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Game theoretical models predict that plants growing in dense stands invest so much biomass in height growth that it trades-off with investment in other organs such as the leaves, leading to decreased plant production. Using the stoloniferous plant Potentilla reptans, we tested the hypothesis that genotypes investing more in the petioles in response to increased density show a greater decrease in total plant mass. We also tested whether a greater increase in mother ramet investment would lead to a greater decrease in investment in vegetative propagation.
To uncouple costs and benefits of investments in petioles, ten genotypes that were known to differ in their response to shading signals were grown in monogenotypic stands at two different densities.
Genotypes differed in their increase in petiole investment in response to an increase in density, but not in their decrease in total plant mass or root mass. Total lamina area per plant did not differ significantly between the densities, nor did the mass invested in the laminae per unit of total plant mass. Genotypes differed considerably in the change in vegetation height and petiole investment, but this was not significantly negatively correlated with the change in total plant mass. The genotypes did differ in the change of mass investment in the mother ramet: a greater increase in investment in the mother ramet was correlated to a greater decrease in vegetative propagation.
While a greater increase in height investment did not lead to a greater decrease in biomass production, it did lead to a decrease in vegetative propagation. This ability to change allocation towards the mother ramets may imply that competition within a stand of stoloniferous plants does not necessarily result in lower total biomass production due to increased height investment.
In many species, height growth of individual plants is strongly regulated by signals that the plants receive from the surrounding vegetation. At higher densities cues such as the photosynthetically active radiation (PAR), the red : far red (R : Fr) ratio, blue light intensity and concentrations of volatiles such as ethylene change, and many plants increase their height growth in response (Schmitt and Wulff, 1993; Smith, 2000; Pierik et al., 2004), which may cause a shift in biomass allocation. Generally, with an increase in density the total biomass of an individual plant decreases, but the proportional investment in vertical spacers increases, while proportional investment in other plant parts such as the roots decreases (Ballaré et al., 1987; Geber, 1989; Weiner and Thomas, 1992; Maliakal et al., 1999).
An individual increasing its height can increase its fitness relative to that of neighbours responding less strongly to these cues, because a taller plant intercepts more light per unit leaf area and shades shorter neighbours (Dudley and Schmitt, 1996; Anten and Hirose, 2001; Schmitt et al., 2003). An increase in height will require a larger biomass investment in vertical spacers, as these will become longer and at the same time may require more mass per unit length for mechanical stability (Huber and Wiggerman, 1997; Leeflang et al., 1998). Since this higher investment in height growth will occur at the expense of investment in other plant organs such as the leaves, the biomass production capacity of the plant might be reduced (King, 1990; Falster and Westoby, 2003; Weiner, 2003). Game theoretical models on height growth thus predict that the competition for light may lead to a ‘tragedy of the commons’ (Hardin, 1968), i.e. individuals with height growth responses that would maximize photosynthesis at the stand level will be outcompeted by plants that invest more in height (Givnish, 1982, 1985; Iwasa et al., 1985; Anten, 2005), and consequently total stand productivity will be reduced.
These theoretical predictions thus depend on the question of whether increased height growth indeed carries a cost. Costs of increased investment in stems in terms of reduced total biomass and reproduction have been found experimentally for erect-growing annuals (Dudley and Schmitt, 1996; Schmitt et al., 1995; Cipollini and Schulz, 1999). On the other hand, near-isogenic lines of the rosette-forming annual Arabidopsis thaliana which had retained functioning phytochrome B maintained their seed production per unit area with increasing density (Ballaré and Scopel, 1997). In addition, neither Ballaré et al. (1991) nor Maliakal et al. (1999) found reduced total biomass of plants with a higher investment in the stems when they were grown in dense canopies, although this may have been triggered by the effects of the R:Fr signal used in these studies to trigger stem elongation on stomatal conductance and photosynthesis rates (Maliakal et al., 1999). These latter studies thus indicate that a tragedy of the commons may not occur when plants compete in high densities. Alternatively, stem elongation may occur at the expense of root allocation (Cippolini and Schultz, 1999). However, this will only be costly to overall performance of the plant if it reduces nutrient or water uptake, for instance in dry periods (Maliakal et al., 1999; Huber et al., 2004).
