Evolutionary Ecology (2004) 18: 493–520
DOI: 10.1007/s10682-004-5141-9
Springer 2005
Research article
Physiological integration affects growth form
and competitive ability in clonal plants
TOMÁŠ HERBEN
_
Institute of Botany, Academy of Sciences of the Czech Republic, CZ-252 43 Pruhonice,
Czech
Republic; Department of Botany, Faculty of Science, Charles University, Praha, Czech Republic
(E-mail: [email protected])
Co-ordinating editor: J. Tuomi
Abstract. Clonal plants translocate resources through spacers between ramets. Translocation can
be advantageous if a plant occurs in heterogeneous environments (‘division of labour’); however,
because plants interact locally, any spatial arrangement of ramets generates some heterogeneity in
light and nutrients even if there is no external heterogeneity. Thus the capacity of a clonal plant to
exploit heterogeneous environment must operate in an environment where heterogeneity is partly
shaped by the plant growth itself. Since most experiments use only simple systems of two connected
ramets, plant-level effects of translocation are unknown. A spatially explicit simulation model of
clonal plant growth, competition and translocation is used to identify whether different patterns of
translocation have the potential to affect the growth form of the plant and its competitive ability.
The results show that different arrangements of translocation sinks over the spacer system can
completely alter clonal morphology. Both runners and clumpers can be generated using the same
architectural rules by changing translocation only. The effect of translocation strongly interacts
with the architectural rules of the plant growth: plants with ramets staying alive when a spacer is
formed are much less sensitive to change in translocation than plants with ramets only at the tip. If
translocation cost is low, translocating plants are in most cases better competitors than plants that
do not translocate; the difference becomes stronger in more productive environments. Key traits
that confer competitive ability are total number of ramet, and their fine-scale aggregation.
Key words: competitive ability, individual-based simulation model, plant architecture, resource
acquisition, resource translocation, spatial autocorrelation
Introduction
One of the major features of many clonal plants is their ability to maintain
connections between ramets. As a result of this, a set of interconnected ramets
may possess the capacity to behave as a unit with some degree of integration.
While many different mechanisms can be involved in clonal integration
(resource translocation, hormonal signals, disease spread etc.), much attention
of both experimentalists and theoreticians has been paid to resource
translocation, i.e. sharing of resource produced, or acquired by, in one ramet
with other ramets.
Many experiments have shown that clonal plants are able to use connections
between ramets to transport resources obtained from resource-rich patches to
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support plant parts located in resource-poor patches (Birch and Hutchings,
1994; Stuefer et al., 1996; Wijesinghe and Hutchings, 1997; Alpert and Stuefer,
1997; Jónsdóttir and Watson, 1997; Hutchings et al., 2000). While doing so,
they are often able to achieve higher total biomass than if the same amount of
resource were homogeneously distributed. Most experiments on resource
translocation have used a simple system of two or several interconnected
ramets (for a review, see Alpert and Stuefer, 1997). This has produced much
information on ecophysiological processes in translocation and identified
major parameters that determine translocation patterns. Among these, four
parameters are the most important: (i) the distance over which a resource is
translocated (Kemball and Marshall, 1994; D’Hertefeldt and Jonsdottir, 1999),
(ii) quantity of resource translocated (De Kroon et al., 1996), (iii) proportion
of basi- vs. acropetal translocation (Kemball and Marshall, 1995; De Kroon
et al., 1996), and (iv) distribution of translocation ‘sinks’ over the plant body
(Marshall, 1990; Kemball & Marshall, 1994).
The whole-plant level effects of translocation processes are still little known. It
has been shown that when the plant occurs in heterogeneous environments,
maintenance of inter-ramet connections is often beneficial in competition (Caraco and Kelly, 1991; Oborny and Cain, 1997; Piqueras et al., 1999; Oborny et al.,
2000). In contrast, in completely homogeneous environments, models show that
plants with no clonal integration are usually favoured (Oborny et al., 2000).
Consequently it has often been assumed that external environmental heterogeneity (biotic or abiotic) is a prerequisite for the maintenance of clonal integration
(Oborny et al., 2000, but see Peterson and Chesson, 2002).
However, translocation operates in an environment that is inherently heterogeneous. Since plants interact locally, each ramet competes with other
ramets for light and nutrients within a certain zone, and the intensity of
competition any ramet experiences differs as a function of the local density.
Each ramet thus generates a limited zone of influence; consequently a part of
the environmental heterogeneity found in the field is due to uneven distribution
of plant individuals themselves (Law and Dieckmann, 2000). The capacity of a
clonal plant to exploit a heterogeneous environment therefore operates in an
environment in which heterogeneity is partly shaped by morphology of the
plant itself. In most clonal plants, new ramets are not placed randomly; their
positioning is constrained by architectural and developmental rules (Bell, 1984;
Mogie and Hutchings, 1990; de Kroon et al., 1994; Newton and Hay, 1995;
Geber et al., 1997; Watson et al., 1997; Huber et al., 1999). As a result, morphology and growth of a clonal fragment is determined by interactions between
ramets arranged in space based on these rules (Bell, 1986; Klimeš, 1992, 2000;
Cowie et al., 1995; Adachi et al., 1996). In such a scenario, uneven distribution
of ramets may mean that resource translocation may be beneficial to the plant
even if the external environment is homogeneous.
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Surprisingly, the feedback relationships between these architectural rules
that determine heterogeneity in competition and translocation patterns have
been little explored [see the review by Oborny and Bartha (1995)]; effects of
translocation at the whole plant and stand levels are almost unknown. This
paper specifically addresses these effects by using a spatial explicit simulation
model developed by Herben and Suzuki (2001) which makes possible to
examine effects of individual traits independently of each other and to scale
them up to the level of the whole plant. This model has three independent
elements: (i) an individual-based model of resource capture as a function of
neighbourhood interactions involving the ramet, (ii) an architectural model of
clonal plant growth, and (iii) a model of resource (photosynthate) translocation within a set of physiologically interconnected ramets. The growth of a
modelled plant is primarily determined by its resource status; architectural
rules serve only as constraints. As a result, effects of ramet competition and
resource translocation between connected ramets can be separated, and
‘experiments’ can be performed by changing only one trait (e.g. translocation)
while keeping other traits (e.g. architectural constraints) unchanged.
The model is used to address the following specific questions: (1) how do
resource translocation patterns affect morphology of a clonally growing plant?
(2) Does the effect of resource translocation change in environments of different productivity? (3) How does the effect of translocation interact with
architectural and growth rules of the plant? (4) how do the traits of resource
translocation affect the success of a clonal plant in competition?
Methods
The model
The model simulates growth of clonal plants on a continuous plane with
toroidal boundaries. (For a more detailed description of the model see the
Appendix A and Herben and Suzuki, 2001.) It works with a set of species, each
of which is allowed to have a different set of growth and architectural
parameters. Basic objects in the model are rhizomes (rhizome fragments) that
grow horizontally (Fig. 1), and ramets. The rhizome fragments are composed
of nodes and internodes. Ramets are the photosynthetically active plant parts
that are attached to (some) rhizome nodes; by definition, they are attached to
all growing terminal nodes. Ramets are of fixed sizes.
