1. While positive effects of biodiversity on temporal stability of communities have been demonstrated in theoretical and empirical studies, diversity–stability relationships at the population level remain poorly understood.
2. We investigated temporal variability of plant populations in experimental grassland plots of varying species richness (1, 2, 4, 8, 16–60 species), functional group richness and composition (presence/absence of legumes × grasses × small herbs × tall herbs) in a long-term biodiversity experiment from 2003 to 2009 (‘Jena Experiment’).
3. Average population stability, defined as the reciprocal of the coefficient of variation of above-ground biomass production over time, differed largely between species but was generally higher in grasses and small herbs than in legumes and tall herbs. Furthermore, population stability was positively related to a species’ proportional contribution to community biomass. Thus, an increasing number of subordinate species explained lower average population stabilities at higher diversity levels.
4. A negative covariance (CV) across all species-richness levels suggested negatively correlated species dynamics. Species belonging to different functional groups fluctuated asynchronously, while species dynamics within functional groups were more synchronous. Community-wide species synchrony decreased with increasing species richness, and temporal stability at the community level increased.
5.Synthesis: Our results suggest that diversity–stability relationships are driven by fluctuations in the population biomass of individual species which are less synchronized in more diverse than in less diverse mixtures and monocultures. Dominant plant species tend to be more stabilized than subdominant species, independently of community species richness. However, asynchrony of population dynamics outweighs decreasing population stability with increasing species richness, resulting in higher temporal stability at the plant community level.
Both statistical and biological mechanisms, which are often not independent of each other, may induce a positive relationship between species diversity and temporal stability Cottingham, Brown & Lennon 2001). Stabilization at the community level may occur by statistically averaging the temporal dynamics of uncorrelated populations. This has been called the ‘portfolio effect’ (Doak et al. 1998; Tilman, Lehman & Bristow 1998), where independent species fluctuations average out with increasing species richness, resulting in a lower variability of an aggregate community property. Statistical averaging occurs when temporal species fluctuations (=variance) increase more slowly with species abundance (=mean) than predicted by the mean-to-variance power law.
Increasing species richness may also increase the chance for asynchronous fluctuations of populations, leading to lower covariances among species within a community (Tilman 1999; Lehman & Tilman 2000; Loreau & de Mazancourt 2008). Population dynamics are driven by three main forces: intra- and interspecific density dependence, environmental fluctuations and demographic stochasticity (Loreau & de Mazancourt 2008). Biological mechanisms that can lower covariances among species are competitive interactions, physiologically or life history determined species-specific responses to environmental changes, or stochastic processes (Ives, Klug & Gross 2000). When species respond similarly to environmental fluctuations, positive covariances among species may increase community variability, while differential responses of species to environmental fluctuations may lower covariances among species and decrease community variability. Functionally similar species that respond similarly to environmental fluctuations are also likely to compete for shared resources, i.e. covariances are probably not independent of interaction strengths (Hughes & Roughgarden 2000). Compensatory effects among species, leading to a reduction in temporal variability at community level, and an increase in the temporal mean of the corresponding aggregate community property are the fundamentals of the ‘insurance hypothesis’ (Yachi & Loreau 1999).
While empirical studies have repeatedly shown that species richness increases the temporal stability of aggregate community properties, fewer studies exist that tested theoretical predictions about the effects of species richness on temporal stability at the population level and on compensatory dynamics among species or functional groups (e.g. van Ruijven & Berendse 2007; Isbell, Polley & Wilsey 2009). The present study is based on data recorded over a study period of 7 years (2003–2009) in a large grassland biodiversity experiment (‘Jena Experiment’; Roscher et al. 2004) comprising 82 plant communities varying in species richness from 1 to 60 and in functional group richness from 1 to 4 (functional groups: legumes, grasses, small herbs and tall herbs). We tested the hypotheses that (i) temporal stability at the population level decreases with increasing species richness, (ii) temporal stability at the population level increases with a species’ proportional contribution to community biomass, (iii) population dynamics of different species are less synchronized between than within plant functional groups and (iv) population dynamics of different species are less synchronized in species-rich than in species-poor communities.