For clonal, rosette-forming plants there is additional evidence that increased height may not lead to a decrease in total mass. Since they have no vertically growing stem, these clonal plants can place their laminae higher up in the canopy only by elongating their petioles (Huber, 1996). This elongation has been found to increase the costs in terms of mass invested in the petioles (Leeflang et al., 1998; Weijschede et al., 2006). However, clonal, rosette-forming plants may have more compartments to buffer the costs of elongation than erect-growing annuals. Results from studies by Méthy et al. (1990) and Huber and Wiggerman (1997) suggest that an increase in petiole investment of clonal, rosette-forming plants does not lead to reduced total biomass, but rather to a decrease in vegetative reproduction. These authors argued that clonal, rosette-forming plants invest in the petioles of the established ramets to maintain them in dense canopies, which then trade-off with clonal expansion. Consequently, while an increase in height may not decrease total plant mass, it should lead to a lower investment in vegetative reproduction.
Within species, genotypes may differ considerably in their degree of shade avoidance (Schlichting, 1986; Sultan and Bazzaz, 1993; Sultan, 2000; Botto and Smith, 2002). This suggests that with an increase in density, genotypes can differ in the increase in biomass invested in height growth, and thus some may show a greater decrease in productivity, or, alternatively, in root or vegetative reproduction, than others. However, in multigenotypic canopies plants that lag behind in height will receive stronger signals, and thus may elongate to a height similar to surrounding plants, thereby reducing the differences in height among genotypes (Aphalo et al., 1999; Ballaré, 1999; Vermeulen et al., 2008a). In addition, genotypes that are not able to reach the top will probably perform worse, because they are shaded. Consequently, the plants of the tallest genotype will intercept more light than will subordinate individuals. Individual biomass will thus simultaneously be affected in different ways by density-dependent shade avoidance responses in multigenotypic stands: being taller requires more biomass for vertical spacers, but exposes leaves to higher light levels which will lead to increased photosynthetic rates. As a consequence, a direct experimental test of whether stronger responding genotypes show a greater decrease in productivity or vegetative reproduction in multigenotypic stands is problematic (cf. Falster and Westoby, 2003).
In monogenotypic stands, however, all plants will have the same response to neighbour proximity. The height investment then depends on the characteristics of the genotype itself, and thus differences among genotypes in the response to an increase in density should be more pronounced if they are growing in monogenotypic stands. Following the assumptions in game theoretical models, plants in monogenotypic stands that greatly increase biomass investment in height have less biomass to invest in other structures, such as the leaves or roots, which will reduce their total photosynthesis. At the same time, height growth will not lead to increased benefits, because all individuals in the stand will show the same response and their leaves will all be at the same height. Therefore, a stand consisting of a genotype that responds to neighbour proximity with a large increase in height investment should have a greater decrease in total biomass than monostands of genotypes with a smaller increase in height growth investment. For clonal, rosette-forming species, there is yet another possibility: a greater increase in petiole investment of the older ramets may lead to a reduced vegetative reproduction and, thus, a lower investment in structures connecting ramets (i.e. stolons). In that case, a stand consisting of a genotype that responds to neighbour proximity with a large increase in height investment in the established ramets should have a greater decrease in investment in vegetative reproduction than monostands of genotypes with a smaller increase in height growth investment.
Clonal, rosette-forming plants may naturally form such monogenotypic stands, as they can propagate vegetatively (DeKroon and Van Groenendaal, 1997). At the same time, different genotypes of such plants may differ in the strength of the response to signals of neighbour proximity (Van Kleunen and Fischer, 2001; Liu et al., 2007; Weijschede et al., 2008), so differences among genotypes in the change in allocation may be expected when density increases. We therefore set up an experiment with ten genotypes of the clonal, rosette-forming plant Potentilla reptans, where a target clone fragment (i.e. the older ramet part, from hereon called the mother ramet) was surrounded by either zero or eight neighbours, thus creating two densities. The target plant was used to represent the changes of the whole stand. In line with the mentioned game theoretical studies, root competition was excluded by growing all plants in their own pots. The ten genotypes were previously used in a long-term competition experiment, where all nine remaining genotypes after 5 years reached similar heights (Vermeulen et al., 2008b). Yet several experiments have shown that they differ in their responses to shade signals (Liu et al., 2007; Vermeulen, 2008).