Rhizomes grow by adding nodes at terminal positions. When a new node is
added, the length and angle of growth of the internode are independent of the
internal state of the rhizome and of its neighbourhood. Two major architectural types of growth are modelled (Fig. 1): (i) Additional rhizome growth: At
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(a)
lateral ramet
terminal ramet
terminal growth
node
node death
adventive
branching
terminal
branching
(b)
Figure 1. Definition of some terms used in the model. The whole structure represents one rhizome
fragment composed of nodes, internodes and ramets. Dashed lines indicate rhizome segments
added in the last simulation step. (a) Plant with replacement rhizome growth type, (b) plant with
additional rhizome growth type.
each time step when a new node is added, the ramet attached to the mother
node stays attached to that node and a new ramet is formed at the daughter
node. The mother ramet thus becomes non-terminal; in this type of growth,
number of ramets increases as new nodes are added to the rhizome. This is the
type of growth found e.g. in Fragaria chiloensis (Alpert, 1995). (ii) Replacement
rhizome growth. In this type of growth, the ramet attached to the mother node
dies and a new ramet is formed at the youngest node; the ramet thus seemingly
‘moves’ to the new node. No ramet remains at the mother position; therefore
the overall number of ramets does not change as new nodes are added (except
for branching). This is a type of growth shown by many forest herbs (e.g.
Anemone nemorosa, Cowie et al., 1995) and many plants with monopodial
growth. These types are modelled separately and are not combined in one
plant.
Nodes may be added to a rhizome by terminal branching (i.e. by adding two
daughter terminal nodes to one terminal mother node at a single time step) and
by lateral (adventive) branching (i.e. by adding a daughter terminal node to a
non-terminal node). Branching angle and direction are independent of the
internal state of the rhizome and of its neighbourhood.
The oldest (basipetal) nodes of a rhizome die as a function of their age. If a
node bearing a branch dies, the branch becomes independent and the rhizome
fragments into two. Both branching and additional rhizome growth result in
new ramets being formed. In addition to this, non-terminal (adventive) ramets
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can also be formed at non-terminal nodes. All non-terminal ramets remain at
fixed positions at the nodes where they were formed.
Ramets produce ‘resource’ for rhizome growth. This resource may be anything that is limiting for the plants and whose accumulation is densitydependent, such as photosynthate. The rate of resource acquisition by a ramet
is determined by competition with neighbouring ramets; at each time step, the
number of ramets in the neighbourhood determines the amount of resource
(photosynthate) accumulated; the amount can be either positive or negative,
the latter being more likely to occur if the density of neighbours is high. The
resource is put into the node bearing the ramet. Resource level at each node
changes by an amount equal to resource acquisition by the ramet attached to
that node minus consumption for growth, and translocation to or from other
nodes. The resource that is not used or translocated is left at the node until the
next time step.
All growth processes (terminal growth of rhizome, rhizome branching, dormant bud activation to form an adventive branch or adventive ramet) can take
place only if the quantity of resource available at the current node exceeds a
given threshold which is one of the model parameters. Resource levels also
determine mortality of ramets and terminal nodes. If the amount of resource is
below the threshold, a new node is not added; if the the amount of resource is zero
or negative, the node loses the capacity for further growth, and dies. Ramets die if
the resource available to them (i.e. sum of the current photosynthesis, resource
left at the node bearing the ramet from the previous step and resource translocation from other nodes) becomes negative. In addition, non-terminal ramets
may be of fixed lifespan and may die after a specified number of steps. Cost of
internode formation was assumed to be zero; this does not qualitatively affect
behaviour of the model.
Translocation modelling
Translocation is modelled using the four parameters that are based on ecophysiological experiments in translocation (Alpert and Stuefer, 1997). Resource
translocation takes place at all nodes, no matter whether terminal or not, or
whether they bear a ramet or not. Translocation is driven by the resource
available at potential donor nodes. Each donor node searches for potential sinks
up to a specific distance, both basipetally and acropetally; all relevant branches
in the acropetal direction are considered for translocation. Branches in the
basipetal direction are not considered, as thus would involve combination of
basipetal (first) and acropetal (later) translocation (see Kemball and Marshall,
1995). Three different types of sinks are distinguished: (i) terminal ramet,
(ii) non-terminal ramet (no matter whether formed by additional rhizome
growth or adventive ramet formation), (iii) non-terminal node that does not bear
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a ramet (‘dormant bud’). Strengths of these sinks may differ according to the
model parameter values. A fraction of the resource at the donor node that is
available for translocation is divided between these sinks in proportion to the
strength of the sinks weighted by direction (acropetal and basipetal translocation may differ). If the translocation cost is non-zero, a fixed proportion of the
resource is lost at each node over which the resource is transported.
Model parameterisation
The model has 19 parameters in total (Table 1). The model was parameterised to
represent a clonally growing plant with ramets with little variation in size. The
simulation plane was assumed to represent an area sufficiently large to cover
reasonably large rhizome systems of this plant. To minimise arbitrariness in the
choice of parameter values, basic parameter values were selected to approximate
values from a stand of grass ramets in short-turf grassland in an area of
0.5 · 0.5 m in size. We used data on architectural and growth parameters from a
previously studied mountain grassland system [Table 1; see also Herben and
Suzuki (2001)].
Simulation experiments
In each set of simulation experiments, two different types of simulations were run.
First, a single-species system was established starting with 30 seedlings randomly
positioned in the simulation plane. No new plants were allowed to establish in
later steps. Simulations were run for 300 time steps; preliminary simulations
showed that this was long enough to attain stable values of the ramet number and
architectural parameters. After the 300 steps, data were collected on number of
ramets and nodes, branching rate (number of branches/number of nodes) and
spatial autocorrelation of ramet density. For spatial autocorrelation, ramet
densities were converted to a grid of 50 · 50 cells and Moran’s I was calculated
for lags 1, 2, 3, 4 and 5 cells (Upton and Fingleton, 1985). Since the neighbourhood size was 1/20th of the simulation plane in all runs (Table 1), a lag of 2 cells
corresponds to the aggregation at the same range as the neighbourhood size.
In the first set of simulation experiments [see (i) below], relative contribution
of individual parameters was assessed by means of ANOVA-type decomposition of total variance using sum of squares III. The contribution of each
parameter and all their pairwise interactions was expressed as the proportion of
total corrected sum of squares.
Second, the competitive ability of the plant with any specific parameter
combination was tested against a ‘phytometer’ plant, i.e. a plant with identical
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Table 1. Parameters of the model
Name
Units
Architectural
parameters
r
Distance
cv_r
1
sd_angle
Angle
branch_angle Angle
prop_primary 1
Base value
Other
values
tested
Definition
(see also Appendix A)
0.01
0.1
0.05
Mean internode length
Variation coefficient of the internode
length
Standard deviation of the angle of rhizome growth
Angle of rhizome growth when branching
Probability of formation of the additional
rhizome (instead of the replacement rhizome).