Materials and methods
This study was carried out in a large biodiversity experiment, the ‘Jena Experiment’ (Roscher et al. 2004), established in May 2002 on a former agricultural field. The study site is located in the floodplain of the River Saale nearby Jena (Thuringia, Germany, 50°55′ N, 11°35′ E, 130 m a.s.l.). There, mean annual air temperature is 9.3 °C, and average annual precipitation is 587 mm (Kluge & Müller-Westermeier 2000). The soil is a Eutric Fluvisol developed from up to 2-m-thick fluvial sediments that are almost free of stones. Soil texture changes gradually from sandy loam in the vicinity of the river to silty clay with increasing distance to the river.
Plant communities were established from a pool of 60 plant species common to Central European semi-natural grasslands (Arrhenatherion communities, Ellenberg 1988). Species were classified into four functional groups according to results of a cluster analysis of a literature-based trait matrix describing morphological, phenological and physiological characteristics: grasses (16 species), legumes (12 species), tall herbs (20 species) and small herbs (12 species). All possible combinations of species number (1, 2, 4, 8 or 16 species) and plant functional group number (1–4 functional groups, presence/absence of legumes × grasses × small herbs × tall herbs) were realized, resulting in a near-orthogonal design of the experiment. Each species-richness level had 16 replicates with the exception of the 16-species mixtures because not enough legumes and small herbs were in the species pool to assemble them in mixtures with 16 species of the same functional group. Mixture compositions were determined by random drawing with replacement. In addition, four replicates of the 60-species mixture were established. In total, 82 plots of 20 × 20 m size were sown. The field site was divided into four experimental blocks parallel to the river each containing an equal number of plots per species-richness level. Sown seed density amounted to 1000 germinable seeds per m2. In mixtures, all species were sown with equal proportions (for further details, see the study of Roscher et al. 2004).
Experimental plots were mown twice a year (early June and September), and the plant material was removed, as it is typical for hay meadows. Two yearly weeding campaigns (early April and July) served to maintain the target species composition. Herbicides were used as spot treatments against selected weed species (Cirsium arvense (L.) Scop., Rumex sp.), and where sown species combinations allowed their application (against herbs in pure grass communities and against grasses in pure herb communities, respectively). Mowing, weeding and herbicide spraying were performed blockwise in rotating order. Plots were not fertilized during the experimental period.
Our analyses are based on data collected at estimated peak biomass before first mowing in late May from 2003 to 2009. Above-ground plant biomass was harvested by clipping the vegetation 3 cm above ground on rectangles of 20 × 50 cm size. Four samples (only three in May 2005, 2008 and 2009) were taken per plot. The location of sample frames was allocated at random for each harvest. Samples were sorted to sown species (species sown at a particular plot), total weeds (species not sown at a particular plot) and detached dead plant material; samples were then dried to constant weight (70 °C, 48 h). Above-ground species biomass per harvest was calculated as the mean of the four (or three) samples per plot. For further details and data, see the study of Weigelt et al. (2010).
Measures of temporal variability
Temporal stability (S) was quantified as the reciprocal of the coefficient of variation (Tilman 1999) using the ratio of the mean (μ) to the standard deviation (σ):
Temporal stability was calculated firstly for the time series of biomass data for each species in each experimental community (=population stability SPop) and secondly for the time series of community biomass, i.e. sum of species biomass (=community stability SCom).
Temporal variances (σ2) and means (μ) in species biomass were analysed according to a power–function relationship between the two parameters (Taylor 1961),
where c is a constant and z is a scaling coefficient. The logarithmic transformation of this equation results in a linear mean–variance function, where z is the slope of the positive relationship between the logarithm of σ2 and the logarithm of μ [log(σ2) = c + z * log(μ)] and describes diversity effects on the strength of the portfolio effect. Based on the assumption that community biomass varies independently of species richness and is equally distributed among species and that covariances are absent, the variance in community biomass is simply related to the sum of individual species variances (Doak et al. 1998). Under these assumptions, the summed variances decrease (and community stability increases) with diversity when z >1. At the same time, population stability decreases with diversity for z <2 and increases when z >2 (Tilman 1999; Cottingham, Brown & Lennon 2001). The z values were fitted for each species separately across all communities in which the species occurred and across species combining all communities. Reduced major axis regression (RMA) as implemented in the lmodel2 package of the statistical software R (R Development Core Team, http://www.r-project.org) was applied, and significance of slopes was tested by 499 random permutations.