We expected (1) that when grown in monogenotypic stands, genotypes would differ in their plastic response to density; (2) consequently, these differences in response should lead to differences between the genotypes in the increase in height and in investment in height growth (i.e.the petioles); (3) with the two positively correlated. (4) Following the game theoretical models, this could potentially lead to a greater decrease in investment in the leaves or roots, and thus to a greater decrease in total plant mass of genotypes that invest more in the petioles. (5) In that case, a negative relationship should be found between the increase in height in response to density and the change in total plant mass.
Alternatively, if there was no such relationship, we expected to find a trade-off between shade avoidance at the level of the established ramets and clonal expansion at the fragment level. In that case (6), the increase in height in response to density should be positively related to the increase of mass invested in the petioles of the established ramet. (7) In addition, the increase in investment of mass in the petioles of the established ramet should be negatively related to the change of mass invested in vegetative reproduction, and therefore (8) the increase in height should be negatively related to the change in vegetative reproduction.
Potentilla reptans is a stoloniferous herb found in moderately disturbed, productive pastures, mown grasslands, lake and river shores, road margins and several other man-made habitats (Van der Meijden, 2005). The plant produces sympodially growing stolons with rooted, rosette-forming ramets. In the absence of physical disturbance the ramets remain interconnected throughout one growing season (Stuefer et al., 2002). Because internodes between leaves remain unextended, and the leaves of the ramet form a basal rosette, the term ‘internode’ herein only refers to the stolon connections between ramets. Each leaf consists of 5–7 palmately arranged leaflets borne on a vertically orientated petiole attached to the ground rosette. Height growth is achieved by elongating this petiole (Huber, 1995). When the lamina reaches the top of a light gradient, petiole elongation stops, which means that the laminae of new leaves are placed above older leaves until height growth of the vegetation stops (Vermeulen et al., 2008a). As the focus in this study is on investment, and not on the way ramets achieve a certain height, height growth investment is taken as the sum of the biomass of all petioles of a mother rosette and its daughters.
From a larger set that was collected in 1997 from different locations in The Netherlands, ten genotypes were kept in the botanical gardens of Utrecht University. These genotypes have been used in a range of experiments, including a long-term competition experiment (Stuefer et al., 2009). Several shading experiments showed marked differences among these genotypes in their plasticity in height investment (Vermeulen, 2008). On 13 June 2006, 160 trays were prepared with nine pots each. The pots had a diameter of 4·8 cm and were 18 cm tall, and were filled with a 1:1 volumetric mixture of compost and river sand, with slow release fertilizer (Osmocote plus, Grace Sierra International, Heerlen, The Netherlands) added to provide 0·5 g N m−2 week−1. One week later, 88 ramets of similar size for each of the ten genotypes were taken from the stock population that was maintained in the botanical gardens of Utrecht University. All stolons were removed and the roots were cut to a length of 5 cm. These ramets were defined as the mother ramets. Eight randomly drawn ramets per genotype were used for measurements at the start of the experiment and were dried at 65 °C for at least 3 d.
The pots were placed in a 3 × 3 arrangement. For each genotype two densities were created. In the low density treatment one ramet was planted in the central pot of the tray, and the surrounding pots stayed empty (LD, 44·4 ramets m−2). In the high density treatment all pots in the 3 × 3 arrangement were planted with similar mother ramets of the same genotype (HD, 400 ramets m−2), with the central ramet being the target plant. The distance to neighbouring ramets was 5 cm. Plants were assigned to the treatments randomly. Root cloth was put on the bare surface of empty pots to prevent rooting of other ramets in each pot. There were eight replicate trays for each combination of treatment and genotype. The trays were randomly placed on two tables in a plastic greenhouse of the botanical gardens (80 % of full daylight, no change in R : Fr).
Black plastic, attached to four sticks 75 cm high at each corner, was put around each tray to limit the area of each ‘arena’ to 15 × 15 cm. The height of this screen was adjustable up to 50 cm above soil level, but at the start of the experiment it was positioned at soil level. Twice a week the black plastic was moved up to the level of the surrounding plants bordering the target plant (HD), to enclose the arena and to prevent light entering from the side into the canopy. The plants were watered daily. Once a week, the height of the vegetation, defined as the height of the highest lamina above the soil surface of the target plant, was measured in each replicate.
