Research article
Physiological integration affects growth form
and competitive ability in clonal plants
TOMA´Sˇ HERBEN
Institute of Botany, Academy of Sciences of the Czech Republic, CZ-252 43 Pr _uhonice, Czech Republic; Department of Botany, Faculty of Science, Charles University, Praha, Czech Republic (E-mail: herben@site.cas.cz)
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
support plant parts located in resource-poor patches (Birch and Hutchings, 1994; Stuefer et al., 1996; Wijesinghe and Hutchings, 1997; Alpert and Stuefer, 1997; Jo´nsdo´ttir 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 (Car-aco 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 heteroge-neity (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 het-erogeneous. 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, mor-phology and growth of a clonal fragment is determined by interactions between ramets arranged in space based on these rules (Bell, 1986; Klimesˇ, 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.
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) transloca-tion 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 dif-ferent 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 architec-tural types of growth are modelled (Fig. 1): (i) Additional rhizome growth: At
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
adventive branching terminal branching terminal growth node death terminal ramet lateral ramet node (a) (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.
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 any-thing that is limiting for the plants and whose accumulation is density-dependent, 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, dor-mant 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 translo-cation 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 eco-physiological 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
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 transloca-tion may differ). If the translocatransloca-tion cost is non-zero, a fixed proportransloca-tion 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 neighbour-hood 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 decomposi-tion of total variance using sum of squares III. The contribudecomposi-tion 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
Table 1. Parameters of the model
Name Units Base value Other
values tested
Definition
(see also Appendix A)
Architectural parameters
r Distance 0.01 0.05 Mean internode length
cv_r 1 0.1 Variation coefficient of the internode
length
sd_angle Angle 5 Standard deviation of the angle of
rhi-zome growth
branch_angle Angle 30 Angle of rhizome growth when branching
prop_primary 1 1 or 0 Probability of formation of the additional
rhizome (instead of the replacement rhi-zome).
sleeping_bud 1/time 0.1 0.01 Probability of an adventive branch
for-mation provided resource is sufficient
to_die time Lifespan of the node
prob_lateral 1/time 0.1 0.01 Probability of an adventive ramet
forma-tion provided resource is sufficient
lifespan time 50 infinity Lifespan of a lateral ramet
Resource and competition parameters
accum Resource/
time
3, 5, 7 A,productivity of the environment
beta Area 0.2 0.3 b, strength of density dependence of a
species for resource accumulation
neighb_size Distance 0.05 D, radius of the neighbourhood size
fr_res_tip 1 0.7 for
replacement growth, 0.3 for additional growth
fg,fraction of the resource available to the
mother node that is put into the daughter node at the moment of its formation
Translocation parameters
sharing_range Nodes 0, 2, 5, 20 T,translocation range in one step
prop_shared 1 0.1, 0.5 ftr,fraction of the resource translocated
p_node 1 0.5, 1, 2 Sink strength of a non-ramet bearing node
relative to a ramet-bearing non-terminal node
p_tip 1 0.5, 1, 2 Sink strength of a ramet-bearing terminal
node relative to a ramet-bearing non-terminal node
p_basipet 1 0.1, 0.5 B, proportion of resource translocated
basipetally
cost_trans 1/node 0 0.01, 0.05,
0.1, 0.2, 0.5
C, fraction of the resource that is lost when translocated over one node Distances are expressed as proportions of the simulation plane, time as time steps.
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-translo-cating 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 parame-ters of plant architecture, three translocation patterns were chosen to rep-resent 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 translo-cated 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.
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 propor-tion of resource translocated (Fig. 2). This effect was stronger if the pro-ductivity 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 transloca-tion 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
was low (data not shown). Proportion of basipetal translocation had a non-trivial effect, lowering the sensitivity to sink arrangement if total translocated resource was low, and increasing it when translocation was high. The sen-sitivity 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 non-translocating plants) of almost all non-translocating plants was far better than that of
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.
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 com-petitive 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,
Table 2. Effect of individual parameters and all their possible pairwise interactions on the number of ramets Additional Replacement accum 0.590 0.394 sharing_range 0.007 0.001 prop_shared 0.017 0.170 p_basipet 0.037 0.003 p_node 0.028 0.190 p_tip 0.001 0.079 accum * p_basipet 0.030 0.002 accum * p_node 0.013 0.008 accum * prop_shared 0.012 0.034 accum * p_tip 0.001 0.003 accum * sharing_range 0.001 0.001 p_node * p_basipet 0.006 0.000 p_node * p_tip 0.000 0.002 prop_shared * p_basipet 0.016 0.000 prop_shared * p_node 0.003 0.020 prop_shared * p_tip 0.001 0.010 p_tip * p_basipet 0.009 0.000 sharing_range * p_basipet 0.001 0.022 sharing_range * p_node 0.010 0.004 sharing_range * prop_shared 0.000 0.003 sharing_range * p_tip 0.005 0.002
Numbers are proportions of total variance in number of ramets due to individual effects. Non-translocating plants are not included in the analysis.
branching had a negative effect, particularly in plants with replacement rhi-zomes. 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
(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 non-translocating plant.
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
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 (non-translocating 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 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
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 translo-cation 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.
dependent on the productivity of the environment; the same cost had a much stronger effect if the environment was less productive. In the com-petition 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.
Figure 6. Effect of proportion of resource translocated on the competitive ability of the translo-cating 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-translo-cating plant). Means of 10 realizations. Bars indicate one standard deviation. (a) Additional rhi-zome type, (b) replacement rhirhi-zome type.