Probability of an adventive branch formation provided resource is sufficient
Lifespan of the node
Probability of an adventive ramet formation provided resource is sufficient
Lifespan of a lateral ramet
5
30
1 or 0
sleeping_bud
1/time
0.1
0.01
to_die
prob_lateral
time
1/time
0.1
0.01
lifespan
time
50
infinity
Resource and
competition
parameters
accum
Resource/ 3, 5, 7
time
beta
Area
0.2
neighb_size
fr_res_tip
Distance
1
Translocation
parameters
sharing_range Nodes
prop_shared 1
p_node
1
0.05
0.7 for
replacement
growth, 0.3
for additional
growth
0, 2, 5, 20
0.1, 0.5
0.5, 1, 2
p_tip
1
0.5, 1, 2
p_basipet
1
0.1, 0.5
cost_trans
1/node
0
A, productivity of the environment
0.3
b, strength of density dependence of a
species for resource accumulation
D, radius of the neighbourhood size
fg, fraction of the resource available to the
mother node that is put into the daughter
node at the moment of its formation
T, translocation range in one step
ftr , fraction of the resource translocated
Sink strength of a non-ramet bearing node
relative to a ramet-bearing non-terminal
node
Sink strength of a ramet-bearing terminal
node relative to a ramet-bearing nonterminal node
B, proportion of resource translocated
basipetally
0.01, 0.05, C, fraction of the resource that is lost
0.1, 0.2, 0.5 when translocated over one node
Distances are expressed as proportions of the simulation plane, time as time steps.
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parameter combination except for the parameter being tested. To do this, a
system starting with 30 seedlings of the phytometer plant was established and it
was run for 300 steps. Then 30 seedlings of the tested plant were added. No
new plants were allowed to establish in later steps. Ten realisations were run
for each parameter combination. After 200 further steps, numbers of ramets of
both species were counted; competitive ability of the tested plant was expressed
as the number of ramets it produced relative to the total number of ramets. A
separate set of simulations where the added species (invader) was identical to
the invaded species was used as a control.
Three sets of simulation experiments were run:
(i) To test the effect of translocation parameters, two basic architectural
models were used (Table 1), one with additional rhizome growth and the
other with replacement rhizome growth. In these plants, all architectural
parameters were varied in all possible combinations; the resulting plants
were grown under three resource levels (parameter accum). A non-translocating plant with all other parameters identical to the plant under test was
taken as the phytometer in the two-species experiments.
(ii) To test the interaction of translocation parameters with other parameters of plant architecture, three translocation patterns were chosen to represent the range of effects that the translocation parameters may have.
These plants were identified using the first set of experiments; branching rate
and Moran I over lag of one cell were taken as the guide; according to their
growth form, these plants are further called linear, medium and branched
type. The plants chosen had parameters of sharing_range, prop_shared,
p_node, p_tip and p_basipet (for explanation see Table 1) as follows: 20, 0.5,
1, 2, 0.5, (linear, additional rhizome); 2, 0.5, 1, 1, 0.1 (medium, additional
rhizome); 2, 0.5, 2, 1, 0.5, (branched, additional rhizome); and 20, 0.5, 0.5,
1, 0.5 (linear, replacement rhizome); 2, 0.5, 1, 1, 0.1 (medium, replacement
rhizome); 2, 0.5, 2, 1, 0.5 (branched, replacement rhizome). These six
selected plants were tested as to their response to change in the following
parameters: internode length, probability of adventive branch formation,
probability of adventive ramet formation, ramet lifespan, and strength of
density dependence (for the values used, see Table 1). Again, all these
experiments were done under three resource levels.
(iii) To test the effect of translocation cost, one pattern of translocation
was taken (translocation distance 5 nodes; proportion of resource translocated 0.5; proportion of basipetal translocation 0.5; all nodes are equal
sinks) and combined with several levels of translocation cost (0.01, 0.05, 0.1,
0.2, 0.5 of resource lost when transported over one node) and three resource
levels. A non-translocating plant with all other parameters identical was
taken as the phytometer in the two-species experiments.
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Results
Effects of translocation
Ramet density varied greatly as a function of translocation parameters. It
was generally higher in translocating plants and increased with the proportion of resource translocated (Fig. 2). This effect was stronger if the productivity of the environment was low (Fig. 2). In unproductive environments,
mean values per parameter combination after 300 steps ranged from 450
ramets to 690 ramets per simulation plane depending on translocation
parameters; the same figures for the productive environment were only 620 to
770. Introducing translocation to the model had much stronger effect on
number of ramets in the replacement rhizome type than in the additional
rhizome type (Table 2, Fig. 2).
Apart from the effect on the overall density of ramets, changing translocation patterns also produced very different clonal morphologies (Fig. 3). Plants
with different translocation parameters differed in branching rate (ratio of
branches to nodes), relative number of ramets (ratio of ramets to nodes), and in
patterns of spatial aggregation, expressed as autocorrelations at different lags
(for an example, see Fig. 4). The resulting plants ranged from clumped plants
with high branching rate and high spatial autocorrelation at small scales to
runners with rather little branching (Fig. 3).
Plant morphology was affected primarily by parameters governing amount
of resource translocated, spatial arrangement of sinks, and rhizome growth
type (additional or replacement). Parameters governing amount of resource
translocated (proportion of resource available for translocation) increased
number of branches, and therefore increased clumping at the small scale (data
not shown), in particular in plants with additional rhizome growth type.
Proportion of basipetal translocation reduced the whole plant size (number of
ramets, number of branches and number of nodes). In plants with replacement
rhizomes, most parameters had similar effects as in plants with additional
rhizome growth type; basipetal translocation had a different effect, slightly
increasing branching rate and number of ramets.
In general, spatial arrangement of resource sinks had smaller effects per se.
The strongest effect was shown by change of sink strength of the terminal
node; if increased, it increased total rhizome length and decreased number of
branches and clumping. The parameters of spatial arrangement of resource
sinks strongly interacted with both parameters governing amount of resource
translocated and rhizome growth type. In particular, total proportion of
resource translocated dramatically increased sensitivity to arrangement of
sinks (expressed as the standard deviation of number of ramets over all tested
sink arrangements; Fig. 5). This effect was much stronger when productivity
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Figure 2. Effect of proportion of the resource translocated on the number of ramets after 300 steps
under different productivity levels (arbitrary units). NT – control (non-translocating plant). All
different sink arranegements are pooled; bars indicate one standard deviation of the all simulation
with the given parameter combination. (a) Additional rhizome type, (b) replacement rhizome type.
was low (data not shown). Proportion of basipetal translocation had a nontrivial effect, lowering the sensitivity to sink arrangement if total translocated
resource was low, and increasing it when translocation was high. The sensitivity of other architectural parameters (number of branches, number of
nodes, and spatial autocorrelation) generally followed the same pattern (data
not shown).
Competitive ability (i.e. the ability to invade stands of otherwise identical nontranslocating plants) of almost all translocating plants was far better than that of
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Table 2. Effect of individual parameters and all their possible pairwise interactions on the number
of ramets
accum
sharing_range
prop_shared
p_basipet
p_node
p_tip
accum * p_basipet
accum * p_node
accum * prop_shared
accum * p_tip
accum * sharing_range
p_node * p_basipet
p_node * p_tip
prop_shared * p_basipet
prop_shared * p_node
prop_shared * p_tip
p_tip * p_basipet
sharing_range * p_basipet
sharing_range * p_node
sharing_range * prop_shared
sharing_range * p_tip
Additional
Replacement
0.590
0.007
0.017
0.037
0.028
0.001
0.030
0.013
0.012
0.001
0.001
0.006
0.000
0.016
0.003
0.001
0.009
0.001
0.010
0.000
0.005
0.394
0.001
0.170
0.003
0.190
0.079
0.002
0.008
0.034
0.003
0.001
0.000
0.002
0.000
0.020
0.010
0.000
0.022
0.004
0.003
0.002
Numbers are proportions of total variance in number of ramets due to individual effects. Nontranslocating plants are not included in the analysis.
non-translocating plants (Fig. 6). Competitive ability was affected by similar
parameters as plant growth and architecture, namely proportion of resource
translocated, proportion of basipetal translocation and sink arrangement. In
general, translocation had a much stronger effect on competitive ability of plants
with replacement rhizomes. The effect of translocation was also much stronger in
more productive environments. Plants with the additional rhizome growth in
non-productive environments were the only case where some translocating
plants were not better competitor than non-translocating plants.