After 9 weeks the target plants were harvested. The plants were separated into seven parts: laminae and petioles of the mother ramet; the stolon internodes between ramets; laminae and petioles of the daughter ramets (defined as all ramets that were formed during the experiment); all dead material (laminae and petioles) pooled together; and roots. Roots were washed free from soil particles. Most daughter ramets did not form roots. However, some of the newly formed ramets of the target plants did root in pots of the surrounding plants. This was limited to 25 ramets in total, and the fraction of their root biomass never exceeded 8 % of total root biomass. This root mass of the daughter ramets was also harvested and added to the total root mass of the target plant. Analysis showed that removing this secondary root mass did not alter the direction of the results. The total lamina area of the leaves from the mother ramet and the lamina area of all the leaves of the daughter ramets were measured using a Licor LI-3100 leaf area meter. All parts were dried at 65 °C for at least 3 d and then their mass was measured. Vegetative reproduction was calculated as the sum of the weights of the laminae and petioles of the daughter ramets and the interconnecting internodes.
Analysis of the initial biomass, using a one-way analysis of variance (ANOVA) with genotype as fixed factor, showed no significant differences between the genotypes. Therefore, starting mass was omitted from further analyses.
Differences in changes of allocation patterns may be due to size differences (Poorter and Nagel, 2000). Therefore, to test hypotheses 1 and 2 properly, a two-way analysis of covariance (ANCOVA) was performed following Poorter and Nagel (2000), with the mass of the focal plant part (log transformed) as dependent variable, genotype and treatment as fixed factors, and total plant mass (also log transformed) as covariate. No significant slope effects were found (no significant covariate × treatment, covariate × genotype or covariate × treatment × genotype interactions), and thus these interactions were left out of the analysis. In such an analysis, a positive allometric relationship may occur between the covariate and the dependent. However, our main interest is whether the genotypes differ in their response to density (i.e. the genotype × density interaction), which will not be affected by such a positive relationship.
To test for differences in height and total biomass, two-way ANOVAs were performed. In both ANCOVAs and ANOVAs, genotype and density were treated as fixed factors, because the responses of the genotypes to several shading treatments are well known (Liu et al., 2007) and we hypothesized that the genotypes with the strongest responses would show the greatest decrease in total plant mass. The biomass data were log-transformed to meet the assumptions of ANOVA. A significant density × genotype interaction would indicate that genotypes differed in their response to density.
To test hypotheses 3, 4, 5, 6 and 7, correlation tests were performed. First, following the procedure of Weijschede et al. (2006), genotypic means of every genotype for each treatment were calculated. These means were used to calculate the plasticity of each genotype i (plXi):
with Xihd and Xild the average of genotypes at high and low density, respectively.
Then we tested whether plasticity in height was correlated with plasticity in total petiole mass (hypothesis 3), with plasticity in root investment (hypothesis 4), with total plant mass (hypothesis 5), with plasticity in mass invested in the mother petioles (hypothesis 6) and with plasticity in mass in vegetative reproduction (hypothesis 8), using Pearson's correlation analysis. In support of hypothesis 4, we also tested if plasticity in total plant mass was negatively related to plasticity in total petiole mass, as opposed to the positive correlation that may be expected as petiole mass is present in both factors, or to plasticity in root investment. Also, we tested whether plasticity in mass invested in the mother petioles was correlated to plasticity in mass invested in vegetative reproduction (hypothesis 7) and if plasticity in height was therefore negatively related to plasticity in vegetative reproduction. Q–Q plots and Kolmogorov tests showed that all plasticity measures did not deviate significantly from normality.
All analyses were performed using SPSS 17·0.
The covariance analyses indicated that when corrected for total plant mass the genotypes differed in their plastic responses to increased density (Fig. 1, Table 1). The allocation of biomass to most plant parts showed a significant genotype × treatment effect (Table 1), showing that the way allocation patterns changed with increasing density depended on the genotype. For instance, some genotypes increased the percentage allocation to the petioles of daughter ramets, while others increased the allocation to the petioles of the mother ramet. Only for root mass and total lamina mass did the genotypes not differ significantly in the way the percentage allocation to these parts changed.
