1Positive effects of biodiversity on plant productivity may result from diversity-induced changes in the size or density of individual plants, yet these two possibilities have never been tested at the same time in a biodiversity experiment with a large species pool. Here, we distinguish between size effects and density effects on plant productivity, using data from 198 experimental grassland communities that contained 1–16 species. Plant modules such as tillers or rosettes were defined as relevant units, being equivalent to plant individuals in the majority of species.
2In agreement with previous studies, we found positive effects of species richness on above-ground productivity. We show that this positive biodiversity effect resulted from diversity-induced increases in module density rather than from increases in module size. In contrast, variation in productivity within diversity levels was related to module size rather than module density.
3The size–density relationships varied among plant functional groups and among species but their average response to increasing species richness paralleled the pattern observed at the level of the entire plant communities: species richness had a positive effect on above-ground species biomass and species module density but not on species module size. Twenty-four out of 26 overyielding species had denser populations and 25 out of 28 underyielding species had smaller modules in mixtures than in monocultures.
4Synthesis. In grasslands, an increase in community productivity must involve an increase in plant size or density. We found that diversity-induced increases in productivity were related to diversity-induced increases in density, whereas diversity-independent increases in productivity were related to increases in plant size. Our results suggest that increased density of overyielding species in mixtures was the main driver of the positive biodiversity–productivity relationship in our experiment. We conclude that the mechanisms leading to enhanced productivity of species-rich as compared with species-poor communities cannot be derived from mechanisms explaining high productivity within communities that contain a particular number of species.
Size–density–yield relationships are a central topic in plant population biology (Harper 1977). They form the basis of our understanding of self-regulation processes in plant populations. For example, they underlie the fundamental population biological principles of constant yield (Kira et al. 1953) and self-thinning (Yoda et al. 1963). In addition, the relationship between plant size and density within a population may strongly affect mortality and reproduction and may therefore have further consequences for the genetic diversity within the population as well as for community composition (Van Kleunen et al. 2005). However, size–density–yield relationships have rarely been investigated in plant mixtures (but see Bazzaz & Harper 1976; Schmid & Harper 1985; He et al. 2005; Roscher et al. 2007) and we still do not understand how they contribute to positive plant diversity–productivity relationships.
Varying the number of species within a plant community involves significant changes in the conditions experienced by individual plants. As species richness increases, intra-specific interactions among plants are replaced by inter-specific interactions and this may lead to a greater proportional light-, water- and nutrient availability for species that are complementary in their resource use (Naeem et al. 1994; Tilman et al. 1997b; Yachi & Loreau 2007) or to a reduced load of specialized pathogens per individual plant (Petermann et al. 2008). A species may respond to such changes in the available niche space by increasing plant size without a compensatory decrease in density or vice versa. In contrast, if niche space remains constant, any increase in size or density should be compensated for by a decrease in the other variable, as known from the law of constant yield in plant monocultures (Kira et al. 1953). Thus, if average overlap of resource or pathogen-niches among individual plants decreases with increasing species richness, different size–density relationships should be observed between and within species richness levels. A diversity-induced increase in density or size without a compensatory reduction in the other variable could thus lead to a positive plant diversity–productivity relationship.
Previous studies concerning positive biodiversity–productivity relationships found that in many species, individual plant biomass remained unchanged or even declined as species richness increased (Van Ruijven & Berendse 2003; Mwangi et al. 2007; Roscher et al. 2007). Given that in these studies sowing density was controlled and supposed to result in constant seedling densities across the diversity gradients, these results were unexpected. Here, we suggest that they were due to diversity-mediated changes in plant densities during the course of the experiments, for example, differential seedling mortality or differential vegetative and sexual reproduction between species-rich and species-poor communities. We assessed both, plant densities and average plant size (calculated from total species biomass and density), for each species in a large-scale biodiversity experiment (Jena Experiment) to test the hypothesis that increased plant density rather than size leads to positive diversity–productivity relationships in plant communities.
