, 1990 ;
Cain et al., 1991), both of which show highly variable clonal
growth. In our simulations some results also differ from
those predicted by deterministic models based solely on
mean values of morphological parameters (Fig. 10). While
a branching angle of 60° was suggested to be efficient in
filling a habitat (Bell and Tomlinson, 1980), in our stochastic
simulations a mean branching angle of 60° caused many
shoot clumps to be concentrated in the central area. Their
distribution was far from being homogenous nor arranged
with the least overlapping of ramets. A smaller branching
angle, say 50°, resulted in more even distribution of clumps
over the patch (Fig. 5C). It had been expected that the shoot
clumps would concentrate in a very narrow ring-like area
when the branching angle was small (e.g. 20° or less) and
they did so in the deterministic simulation (Fig. 10) ;
however, the width of distribution was in practice broader,
being only slightly narrower than 40° (Fig. 5A, B). This is
because, even when the mean angle was smaller, the variance
was relatively large and this prevented the clumps from
converging to a small area. These results suggest that not
only the mean value, but variance and frequency distribution, are also important in determining and analysing
the whole architecture. Now that our stochastic simulation
model successfully showed the effects of various mean
branching angles without resorting to an unrealistic,
deterministic simulation model and since it is suspicious if
any clonal plant species forms regular geometric patterns in
the field (Cain and Cook, 1988 ; Cain et al., 1991), we should
take advantage of stochastic simulation models to analyse
quantitatively the growth trait of clonal plant species.
The general tendency suggested by the deterministic
simulations was, however, largely consistent with the results
of the stochastic simulations. As the mean branching angle
decreased, the edge and the peak of the clump distribution
expanded (Fig. 5C). This implies that R. japonica expands
its habitat centrifugally by having the branching angle of
40° rather than packing the area densely. Furthermore,
since there is a definite life-span for shoot clumps, R.
japonica utilizes the same site for only a limited period and
expands its habitat continuously. The central die-back
brought about by the branching angle of 40° may be a
balanced strategy which realizes both extension of habitat
and maintenance of an almost constant clump density.
If the number of aerial shoots is fixed in a patch, it is
favourable for the patch to keep the shoot density low,
because it makes the whole patch acquire more light and
thus achieve more photosynthetic production. If a low
density of aerial shoots is implemented by elongation of
rhizomes, however, it needs a certain cost to construct extra
rhizomes. On the other hand, if low density is maintained by
the adjustment of branching angles, no extra construction
cost is required. The results of this study show that patches
of R. japonica can arrange aerial shoots further from their
centres and keep the shoot densities low by having an
almost constant branching angle of around 40°. It is notable
that R. japonica achieves such a shoot arrangement that is
advantageous in effective acquisition of light without any
extra construction cost. It is therefore suggested that the
central die-back is adaptive for R. japonica to increase the
productivity as a whole, survive and expand its habitat
vigorously in a sterile land.
A C K N O W L E D G E M E N TS
We are grateful to colleagues in the laboratory, and
postgraduates of the Department for their help in the field
survey and census. T. Kawazu, the University of Tokyo,
was helpful in coding of the simulation program. We also
thank Drs N. Kachi and A. Takenaka, National Institute
for Environmental Studies, and Ms. L. Child,
Loughborough University of Technology, UK, for critical
comments on the draft. Thanks are also due to Drs M. Cain
and C. Marshall, who refereed our manuscript openly and
gave us constructive criticisms on the manuscript. This
study was partly carried out during NA’s tenure of
Fellowships of the Japan Society for the Promotion of
Science for Japanese Junior Scientists and was supported in
part by a Grant-in-aid from the Ministry of Education,
Science, and Culture, Japan.
LITERATURE CITED
Adachi N, Terashima I, Takahashi M. 1996. Central die-back of
monoclonal stands of Reynoutria japonica in an early stage
of primary succession on Mt. Fuji, a Japanese volcano. Annals
of Botany 77 : 477–486.
Batschelet E. 1981. Circular statistics in biology. London : Academic
Press.
Bell AD. 1974. Rhizome organization in relation to vegetative spread in
Medeola Širginiana. Journal of the Arnold Arboretum 55 : 458–468.
Bell AD. 1979. The hexagonal branching pattern of rhizomes of Alpinia
speciosa (Zingiberaceae). Annals of Botany 43 : 209–223.
Bell AD, Roberts D, Smith A. 1979. Branching patterns : the simulation
of plant architecture. Journal of Theoretical Biology 81 : 351–375.
Bell AD, Tomlinson PB. 1980. Adaptive architecture in rhizomatous
plants. Botanical Journal of the Linnean Society 80 : 125–160.
Borchert R, Honda H. 1984. Control of development in the bifurcating
branch system of Tabebuia rosea : a computer simulation. Botanical
Gazette 142 : 184–195.
Borchert R, Slade NA. 1981. Bifurcation ratios and the adaptive
geometry of trees. Botanical Gazette 142 : 394–401.
Borchert R, Tomlinson PB. 1984. Architecture and crown geometry in
a Tabebuia rosea (Bignoniaceae). American Journal of Botany 71 :
958–969.
Cain ML. 1990. Models of clonal growth in Solidago altissima. Journal
of Ecology 78 : 27–46.
Cain ML, Cook RE. 1988. Growth in Medeola Širginiana clones. II.
Stochastic simulations of vegetative spread. American Journal of
Botany 75 : 732–738.