In all genotypes, the height of the stand increased with higher density (F-value 2418·18, P < 0·001). For some genotypes, this increase in height was greater than for others (Fig. 2A, genotype × density interaction F-value 34·83, P < 0·001). Total petiole mass (summed petiole mass of mother ramet and of daughter ramets) also showed a similar significant genotype × treatment interaction (Table 1), revealing differences between the genotypes in the way investment in the petioles changed with density. The same interaction occurred for mass invested in the petioles of the mother ramet and vegetative reproduction (Table 1).
Although both genotype and density affected mass invested in the laminae and the roots, no interaction between these two factors was found, indicating that the genotypes did not differ significantly in the way root mass and lamina mass decreased with increasing density (Table 1). Similarly, although total plant mass did decrease with increasing density (F-value 52·79, P < 0·001), and genotypic differences were found (F-value 2·89, P < 0·01), the genotypes did not differ in the way total plant mass and total mass of living tissue changed with increasing density: for all genotypes total plant mass decreased similarly (Fig. 2B, F-value 0·82, P > 0·1). Total lamina area per plant did not differ significantly between the two densities, and no significant genotype × treatment interaction was found (Fig. 2C, Table 1).
The correlation analyses showed that among genotypes, the way in which height increased with increasing density (i.e. plasticity in height) was not correlated to plasticity in total petiole mass (Fig. 3A). This could be partially attributed to one outlier (genotype B); removing this led to a positive correlation (P = 0·016, r = 0·769). However, plasticity in height was not correlated to the change in total plant mass with increasing density (Fig. 3B), nor was a change in total petiole mass related to a change in total plant mass (Fig. 3C).
Plasticity in height was positively related to plasticity in the petiole mass of the mother ramet (Fig. 3D). Plasticity in the petiole mass of the mother ramet, in turn, was negatively related to plasticity in mass invested in vegetative reproduction (Fig. 3E), while plasticity in root mass was not significantly related to plasticity in height (P = 0·293), or to plasticity in mass invested in vegetative reproduction (P = 0·444). Plasticity in height was marginally negatively related to a change in mass invested in vegetative reproduction (Fig. 3F).
In this experiment, we increased the density of monostands of ten individual genotypes of P. reptans 9-fold. The set-up was chosen based on the expectation that monogenotypic stands would show large differences in plastic responses to increased density between the genotypes. The results confirm this idea: the covariance analysis revealed that for most traits a significant genotype × density interaction had occurred. Consequently, the genotypes showed large differences in vegetation height at high density and the differences in vegetation height at high density were consistent with the maximum petiole lengths in single pot shading experiments where the same genotypes were used (Liu et al., 2007; Vermeulen, 2008). So while results from a 5-year competition experiment between the same ten genotypes showed that they converge to a similar height when competing (Vermeulen et al., 2008b), differences do occur when genotypes determine their own canopy structure and light climate.
Whereas some studies have found a decrease in vegetative reproduction with increasing density (Abrahamson, 1975; Holler and Abrahamson, 1977; Rautiainen et al., 2004), or no significant difference (Eriksson, 1985), the present results indicate that plasticity in mass investment in newly formed ramets is strongly genotype dependent. While some genotypes (such as F, G and H) showed the classical response to an increase in density by investing primarily in the mother ramet and reducing the investments in stolons and daughter ramets, other genotypes (i.e. B, C and D) showed the opposite response. This suggests that different vegetation structures may arise depending on the genotype that makes up the canopy.