Competitive ability and single stand parameters (density, clonal morphology,
spatial structure) were rather well correlated. As a result, it is possible to predict
competitive ability of a simulated plant from its equilibrium ramet density
(Table 3). There are two major patterns in this correlation. First, translocation
parameters that lead to an increase in number of ramets also increased competitive ability, indicating that overall density is the major trait responsible for
competitive success. This effect was much stronger in plants with replacement
rhizomes. Second, there was a strong link with spatial structure in single stands:
aggregation at the spatial lag of 2 cells strongly increased competitive ability.
This effect was also stronger in plants with replacement rhizomes (but it was
present in both types) and in more productive environments. In contrast,
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(a)
(b)
(c)
(d)
Figure 3. Examples of clonal morphologies due to different patterns of translocation of
otherwise identical plants (replacement rhizome type). Lines indicate rhizomes, diamonds are
ramets. Productivity level 7. (a) translocation range 2, proportion of resource translocated 0.5,
relative sink strength of a node 2, relative sink strength of a terminal ramet 1, basipetal
translocation 0.5, (b) translocation range 2, proportion of resource translocated 0.1, relative
sink strength of a node 2, relative sink strength of a terminal ramet 1, basipetal translocation
0.1, (c) translocation range 20, proportion of resource translocated 0.5, relative sink strength of
a node 0.5, relative sink strength of a terminal ramet 0.5, basipetal translocation 0.5, (d) a nontranslocating plant.
branching had a negative effect, particularly in plants with replacement rhizomes. As a result, it is possible to predict competitive ability of a simulated
plant from its equilibrium ramet density (Table 3).
Interaction of translocation with other plant parameters
The three distinct types remained rather distinct even when other growth or
architectural parameters changed. With one exception, ranking of the number
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Figure 4. Effect of proportion of the resource translocated on the branching rate (number of
branches/number of nodes) under different productivity levels (arbitrary units). NT – control (nontranslocating plant). All different sink arrangements are pooled. Boxes cover interquartile ranges,
whiskers cover outliers closer than 1.5 of the interquartile range. (a) Additional rhizome type, (b)
replacement rhizome type.
of ramets produced by the types tested remained unchanged when the growth
or architectural parameters changed (Fig. 7). The only case where the change
of parameter tested lead to a reversal of the ranking was an increase of
internode length to a value that equalled interaction range; the magnitude of
this effect increased with the habitat productivity. Internode length equal to
interaction range favoured plants with less basipetal translocation. Number
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Figure 5. Effect of distribution of sinks over the plant body on the number of ramets. The variable
plotted is standard deviation of the number of ramets when sink distribution is allowed to vary
while the translocation parameters shown are kept constant. All productivity levels and translocation ranges are combined. Bars indicate one standard deviation (over pooled productivity levels
and translocation ranges). (a) Additional rhizome type, (b) replacement rhizome type. Basipetal –
proportion of resource translocated basipetally.
of branches and competitive ability followed a similar pattern (data not
shown).
Translocation cost
Translocation cost was more important for plants with replacement growth
than for plants with additional growth (Fig. 8). Its effect was strongly
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Figure 6. Effect of proportion of resource translocated on the competitive ability of the translocating plant under different productivity levels (arbitrary units). Competitive ability is measured as
the proportion of the ramets of the translocating plant 200 steps after 30 single ramets were planted
into an established stand of an identical but non-translocating plant. NT – control (non-translocating plant). Means of 10 realizations. Bars indicate one standard deviation. (a) Additional rhizome type, (b) replacement rhizome type.
dependent on the productivity of the environment; the same cost had a
much stronger effect if the environment was less productive. In the competition experiment, a percentage cost of approximately 10–20% per node
roughly equalises competition against non-translocating plants. Effects on
number of ramets and branching rate were similar to those on competitive
ability.
Productivity
Productivity
Rhizome type
Rhizome type
Rhizome type
Productivity,
Rhizome type
0.836
0.748
0.768
0.889
0.758
0.835
0.736
0.835
0.891
0.934
0.890
0.843
R2
0.672
0.473
0.290
1.547
1.252
1.129
0.250
1.462
0.710
0.364
0.493
0.590
Ramets
0.073
)0.013
)0.110
)0.649
)0.387
)0.450
)0.147
)0.545
)0.218
)0.081
)0.112
)0.159
Branches
0.395
0.100
)0.454
)0.168
)0.301
)0298
0.013
)0.217
0.098
0.015
)0.271
0.002
Moran I, lag 1
0.101
0.698
0.437
0.280
0.511
0.501
0.254
0.349
0.130
0.204
0.403
0.157
Moran I,
lag 2
Values in the table are standardized regression coefficients from regression of competitive ability (proportion of ramets of the translocating plants, see the
Methods) on parameters of single-species stands (number of ramets, number of branches, and spatial autocorrelation over two different lags). Nontranslocating plants are not included. Moran I is calculated over lags of 1 and 2 cells (cell is 1/50 of the plot). Values greater than 0.2 (in absolute value) are
shown in bold.
Additional, Productivity 3
Additional, Productivity 5
Additional, Productivity 7
Replacement, Productivity 3
Replacement, Productivity 5
Replacement, Productivity 7
All additional
All replacement
All Productivity 3
All Productivity 5
All Productivity 7
All
Covariates
Table 3. Tests to indicate how competitive ability depends on parameters of clonal growth morphology of plants differing in translocation (the underlying
translocation parameters are not taken into account directly)
508
509
Discussion
Translocation parameters and growth form
The simulations show that change of translocation patterns can deeply affect
total ramet density and clonal growth morphology. However, translocation
between ramets is a rather complex phenomenon (Marshall, 1990); as many as
five different parameters are needed to describe (a rather simple version of) this
process. These parameters fall into two main classes: (i) parameters that determine quantities of the matter translocated (i.e. how much is translocated), and (ii)
topological parameters that determine spatial distribution of the sinks; the latter
parameters determine relative investment of the matter along the spacer system.
These two types of parameters interact with each other to determine ramet
density and plant morphology. Ramet density is generally higher in translocating plants and increases with the proportion of resource translocated; it is
not much affected by the spatial distribution of sinks. In contrast, spatial
distribution of sinks (namely role of acropetal component in translocation)
strongly affects plant morphology, especially branching rate and relative rhizome length.
As a result, both clumpers and runners can be generated using the same set
of architectural/developmental rules if different translocation rules are applied.