Adachi et al.—Analysis of Rhizome Growth of Reynoutria japonica
Cain ML, Pacala SW, Silander JA, Jr. 1991. Stochastic simulation of
clonal growth in the tall goldenrod, Solidago altissima. Oecologia
88 : 477–485.
Cain ML, Pacala SW, Silander JA, Jr, Fortin MJ. 1995. Neighborhood
models of clonal growth in the white clover Trifolium repens. The
American Naturalist 145 : 888–917.
Callaghan TV, Svensson BM, Bowman H, Lindley DK, Carlsson BA.
1990. Models of clonal plant growth based on population dynamics
and architecture. Oikos 57 : 257–269.
Cook RE. 1985. Growth and development in clonal plant populations.
In : Jackson JBC, Buss LW, Cook RE, eds. Population biology and
eŠolution of clonal organisms. New Haven : Yale University Press,
259–296.
Cook RE. 1988. Growth in Medeola Širginiana clones I. Field
observations. American Journal of Botany 75 : 725–731.
De Kroon H, Hutchings MJ. 1994. Foraging in plants : the role of
morphological plasticity in resource acquisition. AdŠances in
Ecological Research 25 : 159–238.
De Kroon H, Schieving F. 1990. Resource partitioning in relation to
clonal growth strategy. In : van Groennendael J, de Kroon H, eds.
Clonal growth in plants. The Hague : SPB Academic Publishing,
113–130.
Edwards J. 1984. Spatial pattern and clone structure of the perennial
herb, Aralia nudicaulis L. (Araliaceae). Bulletin of the Torrey
Botanical Club 111 : 28–33.
Eriksson O, Jerling L. 1990. Hierarchical selection and risk spreading
in clonal plants. In : van Groennendael J, de Kroon H, eds. Clonal
growth in plants. The Hague : SPB Academic Publishing, 79–94.
Harper JL. 1981. The concept of population in modular organisms. In :
May RM, ed. Theoretical ecology : principles and applications.
Second Edition. Oxford : Blackwell Scientific Publications, 53–77.
Harper JL. 1985. Modules, branches, and capture of resources. In :
Jackson JBC, Buss LW, Cook RE, eds. Population biology and
eŠolution of clonal organisms. New Haven : Yale University Press,
1–33.
Hirose T, Tateno M. 1984. Soil nitrogen patterns induced by
colonization of Polygonum cuspidatum on Mt. Fuji. Oecologia 61 :
218–223.
Honda H. 1971. Description of the form of trees by the parameters of
the tree-like body : effects of the branching angle and the branch
length on the shape of the tree-like body. Journal of Theoretical
Biology 31 : 331–338.
Kershaw KA. 1958. An investigation of the structure of a grassland
community. I. The pattern of Agrostis tenuis. Journal of Ecology
46 : 571–592.
179
Kershaw KA. 1962. Quantitative ecological studies from
Landmannahellir, Iceland. II. The rhizome behavior of Carex
bigelowii and Calamagrostis neglecta. Journal of Ecology 50 :
171–179.
Marshall C. 1990. Source–sink relations of interconnected ramets. In :
van Groennendael J, de Kroon H, eds. Clonal growth in plants. The
Hague : SPB Academic Publishing, 23–41.
Maruta E. 1981. Size structure in Polygonum cuspidatum on Mt. Fuji.
Japanese Journal of Ecology 31 : 441–445. (In Japanese)
Masuzawa T, Suzuki J. 1991. Structure and succession of alpine
perennial community (Polygonum cuspidatum) on Mt. Fuji.
Proceedings of the National Institute of Polar Research Symposium
on Polar Biology 4 : 155–160.
Pitelka LF, Ashmun JW. 1985. Physiology and integration of ramets in
clonal plants. In : Jackson JBC, Buss LW, Cook RE, eds.
Population biology and eŠolution of clonal organisms. New Haven :
Yale University Press, 399–435.
Shirreffs DA, Bell AD. 1984. Rhizome growth and clone development
in Anemone nemorosa L. Annals of Botany 54 : 315–324.
Smith AP, Palmer JO. 1976. Vegetative reproduction and close
packing in a successional plant species. Nature 261 : 232–233.
Sutherland WJ, Stillman RA. 1988. The foraging tactics of plants.
Oikos 52 : 239–244.
Sutherland WJ, Stillman RA. 1990. Clonal growth : insights from
models. In : van Groennendael J, de Kroon H, eds. Clonal growth
in plants. The Hague : SPB Academic Publishing, 95–111.
Tsuya H. 1971. Topography and geology of volcano Mt. Fuji. In :
Fujisan (Mt. Fuji). Tokyo : Fuji-Kyuko, 1–149. (In Japanese with
English summary)
Waller DM. 1988. Plant morphology and reproduction. In : Lovett
Doust J, Lovett Doust L, eds. Plant reproductiŠe ecology. Patterns
and process. New York : Oxford University Press, 203–227.
Waller DM, Steingraeber DA. 1985. Branching and modular growth :
theoretical models and empirical patterns. In : Jackson JBC, Buss
LW, Cook RE, eds. Population biology and eŠolution of clonal
organisms. New Haven : Yale University Press, 225–257.
Watt AS. 1945. Contributions to the ecology of bracken (Pteridium
aquilinum). III. Frond types and the make-up of the population.
New Phytologist 44 : 156–178.
Watt AS. 1970. Contributions to the ecology of bracken (Pteridium
aquilinum). VII. Bracken and litter. 3. The cycle of change. New
Phytologist 69 : 431–449.
White J. 1979. The plant as a metapopulation. Annual ReŠiew of
Ecology and Systematics 10 : 109–145.