Depending on spatial and temporal heterogeneity of the surroundings, one response may be more beneficial than another. Investment in new ramets implies the differentiation of axillary meristems into new vegetative stolon apices (Geber, 1990; Huber and During, 2001), leading to the production of additional leaf area at some distance from the mother ramet. In heterogeneous environments, a higher investment in new ramets may increase the possibility of increased genet performance through the specialization of individual ramets to different, locally abundant resources, i.e. division of labour (Stuefer et al., 1994, 1996). Increased investment in new ramets may also reduce the risk of genet death in the case of local disturbances (Eriksson and Jerling, 1990). In homogeneous, dense vegetation, as mimicked by our set-up, however, this additional leaf area will not be placed in more favourable conditions, and the added investment in internodes will not pay off. Rather, if height growth of surrounding vegetation is high, a reduction of ramet production and increased biomass allocation to existing ramets may consolidate growth of the ramets that have already been established (Geber et al., 1992). In accordance with this argument, we found that a strong increase in petiole investment of the mother ramet was significantly correlated with a strong decrease in investment in vegetative propagation, and that the ten genotypes differed considerably in their position along this gradient of investment patterns.
The question then remains of how inherent traits expressed in these monogenotypic stands relate to their performance in mixed communities. As mentioned above, in an experiment where the ten genotypes were growing together, all nine of the remaining genotypes had leaves at the top of the canopy (Vermeulen et al., 2008b). This suggests that in these mixtures most of the genotypes that showed a low response to density in our experiment could still adjust their height growth to that of genotypes that responded with a strong increase in height in our experiment. This apparent high degree of plasticity may allow the genotypes to adjust their traits to that of the surrounding competitors, thereby possibly promoting coexistence (Callahan et al., 2003; Vermeulen, 2008). However, this also indicated that the genotypes that responded less strongly to density in our experiment show a phenotype in mixtures that differs more from the phenotype that is expressed at high density in its monogenotypic stand. The ability to express plasticity is found to be costly (Weijschede et al., 2006; Dechaine et al., 2007), but it is not known whether genotypes with an inherently low response to density have higher costs when adjusting to a similar height than do inherently more strongly responding genotypes. If so, the former genotypes may still have higher costs, even if they do reach similar heights.
Costs of an inherently low response to density may also be more direct. Genotypes that respond less strongly to an increase in density may first form new ramets, rather than invest in the petioles of the mother ramet. Therefore, the first formed leaves of such plants will quickly become shaded by plants of genotypes with a strong response to an increase in density, i.e. the former ramets will soon lag behind (see also Ballaré, 1999; Vermeulen et al., 2008a). In addition, these genotypes then have more ramets for which they need to maintain the vertical position in the canopy, which requires the division of biomass investment to multiple growth points. Potentially, these genotypes may not be able to maintain all newly formed ramets when the canopy closes, resulting in shading, or even in a loss of several ramets. Stuefer et al. (2009) did find a weak positive relationship between the frequency of leaves in the competition experiment and the ability to make few, but large offspring when grown in full light (i.e. without competitors). This indicates that inherent traits may play a role in the outcome of competition, and could partly explain why some of the inherently lower genotypes that form many ramets, such as B and C, have greatly decreased when growing in a mixture (see Stuefer et al., 2009). Unfortunately, the number of genotypes used in our study was too small to allow tests for such multivariate interactions between response variables as performed by Cipollini and Schultz (1999).
As the monogenotypic stands also differed in the increase of investment in the petioles, our set-up thus proved to be suitable for testing the main hypothesis: that a greater increase in mass invested in height (i.e. petioles) in response to an increase in density would lead to a greater decrease in total biomass production. Yet although total plant mass did decrease with increasing density, no differences were found between the monogenotypic stands in the size of this decrease. Also, the change in total petiole mass was not significantly correlated to the change in vegetation height, although removing one outlier did result in such a significant, positive correlation. This outlier, genotype B, keeps making many small ramets at high density (see Fig. 2B), and thus the small height increase it shows at the vegetation level has resulted in an increase of investment in the many petioles of these ramets, rather than a large investment in few ramets. Yet, one would still expect that the change in total petiole mass would be negatively correlated to a change in total plant mass. However, we found a non-significant positive correlation to a change in total plant mass, suggesting that if such a correlation would have been significantly different from 0, it would be due to an allometric effect rather than an underlying trade-off. So, the prediction that monogenotypic stands with a greater increase in petiole investment would show a greater decrease in biomass production could not be confirmed.