Summed variances, summed covariances, variance CV, covariance CV and variance ratio VR were calculated across all species per plot, at the between-functional-group level (summing biomass per functional group) and at the within-functional-group level, where, for a given plot, Pi is biomass of species population i (or functional group, respectively), and
(Loreau & de Mazancourt 2008). The variance ratio (VR) relates the variance of an aggregated variable (C = sum of the component populations) to the variance of individual species populations Pi, where
When species vary independently, their covariance is zero, and summed species variances equal the variance of the community property. When species do not vary independently, summed covariances, being predominantly negative or positive, cause a decrease or increase in overall variability. A VR < 1 indicates that the summed covariances are negative, suggesting negatively correlated population dynamics of species, while VR > 1 occurs when the sum of covariances among species is positive, suggesting positively correlated population dynamics of species. A VR = 1 indicates that positive and negative covariances among species cancel each other out (Gonzalez & Loreau 2009).
This statistic ranges between 0, indicating complete asynchrony, and 1, indicating perfect synchrony among species.
Data were analysed with the statistical software R2.11.1 (R Development Core Team, http://www.r-project.org). Analyses of population stability SPop across species were performed with linear mixed-effects models using the lme function in the nlme package (Pinheiro & Bates 2000) of the statistical software R. Block and plot identity were treated as random factors in a nested sequence to account for differences between the experimental blocks and the statistical dependency among species occurring in the same plot. Starting from a constant null model, the fixed-effects species richness (as log-linear term) and number of functional groups (as linear term) were entered, followed by a term for species identity and its interaction with species richness and number of functional groups. In alternative models, species identity was replaced by terms for functional group identity (=factor with four levels) or contrasts for the identity of particular functional groups. Finally, species proportional contribution to community biomass based on biomass per species in each experimental community as a mean value over time was entered as a covariate before the experimental factors to explore the relationship between SPop and species proportions in community biomass. We used a species’ proportional contribution to community biomass to account for the effect of species richness on biomass partitioning (i.e. more plant species in a community may imply proportionally less biomass per species) without explicitly eliminating the effect of species richness on population biomass (i.e. if community biomass increases with species richness, more plant species does not necessarily imply less biomass per species). Then, all species occurrences were grouped according to their contribution to mixture biomass as dominants (>25%), intermediates (5–25%) and subordinates (<5%). Firstly, a grouping term was entered instead of species identity in modelling, and secondly, each group of data was analysed separately with the model described above. The maximum-likelihood method and likelihood ratio tests (L ratio) were applied to assess the statistical significance of model improvement by adding the fixed effects.
Variables at the plot level were analysed with analysis of variance (anova) with sequential sums of squares (type I SS). Following the a priori hypotheses of the ‘Jena Experiment’, model terms were entered in the following sequence: block, species richness (as log-linear term) and number of functional groups (as linear term). In a series of analyses, we fitted alternatively the presence/absence of each plant functional group after the term for number of functional groups. In analyses of summed variances and covariances, variance CV, covariance CV and VR at the between- or within-functional-group level, only communities with two and more functional groups or species per functional group, respectively, were included. This was done to avoid a bias through constant levels of covariance CV (=0) and VR (=1) in communities containing one functional group or one species only. Alternatively, the species-richness term was separated into a monoculture vs. mixture contrast and a log-linear contrast within mixtures, where constant values per definition are restricted to monocultures (covariance CV, VR, community-wide species synchrony ϕP across all species).