The plant communities of the Jena Experiment represent temperate grasslands in which many plant species grow clonally and produce individual units which we refer to as modules (as opposed to genets which include all products of a single zygote, Harper & White 1974; Kays & Harper 1974; Harper 1977). More precisely, modules can be defined as demographic plant units with a high functional independence (e.g. tillers, shoots or rosettes, Schmid 1990). We assessed the effects of plant species richness on the three interrelated variables above-ground plant biomass, number of plant modules (= module density) and their individual biomass (= module size). Above-ground plant biomass, module density and module size were determined for the entire plant community (community level) as well as for the populations of the individual species present in the communities (species level). Furthermore, we investigated the effect of functional composition on these three variables because past research has shown that this component of diversity can be an important driver of above-ground biodiversity effects (Hooper & Vitousek 1997; Marquard et al. 2009).
We asked the following questions: (i) What is the effect of species richness and functional group composition on above-ground biomass, module density and module size at the level of entire plant communities? (ii) What is the effect of species richness, functional group identity and species identity on above-ground biomass, module density and module size at the level of populations of individual species? (iii) Does the relationship between above-ground biomass, module density and module size differ between and within species richness levels? (iv) Is an enhanced above-ground biomass production in mixtures related to changes in module density or module size with increasing species richness?
We show that in the studied grassland communities, diversity-induced increases in above-ground plant community biomass were predominantly caused by diversity-induced increases in module density. In contrast, increases in above-ground community biomass within richness levels were related to an increase in module size.
study area and experimental design
The Jena Experiment is a large-scale biodiversity experiment situated in the floodplain of the river Saale near Jena (Germany, 50°55′N, 11°35′E, 130 m a.s.l.). Mean annual air temperature around Jena is 9.3 °C, and mean annual precipitation amounts to 587 mm (Kluge & Müller-Westermeier 2000). The topsoil of the 10-ha field site consists of sandy loam in the vicinity of the river, changing to silty clay with increasing distance from the river.
In May 2002, 78 experimental plant communities were established from seeds on plots of 20 × 20 m. Species compositions were determined by constrained random selection from a pool of 60 common Central European grassland species. Based on a cluster analysis of ecological and morphological traits, these 60 target species had been assigned to four functional groups: 16 grasses, 12 small herbs, 20 tall herbs and 12 legumes (Roscher et al. 2004). All possible combinations of species richness levels (1, 2, 4, 8 or 16 species) and functional group richness levels (1, 2, 3 or 4 functional groups) were sown, resulting in a near-orthogonal design of the experiment.
In addition to the 78 large plots, two replicate monocultures of each of the 60 species were sown on smaller plots of 3.5 × 3.5 m. On all plots, 1000 germinable seeds per m2 were sown. They were evenly divided among the species in mixtures (seed numbers were adjusted according to germination tests performed in the laboratory prior to sowing, see Roscher et al. (2004) for details). Following the typical mowing regime for hay meadows, plots were mown twice per year in early June and in early September. Non-target species (‘weeds’) occurring within target communities were weeded out by hand during biannual weeding campaigns (early in the growing season and after the first mowing). Herbicides were used where target species composition allowed their application (herbicides against dicots in pure grass communities and against grasses in pure herb communities). The field site was divided into four blocks, each containing four large plots of the species richness levels 1, 2, 4 and 8, three or four 16-species mixtures and 30 monocultures of small plot size. Weeding, mowing and herbicide spraying were completed blockwise.
Because many of our target species grew clonally and produced dense vegetation on most experimental plots, different plant genets were no longer distinguishable 4 years after sowing. Therefore, plant modules were defined as the relevant units. A module represented either a separate plant individual or a plant part that would potentially grow independently if separated from the rest of the genet (Harper & White 1974; Harper 1977; Schmid 1990). Depending on the growth form of the species, these units were mostly single tillers, shoots or rosettes (see Table S1 in Supporting Information for details). For species with creeping shoots we counted the number of nodes present on these shoots (e.g. in Trifolium repens, Ajuga reptans).