If most of the resource is translocated in acropetal direction, the resulting
plants will be runners with long linear structures and little branching; in contrast, if dormant buds along the older parts of the rhizome are the major sinks,
plants will be more clumped with a higher rate of branching and small scale
aggregation of ramets. Importantly, it is not a difference in magnitude of
translocation that underlies this difference; it is a result of relative importance
of individual sinks. Consequently, growth forms of clonal plants (guerrilla vs.
phalanx) might be explained also by the role of translocation and not only by
architectural elements of internode lengths and branching rates.
The effect of translocation on number of ramets and clonal architecture is
modified both by external and internal parameters. First, it interacts with basic
architectural rules that constrain growth of the simulated plants. The effect of
translocation is generally stronger in plants with replacement growth type, i.e.
those that maintain a living ramet only at the growing tip of the rhizome.
Ramet number and branching of these plants is obviously limited by the
number of growing tips; if some of the resource available is translocated
basipetally, dormant buds along the rhizome may become activated leading to
the general increase of branching rate and of number of ramets (Marshall and
Price, 1997). In plants with additional growth (i.e. those with a ramet producing a spacer remaining alive) the effect is much weaker; the obvious reason
is that these need not rely on resource production only by terminal ramets; in
510
Figure 7. Interaction of selected growth and architectural parameters on number of ramets of the
translocating plant under different productivity levels (arbitrary units: a – 3, b – 5, c – 7). Only
plants of replacement rhizome type shown. Branched, Medium, Non-branched are different set of
translocation parameters that produce plants of different growth types; Non-trans – non-translocating plants. Means of 10 realizations. Bars indicate one standard deviation. b – beta ¼ 0.3 (higher
competitive effect); d – to_die ¼ 30 (rhizome live shorter); l – lifespan ¼ 50 (ramets live shorter),
r – r ¼ 0.05 (longer internodia); s sleeping_bud and prob_lateral ¼ 0.01 (lower dormant bud activation), St – standard plants. For parameter definitions and standard values see Table 1.
contrast, these plants can support later activation of dormant buds and (proleptic) branching by resources that are produced by these ramets. Second, the
effect of translocation strongly depends on the productivity of the environment. Generally a higher proportion of translocation is needed in the
511
low-productivity environment to attain the same effect as a smaller proportion
of translocation generates in the highly productive environment. Productivity
of the environment also lowers the role of the topological parameters of
translocation.
Competitive ability
The simulation experiments show that if the translocation cost is low,
translocating plants are generally much better competitors than plants that
do not translocate. The difference becomes greater in more productive
environments (see e.g. Peltzer, 2002 for a field experiment with a similar
result). This seems to contrast with the results of Oborny and Cain (1997),
Oborny et al. (2000) which show that, in homogeneous environments, nontranslocating plants are as a rule better competitors. This is, however, due
to different formulation of both model types. In Oborny’s models the only
resource heterogeneity is generated externally by processes independent of
the presence of plant individuals. In contrast, there is no external heterogeneity in resource in the current model; any short-range heterogeneity in
the resource availability in the model is generated by neighbourhood competition between ramets. These heterogeneities provide advantage to translocating plants, which possess the ability to buffer heterogeneity by
supporting ramets and nodes at less favourable positions and, as a result,
allocate resources better.
The current study also confirms that there is a tight link between plant
traits in monoculture (Such as number of ramets, branching rate, spatial
aggregation etc.) and competitive ability. Number of ramets is always the
best predictor of competitive success (see also Chesson and Peterson, 2002),
but finer differences in the importance of individual plant traits depends on
the productivity of the environment and on the growth form of the plant.
First, the importance of number of ramets decreases with productivity. In
good environments the ability to arrange ramets spatially becomes more
important: in particular, clumpers with clumps of diameter comparable to
the size of the interaction neighbourhood have a great advantage. This
would support the notion that phalanx species are better competitors in
more productive environments whereas species capable of guerrilla-type
growth are better competitors in poor environments (Gough et al., 2001;
D’Hertefeldt and Falkengren-Grerup, 2002). Second, there are also differences according to the architectural rules. In particular, competitive success
of plants with replacement growth is much better predicted by the number
of ramets; this agrees well with the notion that these plants are strongly
limited by the ability to form ramets.
512
Figure 8. Effect of translocation cost on the competitive ability of the translocating plant under
different productivity levels (arbitrary units). It is measured as the proportion of the ramets of the
translocating plant 200 steps after 30 single ramets were planted into an established stand of an
identical but non-translocating plant. NT – control (non-translocating plant). Means of 10 realisations. Bars indicate one standard deviation. (a) Additional rhizome type, (b) replacement rhizome
type.
Translocation cost
All the effects described above are based on the assumption that translocation
costs can be neglected; in contrast, in real plants there will always be a cost. If
translocation is beneficial (as the models shows to be the case in most
parameter combinations), a trade-off will develop. The models shows that, at
513
moderate translocation costs, translocating plants do better, in spite of the fact
that there is an absolute resource loss due to the translocation cost. This seems
to be supported by experimental data in homogeneous conditions (van Kleunen et al., 2000; Peterson and Chesson, 2002). It also indicates that the spatial
separation of sources and sinks in a translocating system is just as important a
constraint for the growth of a clonal plant as the resource production itself. It
therefore may pay the plant to invest some resource into maintenance of
translocation even at the expense of the total energy available for growth.
Predictably, the proportion that can be lost as the translocation cost increases
with the productivity of environment.
Limitations of the model
The major strengths of such simulation models is in the possibility to examine
effects of individual traits by performing ‘experiments’ that change only one
trait. Effects of individual parameters (trait values) can thus to be separated
from each other in a way that can never be attained in an experiment.
One of the critical assumptions of this model is the assumption that developmental decisions are made based on the amount of resource that is available
at the living bud. The only causal relationship in the model is thus resource
available in the node -> developmental decision. While there is a hierarchy of
sinks (nodes/ramets/tips, depending on the particular parameter choice) in the
model, all sinks of the same type within this hierarchy (e.g. all tips within a
given distance and direction) are equivalent and they compete equally for the
resource available. In real plants, this need not be true, as developmental
decisions may depend on other factors as well. If a node makes a developmental decision to grow, it will become a stronger sink than other, seemingly
equivalent, nodes (Novoplansky pers. comm.) and sink strength will differ even
between sinks of one type. This feedback effect may be an important element in
the economy of the resource by reducing investment of resource into many
sinks at the same time.
Second, the model works in space that is perfectly homogeneous, i.e. the
ramet distribution in space is the source of heterogeneity. Obviously, this is not
always true; many plants are exposed to environments where the source of
heterogeneity is indeed independent of the plants. The translocation patterns
that are favoured by these conditions may be different from those favoured by
competitive interactions in temporally and spatially homogeneous conditions.
Preliminary experiments show that the basic patterns are robust even if
external heterogeneity is added (unpubl. data), but examination of interaction
between external heterogeneity (see e.g. Oborny et al., 2000) and feedbacks due
to ramet distribution in space is an exciting field of research that should be
pursued in future, both by modelling and experiments.
514
Implications
The simulations show that translocation between ramets can have non-trivial
effects at the stand level. Translocation can affect growth form and/or competitive ability; some predictions about these effects can be tested by experimental or observational data. Among these are: (i) Patterns of translocation
should be different between clumpers and runners: while acropetal translocation should prevail in runners, dormant buds (even those positioned basipetally) should be more important sinks in clumpers. (ii) Advantage in
competition associated with translocation should increase with environmental
productivity. (iii) In un-productive environments, plants should be more
selected for specific translocation patterns. There are hardly any data that
would permit testing such hypotheses; collecting such data is much desirable
and may help predictive analysis of differentiation of clonal plants into these
growth forms.