Population stability (hypotheses 1 and 2)
Population stabilities (SPop; μ/σ) based on peak above-ground biomass varied strongly among species (Fig. 1). Population stability on average decreased with increasing species richness, which was significant for 30 of 60 species in separate per-species analyses (Table 1; Fig. 2). The number of functional groups fitted after species richness did not explain additional variation in population stability (Table 1). However, population stability within plots and its variation in response to increasing species richness and number of functional groups differed largely between species (significant interaction terms for ‘Species ID × SR’ and ‘Species ID × FG’). Population stability varied among species assigned to different plant functional groups with average values of 0.99 (±0.05 SE) for grasses, 0.96 (±0.04 SE) for small herbs, 0.83 (±0.03 SE) for legumes and 0.81 (±0.03 SE) for tall herbs. However, the relationship between population stability and increasing species or functional-group richness did not vary among the four functional groups (see Table 1 for nonsignificant interaction terms among ‘SR’, ‘FG’ and ‘Functional group ID’, or contrasts for any particular functional group).
Table 1. Summary of mixed-effects model analysis for population stability SPop (=μ/σ) based on peak above-ground biomass of species from 2003 to 2009
Models were fitted by stepwise inclusion of fixed effects. Likelihood ratio tests were applied to assess model improvement (L ratio) and the statistical significance of the explanatory terms (P values). Significant effects are marked in bold. The arrow indicates a decrease (↓) with increasing species richness. Note that contrasts for functional group identity (factor with four levels) and identity of each functional group separately (absent vs. present) were fitted in series of analyses replacing the term for species identity.
Species richness (SR)
Functional group number (FG)
Functional group ID
Species ID × SR
Functional group ID × SR
Legumes × SR
Grasses × SR
Small herbs × SR
Tall herbs × SR
Species ID × FG
Functional group ID × FG
Legumes × FG
Grasses × FG
Small herbs × FG
Tall herbs × FG
The inclusion of a species’ proportional contribution to community biomass (mean species proportion over time for each species in each experimental community) fitted as covariate before the experimental factors showed that temporal stability was larger in populations that contributed a larger proportion to community biomass production (L = 317.24, P < 0.001, Fig. 3a). Negative effects of increasing species richness on population stability remained statistically significant after correcting for species biomass proportions, but model improvement was small (L = 6.86, P = 0.009) compared to analysis without species biomass proportions as a covariate (L = 49.19, P < 0.001, Table 1). Grouping of species occurrences according to their biomass proportions (dominants, intermediates, subordinates) had significant effects on population stability (L = 169.31, P = 0.001), but these groups did not differ in their response to increasing species richness (L = 0.89, P = 0.641) or functional group number (L = 3.86, P = 0.145). Dominants represented 16% of cases, intermediate 23% of cases and subordinates 61% of cases across all species and communities, which were equally distributed among species assigned to different functional groups (χ2 = 5.25, P = 0.512). Separate analyses of each group showed that population stabilities of neither dominants (L = 0.01, p = 0.973) nor intermediates (L = 0.27, P = 0.602) or subordinates (L = 2.48, P = 0.115) depended on species richness (Fig. 3b).
Variance and covariance relationships (hypotheses 3 and 4)
Summed variances across all species for a given plot decreased from monocultures to mixtures but did not change in response to increasing species richness of mixtures. Summed variances were higher when legumes were present and lower when small herbs were present compared to communities without these functional groups (Table S1 in Supporting Information). Summed covariances across all species did not change in response to increasing species richness but decreased with increasing functional group richness (Table S1).
The variance CV among all species decreased from monocultures to mixtures and with increasing species richness of mixtures (Table S1, Fig. 4a). Functional group richness or the presence of particular functional groups did not affect the variance CV. In contrast, the covariance CV increased slightly with increasing species richness of mixtures, but functional group richness fitted after species richness had decreasing effects on covariance CV. The VR did not change in response to increasing species richness but decreased at increasing functional group richness. Covariance CV < 0 and VR < 1 indicated negatively correlated population dynamics among species.
The variance CV also decreased with increasing species richness at the between-functional-group level (Table S2 in Supporting Information, Fig. 4b) and was lower in communities with legumes. The covariance CV and the VR at the between-functional-group level varied independently of plant diversity except for a higher covariance CV in communities with tall herbs (Table S2). The significance of covariance CV < 0 and of VR < 1 across all species-richness levels showed that temporal dynamics were negatively correlated between functional groups.