In May 2006, we counted the number of plant modules per species (species module density) on all experimental plots (78 large plots and 120 small monocultures) in two rectangular subplots of 0.2 × 0.5 m. Community module density was calculated as the sum of species module densities per plot. On all large plots, we harvested the above-ground biomass within the subplots (above-ground community biomass) and separated it according to species (above-ground species biomass). Biomass samples were dried at 70 °C for at least 48 h. For all large plots, mean module size was calculated by dividing above-ground biomass by module density, at the level of the entire community (community module size) as well as at the level of species (species module size). Using mean values for ‘size’ neglected the variation in size within the species and within the individual communities. However, measuring all or a selection of modules in our biomass samples individually would have taken too much time and was not necessary in order to test our hypothesis.
In the small monocultures, above-ground community biomass was not harvested. Instead, five or six plant modules were selected randomly and their dry mass was determined. Above-ground community biomass was then calculated by multiplying community module density with the mean size of these modules. Samples of Anthriscus sylvestris, Bromus hordeaceus, Holcus lanatus, Pastinaca sativa and Primula veris were not taken in 2006. For these five species, five or six plant modules were collected in May 2008, treated as described above and their dry mass was used to supplement the data set.
We assessed the effects of species richness and functional group composition (presence of particular functional groups and their interactions) on above-ground community biomass, community module density and community module size using analysis of variance (anova) with sequential sums of squares (Table 1, for effects of species richness see also Fig. 1). The data were log-transformed (base 10) in order to improve the normality of the error distribution. The term ‘functional group composition’ was partitioned into a set of orthogonal contrasts for the main effects of the presence of each of the four functional groups and their 2- and 3-way interactions. The main effects of the four functional groups were fitted in decreasing order of the percentage of total variation explained by these functional groups if fitted first in the set of contrasts. We assessed the relationship between community module density and above-ground community biomass (Fig. 2a), between community module size and above-ground community biomass (Fig. 2d) and between community module density and community module size (Fig. 2g) by plotting these variables against each other on a log–log scale. To analyse how these relationships varied between species richness levels, we constructed a second series of graphs, using the means of the variables per species richness level (Fig. 2b,e,h). This removed the variation within the species richness levels and, therefore, a significant slope indicated a relationship between the corresponding variables due to variation between the species richness levels. To analyse how the above-mentioned relationships varied within species richness levels, we constructed a third series of graphs, using the residuals of simple linear regressions that included either above-ground community biomass, community module density or community module size as dependent variable and the natural logarithm of species richness as explanatory variable (Fig. 2c,f,i). Because deviations from the log-linear effect of species richness were small, the log-linear fit removed most of the variation among the species richness levels and, therefore, a significant slope indicated a relationship between the corresponding variables due to variation within the species richness levels. To infer the significance of the above-mentioned relationships we estimated the slope of the major axis regression line (MA-slope) and tested its significance by 10 000 random permutations using the Model-II program by Legendre (2001). Only significant MA-slopes are displayed with their P-value in the corresponding panels of Fig. 2.
Table 1. Summary of anovas for the logarithm of above-ground community biomass, the logarithm of community module size and the logarithm of community module density, using sequential sums of squares. Indented terms show orthogonal contrasts for the effects of the presence of particular functional groups (summarized as ‘Main FG effects’) and their 2- and 3-way interactions (summarized as ‘FG interactions’). The sum of contrast terms corresponds to FG composition
Log (above-ground community biomass)
Log (community module size)
Log (community module density)
Includes: presence legumes × grasses, legumes × small herbs, legumes × tall herbs, grasses × small herbs, grasses × tall herbs, small herbs × tall herbs, legumes × grasses × small herbs and legumes × small herbs × tall herbs.