The necessary empirical data on translocation patterns could be provided by
experimental manipulation of translocation and checking resulting morphology of the plant. However, experimental manipulation of translocation is
difficult and no fully satisfactory approach to it is available (Gough et al.,
2001). Another possible approach may be to collect data on translocation
patterns over a variety of environments and species (see e.g. Pennings and
Callaway, 2000). However, data on amounts of resource translocated and on
translocation patterns are only available for a few plants, and cannot be
compared over different productivity levels or growth forms. Further, a lot of
these data concern only short-term translocation intensities which are not easy
to scale up to long-term differences. Still the available data are rather in
agreement that low productivity environments favour integration (Jónsdóttir
and Watson, 1997), but the link to competition is less clear (Gough et al.,
2001). Clonal integration has been invoked not only in low-productivity/low
competition environments, but also for competitors in high productivity
environments (consolidation strategy of de Kroon and Schieving, 1990, see also
Peltzer, 2002).
The model shows almost invariably a strong positive effect of translocation
on plant fitness (particularly in replacement rhizome plants). While there are
systems where large-range translocation is rather a rule (Jónsdóttir and Watson, 1997), in many clonal plants its effects are rather restricted (Kemball and
Marshall, 1994). Many clonal plants fragment early, thus discarding the connections that the model predicts to be potentially beneficial. This clearly shows
that in the field there must be important forces that counteract the effect of
integration, such as translocation cost or other possible interactions such as
parasite or disease spread. In spite of decades of research on physiological
integration, its importance is yet to be fully evaluated.
515
Acknowledgements
The model was developed in collaboration with Jun-ichirou Suzuki and
Toshihiko Hara while I was staying at the Institute of Low Temperature Science, Hokkaido University, Sapporo. Most of data were analysed and the draft
paper was written while I was staying with Beáta Oborny at the Santa Fe
Institute, New Mexico. Support of both institutions is gratefully acknowledged. I thank Deborah Goldberg, Beáta Oborny, Jun-ichirou Suzuki and
Radka Wildová for many discussions of plant clonality (including translocation) and of the model. Jan Wild drew the maps of rhizome structures. The
research was also partly funded by the GAČR grant no 206/02/0953 and
MŠMT programme KONTAKT.
Appendix A. Main structural assumptions and formulae used in the model
Resource accumulation
In all nodes with ramets present, the resource is accumulated at individual nodes following this
formula:
Rtþ1 ¼ Rt þ A ð1 b NÞ=ð1 þ b NÞ;
ðA:1Þ
where Rt is the resource status of the node at time t, A is the productivity of the environment
(resource accumulaztion rate), b is the density-dependence constant of resource accumulation for
that species and N is the number of all ramets within a specified circular neighbourhood of that
ramet.
Resource translocation
If a plant is able to translocate, then translocation takes place at all nodes, no matter whether
terminal or not, or whether they bear a ramet or not. Translocation is driven by the resource
available at potential donor nodes and by distribution of sinks in the nearby nodes. Each donor
node searches for potential sinks up to the distance given by the parameter T (sharing_range),
both basipetally and acropetally; all relevant branches in the acropetal direction are also
scanned. Branches in the basipetal direction are not scanned, as thus would involve combination of basipetal (first) and acropetal (later) translocation. At each time step, each (donor) node
j evaluates the following quantity:
Uj ¼ RDi Bi ;
dði; jÞ<T
ðA:2Þ
where d(i,j) is the distance of nodes i and j along the rhizome in acropetal or basipetal
direction, measured in nodes, T is the translocation distance in nodes (identical both acropetally
and basipetally), Di is the weight determining the sink strength of the ith node (1 for nonterminal nodes bearing a ramet, p_tip for terminal nodes bearing a ramet, and p_node for
non-terminal nodes not bearing a ramet) and Bi is the relative weight of basipetal vs. acropetal
transport (p_basipet if the ith node is positioned basipetally relative to the donor node and
1 – p_basipet otherwise).
At the next stage, each (acceptor, i) node up to the distance T nodes from the donor node gets
from the donor (j) node the following amount of resource
516
Radded ði; jÞ ¼ ð1 CÞdði;jÞ Di Bi ftr = Uj ;
ðA:3Þ
where Rj is the resource level of the donor ramet, ftr is the proportion of the resource that is
available for translocation, C is the cost of translocation (the fraction of the resource that is
lost when resource is translocated over one node), d(i,j) is the number of internodes between
nodes i and j and T is the translocation distance (number of nodes over which translocation
takes place in one step). For each acceptor node, Radded is summed over all potential donor
nodes; the resulting amount of resource is added to Ravail, i.e. the resource used to make
decisions on growth and branching. Each donor node involved in translocation has its resource
diminished to Rj ð1 ftr Þ; the difference between this quantity and the quantity brought to the
sink node is due to translocation cost. Each node serves both as acceptor and donor. As the
result, Ravail is given by
Ravail ðiÞ ¼ Ri ð1 ftr Þ þ RRadded ði; jÞ
dði:; jÞ < T:
ðA:4Þ
If Uj ¼ 0 (i.e. no acceptor nodes are within the translocation distance), no translocation takes
place and all resource is kept at the donor node (Ravail (i) ¼ Ri). Translocation always takes
place, no matter whether the node involved happens to have sufficient resource for growth or
branching or not. For T ¼ 0 or ftr ¼ 0, the model defaults to a resource-limited architectural
model without translocation.
A terminal node forms a new node always when it has sufficient resource for the daughter node, i.e.
the following condition is met:
Ravail > Rmin = fg ;
ðA:5Þ
where Ravail is the value defined by Equation (A.4), fg is the proportion of resource put into the new
ramet at the growing tip, Rmin is the minimum resource required for ramet formation (ramet cost).
When a new node is added, it is formed at a distance from the current terminal node drawn from
the Gaussian distribution with mean and standard deviation given by the values from the Table 1.
The angle of the newly formed internode with the previous internode is drawn from the Gaussian
distribution with mean zero and a given standard deviation.
The initial ramet resource is consequently
Rt ¼ Ravail fg ;
ðA:6Þ
where Ravail is the value defined by Equation (A.4), and fg is the proportion of resource put into the
new ramet at the growing tip. This is identical also for branching.
A node forms a lateral branch (after the new terminal node has been formed; the branch is consequently attached to the second youngest node and is thus of the same plastochron age as the tip) with
the specified probability (probability of terminal branching) if the following conditions are met
Ravail0 > Rmin =fg ;
ðA:7Þ
where Ravail¢ is the value defined by Equation (A.4) reduced by the cost of producing the terminal
ramet and the internode, Rmin is the minimum resource required for ramet formation, and fg is the
proportion of resource put into the new ramet at the growing tip.
A non-terminal (adventive) ramet (i.e. a ramet attached to a non-terminal node) is formed with a
specified probability (parameter probability of non-terminal ramet formation) if the following condition is met:
Ravail > Rmin
ð1 k b NÞ > 0;
ðA:8Þ
where Ravail is defined by Equation (A.4), Rmin is the resource required to produce a ramet, b is the
density-dependence constant of resource accumulation for that species, k is a positive constant and N
is the number of all ramets in the neighbourhood of that ramet. The second part of the condition
517
assures that ramet is formed only when it is likely to have a positive photosynthetic balance (i.e. when
N 1/b).