The overall VR > 1 among species within legumes indicated correlated dynamics of legume species (Table S2, Fig. 4c), whereas the VR close to 1 within grasses, small herbs and tall herbs suggested that positive and negative covariances among species cancelled each other out within these functional groups (Table S2, Fig. 4d–f). The overall mean of the covariance CV among species within functional groups was not significantly different from zero. However, the covariance CV within legumes increased with increasing species richness of mixtures and resulted in an increasing VR (Table S2, Fig. 4c). Similarly, the covariance CV increased with increasing species richness of mixtures within small herbs, while the increase in VR was only marginally significant (Table S2, Fig. 4e). The covariance CV varied independently of the species richness of mixtures within grasses and tall herbs. The VR tended to increase with increasing species richness of mixtures within grasses (Table S2, Fig. 4d). The VR within tall herbs decreased with increasing functional group richness, was lower in communities with legumes and was higher in communities with grasses than in communities without the respective functional groups (Table S2). Increasing species richness of mixtures did not affect the variance CV within any functional group, but the variance CV within grasses and within tall herbs increased at increasing functional group number. The variance CV within grasses was higher when legumes were present (Table S2).
Community-wide species synchrony and mean–variance scaling (hypothesis 4)
Community-wide species synchrony (ϕP) was highly variable at low species-richness levels. Overall, species synchrony decreased with increasing species richness and was lower in communities with small herbs (Table 2, Fig. 5a). Community stability increased with sown species richness (Table 2, Fig. 5b). In plant communities with a large stability in biomass production, species synchrony was low, while communities with lower stability varied largely in species synchrony (Fig. 5c).
Table 2. Summary of analyses of variance (anova) of species synchrony ϕP and community stability SCom (=μ/σ) based on peak above-ground biomass of species from 2003 to 2009
Species synchrony ϕP
Community stability SCom
Given are the degrees of freedom (d.f.), mean sums of squares (MS), F ratios (F) and P values (P). Note that contrasts for the presence/absence of particular plant functional groups were fitted in series of analyses. Significant effects are marked in bold. Arrows indicate a significant decrease (↓) or increase (↑) in analysed variables with increasing species richness, functional group number or presence of particular plant functional groups.
Monoculture vs. Mixture
Mixture species richness
Functional group number
The z value calculated across all species was z =1.77. Values of z for individual species ranged from 1.45 to 2.19, but only seven species reached z >2.0.
We studied population and community stability defined as reciprocal of the coefficient of temporal variation, explored mean–variance relationships and summed variances to test for the portfolio effect and statistical averaging and used variance–covariance relationships to assess compensatory dynamics among species. The main results of these analyses show that temporal stability at the population level decreases with increasing species richness (hypothesis 1), that populations are temporally stabilized dependent on their proportional contribution to community biomass production and almost independently of plant species richness (hypothesis 2), that uncorrelated dynamics are more likely among species assigned to different functional groups than within functional groups (hypothesis 3) and that plant species richness has little effects on community stability when species dynamics are synchronous (hypothesis 4). These findings suggest that the diversity–stability relationships, widely observed at the community level across a range of taxonomic groups, are driven by abundance distributions of individual species and by their less-synchronized dynamics with increasing richness.
Although productivity at the community level increases with species richness in the majority of biodiversity experiments, including the ‘Jena Experiment’, effects of species richness on biomass production of individual species are highly variable (Hooper et al. 2005; Marquard et al. 2009a). However, owing to the substitutive design often used in biodiversity experiments and the constant final yield law which also applies to plant mixtures (He et al. 2005; Roscher et al. 2007; Weiner & Freckleton 2010), it is likely that biomass proportions of individual species populations decrease at increasing species richness (hypothesis 1) if single species do not become highly dominant. Therefore, the close correlation between species proportional contribution to community biomass and temporal population stability SPop in a community (hypothesis 2) may explain the mostly destabilizing effects of diversity on populations (Fig. 2), which have been observed in a number of biodiversity experiments (e.g. Tilman, Reich & Knops 2006; van Ruijven & Berendse 2007; Hector et al. 2010). However, our grouping of species occurrences into dominants (species biomass contributes >25% to community biomass), intermediates (species biomass contributes between 5% and 25% to community biomass) and subordinates (species biomass contributes <5% to community biomass) provided clear evidence that species which contributed a larger proportion to community biomass had more stable populations (Fig. 3). A greater stability in dominant than in subordinate species has been observed in several empirical studies (Bai et al. 2004; Lepš 2004; Steiner et al. 2005; Polley, Wilsey & Derner 2007; Grman et al. 2010). However, we also showed that population stabilities of neither subordinates nor intermediates or dominants changed in response to increasing species richness (Fig. 3b). Therefore, overall negative effects of increasing species richness on population stabilities in our experiment are attributable to an increasing proportion of subordinate species in more diverse communities. Thus, different patterns of species diversity–abundance relationships are a possible explanation for contrasting results. For instance, Valone & Hoffmann (2003b) found positive effects of diversity on population stability, but population sizes increased with diversity in their study. Similarly, Bai et al. (2004) observed positive relationships between the stability of single species populations and plant functional groups and their relative contribution to community biomass in natural grasslands.