We performed anovas with sequential sums of squares to analyse how above-ground species biomass, species module size and species module density were affected by species richness, functional group identity and species identity (Table 2). As a caveat we note that these three analyses are interdependent because biomass is the product of size and density. However, because our aim was to find out to which extent variation in biomass was paralleled by variation in size or density, it was essential to carry out all three analyses. To assess how species richness, functional group identity and species identity influenced the relationship between the two variables contributing to species biomass, that is, species module density and species module size, we used an analysis of covariance in which the sums of products of these two variables were decomposed (Kempthorne 1969, pp. 264–268, Table 3). For both types of analyses, anova and analysis of covariance, the data were log-transformed (base 10) in order to improve the normality of the error distribution. Figure S1 illustrates the effect of species identity and functional group identity on the relationship between species module density and species module size. For all species-specific analyses (presented in Fig. S1 and Tables 2 and 3) above-ground species biomass and species module density were corrected for sowing proportions.
Table 2. Summary of anovas for the logarithm of above-ground species biomass, the logarithm of species module size and the logarithm of species module density, using sequential sums of squares. The natural logarithm of species richness, species identity and the interaction between these terms were tested against the residuals. Functional group identity and the interaction between the natural logarithm of species richness and functional group identity were tested against species identity and the interaction between the natural logarithm of species richness and species identity, respectively. Above-ground species biomass and species module density were corrected for sowing proportions
Log (above-ground species biomass)
Log (species module size)
Log (species module density)
Ln (species richness (SR))
Functional group (FG) identity
Ln (SR) × FG identity
Ln (SR) × Species identity
Table 3. Summary of the analysis of covariance (Kempthorne, 1969, see ‘Methods’) for the relationship between the logarithm of species module density and the logarithm of species module size, using sequential sums of products. The natural logarithm of species richness, species identity and the interaction between these terms were tested against the residuals. Functional group identity and the interaction between the natural logarithm of species richness and functional group identity were tested against species identity and the interaction between the natural logarithm of species richness and species identity, respectively. Species module density was corrected for sowing proportions. Abbreviations: d.f. cov., degrees of freedom for covariance analysis; SP, sums of products; MSP, mean sums of products
Ln (species richness (SR))
Functional group (FG) identity
Ln (SR) × FG identity
Ln (SR) × Species identity
To improve the species’ comparability we calculated the relative yield, relative size and relative density for 54 of our 60 target species. For the remaining six species this was impossible due to their very low abundance either in monoculture (Campanula patula, Cardamine pratensis, Luzula campestris and Sanguisorba officinalis) or in mixtures (B. hordeaceus, Cynosurus cristatus). The relative yield of a species (RYi) is the quotient of the yield of a species in mixture (here: above-ground species biomass) and the yield of this species in monoculture (Trenbath 1974). Similarly, we calculated the relative size (RSi) and relative density (RDi) of a species as the quotient of its module size or module density in mixture and its module size or module density in monoculture, respectively. We then calculated the mean relative yield (RYI), mean relative size (RSI) and mean relative density (RDI) per species as follows:
where Ni denotes number of plots on which species i was present. We compared RYI, RSI and RDI to explore differences in biomass allocation to module size and module density between monocultures and mixtures among the different species (Fig. 3).
With the exception of the major axis regressions and permutation tests presented in Fig. 2 (performed with the Model-II program by Legendre (2001)), we used the statistical software R (Version 2.7.2, http://www.r-project.org) for all calculations and statistical analyses.
As has been found in previous biodiversity experiments including the Jena Experiment, above-ground community biomass (log-transformed) increased with the logarithm of species richness in our experimental plant communities (Fig. 1a, Table 1) and was higher in plots containing legumes (614.4 vs. 230.8 g m−2, Table 1). The presence of the remaining three functional groups (main effects) did not affect above-ground community biomass.
Community module size (log-transformed) was not significantly affected by the logarithm of species richness (Fig. 1b, Table 1). However, plants had larger modules in plots containing legumes (0.85 vs. 0.42 g) and smaller modules in plots containing grasses (0.33 vs. 0.96 g, Table 1).