A ramet dies if its resource calculated by Equation (A.1) is ( zero. The same process applies to
non-terminal and terminal ramets. A node at the basipetal position dies if its age (i.e. current time
step time minus step of its formation) exceeds a specified constant (Node Lifespan).
An adventive branch (i.e. an internode with a node with a terminal ramet attached) is formed
by activation of a dormant bud with a specified probability (dormant bud activation probability)
if the following conditions are met:
Ravail > Rmin =fg ;
ðA:9Þ
where Ravail is defined by Equation (A.3), Rmin is the resource required to produce a ramet, and fg is
the proportion of resource put into the new ramet at the growing tip.
The processes are simulated in the following order: (1) terminal internode growth (including
associated translocation), (2) branching, (3) adventive ramet formation and adventive branching,
(4) ramet mortality, (5) resource production, (6) translocation. Along the rhizome, nodes are always
evaluated in basipetal direction (i.e. starting with the youngest node).
References
Adachi, N., Terashima, I. and Takahashi, M. (1996) Mechanisms of central die-back of Reynoutria
japonica in the volcanic desert on Mt. Fuji. A stochastic model analysis of rhizome growth.
Annals Bot. 78, 169–179.
Alpert, P. (1995) Does clonal growth increase plant performance in natural communities? Abstr.
Bot. (Budapest) 19, 11–16.
Alpert, P. and Stuefer, J. (1997) Division of labour in clonal plants. In H. de Kroon and van J.
Groenendael (eds.), The Ecology and Evolution of Clonal Plants. Backhuys Publishers, Leiden,
pp. 137–155.
Bascompte, J. and Solé, R.V. (eds.) (1997) Modeling Spatiotemporal Dynamics in Ecology. Springer,
Berlin.
Bell, A.D. (1984) Dynamic morphology: a contribution to plant population ecology. In R. Dirzo
and J..Sarukhán, (eds.), Perspectives in Plant Population Ecology. Sinauer, Sunderland, pp.
48–65.
Bell, A.D. (1986) The simulation of branching patterns in modular organisms. Phil. Trans. Roy.
Soc. London 313B, 143–159.
Birch, C.P.D. and Hutchings, M.J. (1994) Exploitation of patchily distributed soil resource by the
clonal herb Glechoma hederacea. J. Ecol. 82, 653–664.
Cain, M.L., Pacala, S.W., Silander, J.A. and Fortin, M.J. (1995) Neighborhood models of clonal
growth in the white clover Trifolium repens. Am. Natur. 145, 888–917.
Caldwell, M.M. and Pearcy, R.W. (1994) Exploitation of Environmental Heterogeneity in Plants:
Ecophysiological Processes above- and belowground. Academic Press, San Diego.
Caraco, T. and Kelly, C.K. (1991) On the adaptive value of physiological integration in clonal
plants. Ecology 72, 81–93.
Chesson, P. and Peterson, A.G. (2002) The quantitative assessment of the benefits of physiological
integration in clonal plants. Evol. Ecol. Res. 4, 1153–1176.
Cowie, N.R., Watkinson, A.R. and Sutherland, W.J. (1995) Modelling the growth dynamics of the
clonal herb Anemone nemorosa L. in an ancient coppice wood. Abstr. Bot. (Budapest) 19, 35–49.
de Kroon, H., Fransen, B., van Rheenen, J.W.A., van Dijk, A. and Kreulen, R. (1996) High levels
of inter-ramet water translocation in two rhizomatous Carex species, as quantified by deuterium
labelling. Oecologia 106, 73–84.
de Kroon, H. and Schieving, F. (1990) Resource partitioning in relation to glonal growth strategy.
In J. van Groenendael and H. de Kroon (eds.), Clonal growth in plants: regulation and function.
SPB Academic Publishing, The Hague, pp. 113–130.
518
de Kroon, H., Stuefer, J.F., Dong, M. and During, H.J. (1994) On plastic and non-plastic variation
in clonal morphology and its ecological significance. Folia Geobot. Phytotax. 29, 123–138.
D’Hertefeldt, T. and Falkengren-Grerup, U. (2002) Extensive physiological integration in Carex
arenaria and Carex disticha in relation to potassium and water availability. New Phytologist 156,
469–477.
D’Hertefeldt, T. and Jonsdottir, I.S. (1999) Extensive physiological integration in intact clonal
systems of Carex arenaria. J. Ecol. 87, 258–264.
Dieckmann, U., Law, R. and Metz, J.H.J. (eds.) (2000) The Geometry of Ecological Interactions:
Simplifying Spatial Complexity. Cambridge University Press, Cambridge.
Eriksson, O. (1993) Dynamics of genets in clonal plants. Trends Ecol. Evol. 8, 313–316.
Eriksson, O. and Jerling, L. (1990) Hierarchical selection and risk spreading in clonal plants. In
J. van Groenendael and H. de Kroon (eds) Clonal Growth in Plants: Regulation and Function.
SPB Academic Publishing, The Hague, pp. 79–94.
Fahrig, L., Coffin, D.P., Lauenroth, W.K. and Shugart, H.H. (1994) The advantage of long distance spreading in highly disturbed habitats. Evol. Ecol. 8, 172–187.
Farley, R.A. and Fitter, A.H. (1999) Temporal and spatial variation in soil resources in a deciduous
woodland. J. Ecol. 87, 688–696.
Geber, M.A., de Kroon, H. and Watson, M. (1997) Organ preformation in mayapple as a
mechanism for historical effects on demography. J. Ecol. 85, 211–224.
Gough, L., Goldberg, D.E., Hershock, C., Pauliukonis, N. and Petru, M. (2001) Investigating the
community consequences of competition among clonal plants. Evol. Ecol. 15, 547–563.
Hara, T. and Herben, T. (1997) Shoot growth dynamics and size-dependent shoot fate of a clonal
plant, Festuca rubra, in a mountain grassland. Res. Popul. Ecol. 39, 83–93.
Herben, T. and Suzuki, J. (2001) A simulation study of the effects of architectural constraints and
resource translocation on population structure and competition in clonal plants. Evol. Ecol. 15,
403–423
Herben, T., Krahulec, F., Hadincová, V., Kovářová, M. and Skálová, H. (1993) Tiller demography
of Festuca rubra in a mountain grassland: seasonal development, life span, and flowering. Preslia
65, 341–353.
Huber, H., Lukács, S. and Watson, M.A. (1999) Spatial structure of stoloniferous herbs: an interplay between structural blue-print, ontogeny and phenotypic plasticity. Plant Ecol. 141, 107–115.
Hutchings, M.J. and de Kroon, H. (1994) Foraging in plants: the role of morphological plasticity in
resource acquisition. Adv. Ecol. Res. 25, 159–238.
Hutchings, M.J., Wijesinghe, D.K. and John, E.A. (2000) The effects on heterogeneous nutrient
supply on plant performance: a survey of responses, with special reference to clonal herbs. In
M.J. Hutchings, E.A. John, and A.J.A. Stewart (eds) The Ecological Consequences of Environmental Heterogeneity. Blackwell Science Ltd., Oxford, pp. 91–110.