The mean–variance scaling examined for each species separately, which mostly varied between 1 < z <2 and only rarely was z >2, also supported the interpretation that temporal fluctuations of populations increased with increasing species richness (hypothesis 1). The z value estimated across all species was 1.77, which is consistent with other studies, where z values in a range between 1 and 2 have been interpreted as indicative of the portfolio effect (e.g. Tilman 1999; Steiner et al. 2005; Polley, Wilsey & Derner 2007; van Ruijven & Berendse 2007).
In addition to the portfolio effect or statistical averaging, i.e. the manner in which temporal species variances scale with their abundances, other mechanisms such as increasing negative covariances in abundance of co-occurring species at higher diversity (covariance effect) and overyielding effects have been predicted to cause higher community stability and lower species stability with increasing species diversity (Tilman 1999). Overyielding effects occur in most biodiversity experiments with grassland species, including the ‘Jena Experiment’ (Roscher et al. 2005; Marquard et al. 2009b). In our study, summed covariances and the covariance CV did not show a dependence on species richness, but the overall mean of the covariance CV < 0 and the variance ratio VR < 1 indicated negatively correlated dynamics among species.
When variance–covariance relationships across species were decomposed into the between-functional-group level and the species level within functional groups, a covariance CV < 0 and a VR < 1 was observed at the between-functional-group level. In contrast (hypothesis 3), the VR was not significantly different from 1 between species within functional groups or even larger than 1 in the case of legumes (Fig. 4). At higher species richness (8, 16 and 60 plant species), we observed covariance CV > 0 and VR > 1 among species within the functional groups of legumes, small herbs and grasses, suggesting positively correlated population dynamics of species within these functional groups (Fig. 4c–e). Thus, it is likely that two processes counteract at the within-functional-group level when functionally similar species respond similarly to environmental fluctuations or changes in resource availability (positive covariances) but compete more strongly for resources (negative covariances) than species that are functionally less similar (Hughes & Roughgarden 2000).
Although species synchrony on average decreased at increasing species richness (hypothesis 4), it was highly variable between different mixtures at lower species richness of two and four species and less variable at the higher species-richness levels (Fig. 5a). Obviously, low community-wide species synchrony seemed to be a prerequisite for stability at the community level, but temporal community stability was highly variable at low levels of species synchrony (Fig. 5c). Thus, negative covariances attributable to either competitive interactions between species or different responses to environmental fluctuations are responsible for community stability.
In summary, in accordance with a recent study by Isbell, Polley & Wilsey (2009) in experimental grasslands, we found that plant species richness increased community temporal stability through both a portfolio effect and a reduction in species synchrony. However, our study emphasizes the prominent role of species abundance distributions on the diversity–stability relationship. We have clearly shown that dominant plant species tend to be more stabilized than subordinate species, independent of community species richness. Thus, increasing proportions of subordinate species at increasing species richness are related to on average decreasing levels of population stability, which are compensated through stabilizing effects of asynchronous species dynamics.
The ‘Jena Experiment’ is funded by the German Science Foundation (FOR 456) with additional support from the Max Planck Society and the University of Jena. We thank all the people, especially the gardeners, who helped in maintaining the experiment and harvesting biomass. We thank two anonymous reviewers for valuable comments on a previous version of the manuscript.