Community module density (log-transformed) increased with the logarithm of species richness (Fig. 1c, Table 1). Communities containing grasses were on average more than twice as dense as communities without grasses (2236 vs. 1032 modules m−2); communities containing tall herbs produced on average 1426 modules m−2, whereas communities without tall herbs produced 1907 modules m−2 (see corresponding effects in Table 1).
When we explored the interdependency between the three response variables above-ground community biomass, community module density and community module size, we found a positive relationship between community module density and above-ground community biomass (Fig. 2a) which largely resulted from an increase in both variables with increasing species richness (Figs 1a,c and 2b, Table 1). When the variation explained by species richness was removed from the total variation between the plots, the residual variation in above-ground community biomass was no longer positively correlated with the residual variation in community module density (Fig. 2c). This suggested that within a particular level of species richness, communities with a higher number of modules were not more productive than communities with fewer modules.
Furthermore, above-ground community biomass was positively related to community module size (Fig. 2d). However, community module size did not increase with increasing species richness (Figs 1b and 2e, Table 1). When the variation explained by species richness was removed from the total variation between the plots, the relationship between the residual variation in community module size and the residual variation in above-ground community biomass remained positive (Fig. 2f). Thus, while a larger module size did not drive the increase in above-ground community biomass between species richness levels, module size was determinant for the productivity within a particular level of species richness.
A trade-off between community module density and community module size existed among the plots (Fig. 2g). However, this trade-off did not exist between the different species richness levels (Fig. 2h). When the variation explained by species richness was removed from the total variation, the relationship between the residual variation in community module density and the residual variation in community module size remained significantly negative (Fig. 2i) with an MA-slope of −1.333. This value was more negative than the value of –1 expected according to the law of constant final yield (Kira et al. 1953), indicating the occurrence of thinning processes in communities within richness levels (expected slope of –3/2 or –4/3, Yoda et al. 1963; Enquist et al. 1998).
Averaged over all species, the logarithm of species richness had a positive effect on above-ground species biomass and species module density but not on species module size (Table 2). Furthermore, the identity of the species and the particular functional group to which it belonged influenced its biomass allocation to module size and module density (Fig. S1, Tables 2 and 3). Generally, the relationship between species module density and species module size was strongly negative among species (Fig. S1) and was not affected by species richness (Table 3). Tall herbs tended to produce large but few modules and grasses produced small but numerous modules. Legumes and small herbs varied considerably in size and numbers of modules (Fig. S1).
Ranking the species according to their RYI revealed that 26 species were on average more productive and 28 species less productive in mixtures than in monocultures (Fig. 3). Legumes were mostly among the overyielding species (RYI > 1) and grasses mostly among the underyielding species (RYI < 1). Furthermore, an RYI > 1 was nearly always linked to an RDI > 1 (24 out of 26 species) whereas an RYI < 1 was nearly always linked to an RSI < 1 (25 out of 28 species). This pattern indicated that most of the overyielding species produced denser populations in mixtures than in monocultures while underyielding species had nearly always smaller modules in mixtures than in monocultures. Some species were able to increase their density as well as their size in mixtures compared with monocultures (evident particularly for Lathyrus pratensis, T. repens, Rumex acetosa, Veronica chamaedrys, Galium mollugo). However, an RDI ≤ 1 was rarely overcompensated by an increased module size to result in an RYI > 1 (except in Poa pratensis and Plantago lanceolata).
The positive effect of species richness on above-ground community biomass was mainly driven by a diversity-induced increase in the number of plant modules per area. Thus, communities became denser as species richness increased but the average size of plant modules remained constant. Some evidence for a positive effect of species richness on community module density has been reported previously (Kennedy et al. 2002; Mwangi 2006; Schmitz 2007), but could not directly be related to increased community biomass because density and biomass were not measured on the same sample and thus mean module size could not be calculated. In another study a positive effect of plant species richness on above-ground community biomass was mainly due to one particular species (the grass Arrhenatherum elatius) that increased its density as well as its size (Roscher et al. 2007; Lorentzen et al. 2008).