Table 3. Test s to indicate how competit ive ability depe nds on param eter s of clo nal growth morp hology of plant s diffe ring in trans location (the unde rlying trans location param eters are not taken into accoun t directly) C ovariate s R 2 Ram ets Branche s Mora n I, lag 1 Moran I, lag 2 Additio nal, Produc tivity 3 0.836 0.672 0.073 0.395 0.101 Additio nal, Produc tivity 5 0.748 0.473 ) 0.013 0.100 0.698 Additio nal, Produc tivity 7 0.768 0.290 ) 0.110 ) 0.454 0.437 Replac ement , Produc tivity 3 0.889 1.547 ) 0.649 ) 0.168 0.280 Replac ement , Produc tivity 5 0.758 1.252 ) 0.387 ) 0.301 0.511 Replac ement , Produc tivity 7 0.835 1.129 ) 0.450 ) 0298 0.501 All addit ional Pr oductivit y 0.736 0.250 ) 0.147 0.013 0.254 All replac emen t Pr oductivit y 0.835 1.462 ) 0.545 ) 0.217 0.349 All Prod uctivity 3 Rhi zome type 0.891 0.710 ) 0.218 0.098 0.130 All Prod uctivity 5 Rhi zome type 0.934 0.364 ) 0.081 0.015 0.204 All Prod uctivity 7 Rhi zome type 0.890 0.493 ) 0.112 ) 0.271 0.403 All Pr oductivit y, Rhi zome type 0.843 0.590 ) 0.159 0.002 0.157 Valu es in the table are standar dized regression co efficients fr om regr ession of competit ive abil ity (proportio n of ram ets of the transloc ating plant s, see the Meth ods) on par ameters of sing le-spec ies stand s (nu mber of ram ets, numbe r of bra nches, and spa tial autocorre lation over two diffe rent lags). Non-trans locating plant s are not included. Mora n I is calculated over lags of 1 and 2 cells (cell is 1/50 of the plot ). Valu es great er than 0.2 (in absolu te va lue) are shown in bold.
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 deter-mine 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 translo-cating 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 rhi-zome 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 con-trast, 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 pro-ducing 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
contrast, these plants can support later activation of dormant buds and (pro-leptic) branching by resources that are produced by these ramets. Second, the effect of translocation strongly depends on the productivity of the environ-ment. Generally a higher proportion of translocation is needed in the
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-translo-cating plants. Means of 10 realizations. Bars indicate one standard deviation. b – beta¼ 0.3 (higher
competitive effect); d – to_die¼ 30 (rhizome live shorter); l – lifespan ¼ 50 (ramets live shorter),
r – r¼ 0.05 (longer internodia); s sleeping_bud and prob_lateral ¼ 0.01 (lower dormant bud
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, non-translocating 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 hetero-geneity in resource in the current model; any short-range heterohetero-geneity in the resource availability in the model is generated by neighbourhood com-petition between ramets. These heterogeneities provide advantage to trans-locating 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 differ-ences 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.
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
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 reali-sations. Bars indicate one standard deviation. (a) Additional rhizome type, (b) replacement rhizome type.
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 Kle-unen 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 devel-opmental 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 develop-mental 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.
Implications
The simulations show that translocation between ramets can have non-trivial effects at the stand level. Translocation can affect growth form and/or com-petitive ability; some predictions about these effects can be tested by experi-mental or observational data. Among these are: (i) Patterns of translocation should be different between clumpers and runners: while acropetal transloca-tion should prevail in runners, dormant buds (even those positransloca-tioned basipe-tally) 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 morphol-ogy 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 (Jo´nsdo´ttir 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 (Jo´nsdo´ttir and Wat-son, 1997), in many clonal plants its effects are rather restricted (Kemball and Marshall, 1994). Many clonal plants fragment early, thus discarding the con-nections 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.
Acknowledgements
The model was developed in collaboration with Jun-ichirou Suzuki and Toshihiko Hara while I was staying at the Institute of Low Temperature Sci-ence, Hokkaido University, Sapporo. Most of data were analysed and the draft paper was written while I was staying with Bea´ta Oborny at the Santa Fe Institute, New Mexico. Support of both institutions is gratefully acknowl-edged. I thank Deborah Goldberg, Bea´ta Oborny, Jun-ichirou Suzuki and Radka Wildova´ for many discussions of plant clonality (including transloca-tion) and of the model. Jan Wild drew the maps of rhizome structures. The research was also partly funded by the GACˇR grant no 206/02/0953 and MSˇMT 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 Rtþ A ð1 b NÞ=ð1 þ b NÞ; ðA:1Þ
where Rtis 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 combina-tion of basipetal (first) and acropetal (later) translocacombina-tion. At each time step, each (donor) node
j evaluates the following quantity:
Uj¼ 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
non-terminal nodes bearing a ramet, p_tip for non-terminal nodes bearing a ramet, and p_node for
non-terminal nodes not bearing a ramet) and Biis 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
Raddedði; jÞ ¼ ð1 CÞdði;jÞDi 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 ftrÞ; 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, Ravailis given by
RavailðiÞ ¼ Ri ð1 ftrÞ þ RRaddedði; jÞ dði:; jÞ < T: ðA:4Þ
If Uj¼ 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 T¼ 0 or ftr¼ 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 Ravailis the value defined by Equation (A.4), fgis the proportion of resource put into the new
ramet at the growing tip, Rminis 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
Rt¼ Ravail fg; ðA:6Þ
where Ravailis the value defined by Equation (A.4), and fgis 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 con-sequently 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, Rminis the minimum resource required for ramet formation, and fgis 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 con-dition is met:
Ravail> Rmin ð1 k b NÞ > 0; ðA:8Þ
where Ravailis defined by Equation (A.4), Rminis 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
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 Ravailis defined by Equation (A.3), Rminis the resource required to produce a ramet, and fgis
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).
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