Jónsdóttir, I.S and Watson, M.A. (1997) Extensive physiological integration: an adaptive trait in
resource-poor environments. In H. de Kroon and J. van Groenendael (eds) The Ecology and
Evolution of Clonal Plants. Backhuys Publishers, Leiden, pp. 109–136.
Keddy, P.A. (1990) Competitive hierarchies and centrifugal organization of plant communities. In
J.B. Grace and D. Tilman (eds). Perspectives on Plant Competition. Academic Press, San Diego,
pp. 265–290.
Kemball, W.D. and Marshall, C. (1994) The significance of nodal rooting in Trifolium repens L. - P32 distribution and local growth-responses. New Phytol. 127, 83–91.
Kemball, W.D. and Marshall, C. (1995) Clonal integration between parent and branch stolons in
white clover – a developmental-study. New Phytol. 129, 513–521.
Klimeš, L. (1992) The clone architecture of Rumex alpinus (Polygonaceae) Oikos 63, 402–409.
Klimeš, L. (2000) Phragmites australis at an extreme altitude: rhizome architecture and its modelling. Folia Geobot. 35, 403–417.
Klimeš, L. and Klimešová, J. (1999) Root sprouting in Rumex acetosella under different nutrient
levels. Plant Ecol. 141, 33–39.
Law, R. and Dieckmann, U. (2000) A dynamical system for neighborhoods in plant communities.
Ecology 81, 2137–2148
519
Marshall, C. (1990) Source-sink relationships of interconnected ramets. In J. van Groenendael and
H. de Kroon (eds). Clonal Growth in Plants: Regulation and Function. SPB Acad. Publ., The
Hague, pp. 23–42.
Marshall, C. and Price, E.A.C. (1997) Sectoriality and its implications for physiological integration.
In H. de Kroon and van J. Groenendael (eds) The Ecology and Evolution of Clonal Plants.
Backhuys Publishers, Leiden, pp. 79–107.
Mogie, M. and Hutchings, M.J. (1990) Phylogeny, ontogeny, and clonal growth in clonal plants. In
J. van Groenendael and H. de Kroon (eds). Clonal Growth in Plants: Regulation and Function.
SPB Acad. Publ., The Hague, pp. 3–22.
Newton, P.C.D. and Hay, M.J.M. (1995) Non-viability of axillary buds as a possible constraint on
effective foraging of Trifolium repens L. Abstr. Bot. (Budapest) 19, 83–88.
Oborny, B. (1994a). Growth rules in clonal plants and predictability of the environment: a simulation study. J. Ecol. 82, 341–351.
Oborny, B. (1994b). Spacer length in clonal plants and the efficiency of resource capture in heterogeneous environments: a Monte Carlo simulation. Folia Geobot. Phytotax. 29, 139–158.
Oborny, B. and Bartha, S. (1995) Clonality in plant communities – an overview. Abstr. Bot.
(Budapest) 19, 115–127.
Oborny, B. and Cain, M.L. (1997) Models of spatial spread and foraging in clonal plants. In H. de
Kroon and van J. Groenendael, (eds) The Ecology and Evolution of Clonal Plants. Backhuys
Publishers, Leiden, pp. 155–183.
Oborny, B., Kun, Á., Czárán, T. and Bokros, S. (2000) The effect of clonal integration on plant
competition for mosaic habitat space. Ecology 81, 3291–3304.
Pacala, S.W. and Silander, J.A. (1990) Field tests of neighborhood population dynamic models of
two annual weed species. Ecol. Monogr. 60, 113–134.
Pecháčková, S., During, H.J., Rydlová, V. and Herben, T. (1999) Species-specific spatial pattern of
below-ground plant parts in a montane grassland community. J. Ecol. 87, 569–582.
Peltzer, D.A. (2002) Does clonal integration improve competitive ability? A test using aspen
(Populus tremuloides [Salicaceae]) invasion into prairie. Am. J. Bot. 89, 494–499.
Pennings, S.C. and Callaway, R.M. (2000) The advantages of clonal integration under different
ecological conditions: A community-wide test. Ecology 81, 709–716
Peterson, A.G. and Chesson, P. (2002) Short-term fitness benefits of physiological integration in the
clonal herb Hydrocotyle peduncularis. Austral Ecol. 27, 647–657
Piqueras, J., Klimeš, L. and Redbo-Torstensson, P. (1999) Modelling the morphological response
to nutrient availability in the clonal plant Trientalis europaea L. Plant Ecol. 141, 117–127.
Robinson D., Linehan D.J. and Gordon, D.C. (1994) Capture of nitrate from soil by wheat in
relation to root length, nitrogen inflow and availability. New Phytol. 128, 297–305.
Silander, J.A. and Pacala, S.W. (1990) The application of plant population dynamics models to
understanding plant competition. In J.B. Grace and D. Tilman (eds) Perspectives on Plant
Competition. Academic Press, San Diego, pp. 67–92.
Stuefer, J.F., de Kroon, H. and During, H.J. (1996) Exploitation of environmental heterogeneity by
spatial division of labour in clonal plants. Funct. Ecol. 10, 328–334.
Suzuki, J. and Hutchings, M.J. (1997) Interactions between shoots in clonal plants and the effects of
stored resources on the structure of shoot populations. In H. de Kroon and J. van Groenendael
(eds). The Ecology and Evolution of Clonal Plants. Backhuys Publishers, Leiden, pp. 311–330.
Suzuki, J., Herben, T., Krahulec, F. and Hara, T. (1999) Size and spatial pattern of Festuca rubra
genets in a mountain grassland: its relevance to genet establishment and dynamics. J. Ecol. 87,
942–953.
Tilman, D. and Kareiva, P. (eds) (1996) Spatial Ecology. Monographs in population biology 30,
Princeton University Press, Princeton.
Upton, G.J.G. and Fingleton, B. (1985) Spatial Data Analysis by Example. Vol. I. Point Pattern and
Quantitative Data. Wiley and Sons, Chichester.
Van Kleunen, M., Fischer, M., Schmid, B. and van Kleunen, M. (2000) Clonal integration in
Ranunculus reptans: by-product or adaptation? J. Evol. Biol. 13, 237–248
520
Watson, M.A., Hay, M.J.M. and Newton, P.C.D. (1997) Developmental phenology and the timing
of determination of shoot bud fates: ways in which the developmental program modulates fitness
in clonal plants. In H. de Kroon and J. van Groenendael (eds). The Ecology and Evolution of
Clonal Plants. Backhuys Publishers, Leiden, pp. 31–53.
Wijesinghe, D.K. and Hutchings, M.J. (1997) The effect of spatial scale of environmental heterogeneity on the growth of a clonal plant: an experimental study with Glechoma hederacea. J. Ecol.
85, 17–29.
Wilhalm, T. (1995) A comparative study of clonal fragmentation in tussock-forming grasses. Abstr.
Bot. (Budapest) 19, 51–60.
Wilson, J.B. (1995) Testing for community structure: a Bayesian approach. Folia Geobot. Phytotax.
30, 461–469.
Winkler, E. and Schmid, B. (1995) Clonal strategies of herbaceous plant species: a simulation study
on population growth and competition. Abstr. Bot. (Budapest) 19, 17–28.