Here, we could show that only diversity-induced increases in community module density resulted in an increase in community biomass whereas diversity-independent increases in module density did not. The diversity-induced increase in density could have resulted from an increased availability of germination or establishment sites for the different species as intraspecific neighbours were replaced by interspecific ones, reducing overlap in resource or pathogen niches between neighbouring individuals (Mwangi et al. 2007; Petermann et al. 2008). A previous study in the Jena Experiment found that the establishment of individual plant genets was indeed enhanced in species-rich communities (Schmitz 2007). It is thus likely that this process also worked in our communities.
Within species richness levels, the lack of a positive relationship between community module density and community biomass indicated that an increase in community module density must have been balanced by a reduction in community module size and, here, community module density was indeed negatively related to community module size. However, the log–log slope of this size–density relationship was more negative than −1. This was consistent with our finding that within species richness levels an increase in module size resulted in an increase in community biomass. Furthermore, the empirical value of −1.333 for the log–log slope of the size–density relationship within richness levels equalled exactly the slope −4/3 predicted by Enquist et al. (1998) for size–density relationships in resource-limited plant populations, and was close to the slope of −3/2 predicted by Yoda et al. (1963) for monocultures undergoing thinning. Therefore, thinning, that is density-dependent mortality, probably occurred among communities of the same species richness. We conclude that the effects of increased module density and possibly also its causes differed between and within species richness levels. Whereas communities of the same species richness seemed to follow the common thinning rules (He et al. 2005), these rules could not explain differences in productivity between communities of different species richness.
In contrast to the well-studied size–density relationships in monocultures (Harper 1977), community-wide size–density relationships in mixtures may be determined by particular species while others diverge from the mean trend. Indeed, similar to the mixed responses of individual species to changes in species richness that were reported from previous experiments (Naeem et al. 1996; Tilman et al. 1997a; Hector et al. 1999; Troumbis et al. 2000; Hector et al. 2002; Van Ruijven & Berendse 2003; Dimitrakopoulos & Schmid 2004; Hooper & Dukes 2004; Roscher et al. 2007; Lorentzen et al. 2008), not all of our target species reacted in the same way to increasing species richness (Tables 2 and 3, Fig. 3). However, their average response confirmed the pattern observed at the level of entire plant communities (compare Table 1 with Table 2). Comparisons between the performance of species in monoculture and mixture revealed that about half of the species had on average a lower biomass in mixture than in monoculture (see Fig. 3). The nevertheless positive relationship between species richness and above-ground community biomass therefore resulted from compositional effects: with increasing species richness the sum of the absolute differences between monocultures and mixtures of the overyielding species must have been increasingly larger than the sum of the absolute differences between monocultures and mixtures of the underyielding species. Being a relative measure, the sum of relative yields of the individual species in a community (i.e. the relative yield total) does not reflect such overcompensation. We further conclude from our observation of positive as well as negative relative yields of individual species that the positive effect of species richness on above-ground community biomass was not exclusively caused by complementarity effects but in part by selection effects. A mixture of both these mechanisms has been found to operate in the Jena Experiment also in other years (Marquard et al. 2009) and has been suggested to commonly underlie positive effects of plant diversity on plant community biomass (Cardinale et al. 2007).
In conclusion, we showed that in our experimental grassland communities diversity-induced increases in community module density explained the positive species richness–productivity relationship while positive effects of community module size on productivity were diversity-independent. Both measures, module size and module density, might be affected by resource availability. However, changes in module density may also reflect differential success of germination or establishment as well as differential mortality with potential consequences for the genetic diversity within the plant communities and for community composition (Van Kleunen et al. 2005). Distinguishing between size effects and density effects may therefore help to elucidate further consequences of biodiversity effects.
We thank the gardeners of the Jena Experiment and the many students who assisted with the field work. Markus Fischer provided helpful comments on an earlier draft of the manuscript. The Jena Experiment is funded by the German Research Foundation (FOR 456) and supported by the Friedrich Schiller University of Jena, the Max Planck Society and the Swiss National Science Foundation (grant no. 31-65224-01 to B.S.).