A possible explanation for this result is that although the mass invested in the laminae per unit total plant mass did decrease with increasing density, no genotype × density interaction was found. Also, the total lamina area per plant did not decrease with an increase in density. Thus genotypes that had a greater increase in allocation to the petioles did not have a significantly greater decrease in the allocation to the photosynthetic tissue, nor was there a reduction in the total lamina area of the whole plant. This is in contrast to the general notion that increasing height investment trades-off with investment in the light harvesting apparatus (Givnish, 1984, 2002; Hirose and Werger, 1995). Yet, when taking the total lamina area of the target plant as an estimate of average total lamina area per plant, at high densities the total leaf area per unit ground area was approx. 4–6 m2 m−2, similar to what was found in stands in which all ten genotypes were competing (Vermeulen, 2008), compared with about 0·5 at low density, indicating that at high density a large part of the leaves was extremely shaded. This may explain why total biomass per plant was lower at high density. However, this apparent strong competition for light did not lead to differences between the genotypes in the decrease of total plant biomass with increasing density. These findings thus do not show that increased height growth is costly, in the sense that it reduces investment in the production capacity (roots and leaves), as has often been found in species that have an erect-growing stem (Casal and Smith, 1989; Schmitt and Wulff, 1993; Cipollini and Schultz, 1999).
Our results do support the findings of Ballaré et al. (1991) and Maliakal et al. (1999), who found no decrease in total plant mass in erect-growing plants with increased stem elongation, and those of Ballaré and Scopel (1997), who found no decrease in the number of seeds per unit ground area with increasing density of A. thaliana. Also, our results are in line with the results of Méthy et al. (1990) and Huber and Wiggerman (1997) on clonal, rosette-forming plants: if a genotype responds to an increased density with an increase in investment in the mother ramet, the investment in vegetative propagation decreases. This may prevent the lamina area from being placed further away from the mother ramet with the additional costs of internodes, without the benefits of better light conditions for both the mother and the newly formed ramets if the density is locally homogeneous (see also Geber et al., 1992). This, in turn, could prevent monogenotypic stands with a greater increase in petiole investment from showing a greater decrease in biomass production.
Still, the investment in vegetative reproduction decreased with increased investment in height. This is similar to the prediction of game theoretical models that competition for light will result in plants that set seed at a larger size than the size that would maximize total seed production (Kawecki, 1993; Rees and Rose, 2002), and similar to the findings of Gersani et al. (2001) that increased root growth resulted in lower seed production rather than reduced total biomass. Apparently, although in this case a tragedy of the commons has not been found in terms of total plant production, it did occur in terms of a lower investment in offspring.
Whether or not our findings are only valid for clonal, rosette-forming plants remains to be seen. On the one hand, Liu et al. (2007) argued that, for the plant as a whole, petiole elongation in stoloniferous plants is more costly than elongation of the stem in erect-growing plants, because each petiole needs to support its own weight. Consequently, stem elongation would be less costly, which together with the findings of Ballaré et al. (1991) and Maliakal et al. (1999) on erect-growing annual plants suggests that a tragedy of the commons, in terms of reduced total biomass due to increased height investment, would also not occur in plants with stem elongation. However, other studies on erect-growing plants do find that stem elongation comes at a cost of lower fitness (Schmitt et al., 1995; Dudley and Schmitt, 1996; Cipollini and Schultz, 1999), which would suggest otherwise. Experiments which prove that costs of increased height growth are lower for erect-growing annuals compared with plants that increase in height through petiole elongation have, to our knowledge, not been performed. So, if such experiments show that costs of increased height are higher for erect-growing plants, a reduced total biomass with increased investment in height may still arise.
The vegetation structure of a stand of clonal, rosette-forming plants is strongly affected by the way genotypes respond to neighbour proximity, and may differ depending on the genotype that dominates the canopy. However, although a greater increase of mass investment in height growth of the mother ramet in response to increased density led to a lower mass investment in newly formed ramets, it did not result in a greater decrease of total plant mass. As such, the data do not support the idea that competition for light will lead to a tragedy of the commons within a stand of clonal plants that can only achieve height growth by elongating the petiole, at least not in terms of total biomass production.
The authors would like to thank Sander van Hal, Sonja Huggers, Henri Noordman, Betty Verduyn and Fred Siesling for technical assistance, and N. P. R. Anten, M. J. A. Werger and three anonymous reviewers for valuable comments on earlier drafts. This research was carried out in compliance with the laws of The Netherlands.