Table S1.

List of the studies investigating relationships between functional diversity measures and ecosystem functioning. We surveyed the literature published up to the end of 2013 using ISI

Web of Knowledge and Google Scholar (last accessed: 20 December 2013). We used combinations of the term “functional diversity*” with one of the following: “ecosystem function*” or “ecosystem service*” or “ecosystem process*”. We then scanned the cited literature in the articles we found. The criterion for including an article in the synthesis was that it had to evaluate effects of multivariate continuous functional diversity measures on ecosystem functioning (Fig.1c, d). In cases where a study compared single- and multi-trait indices, and species taxonomic diversity, we also recorded the measure or model that performed best in explaining ecosystem functioning. In addition, we recorded the direction of the effect (positive, negative, or no significant effect) and the explanatory power (R2) if reported, whether the study was observational or experimental, and the taxonomic identity of the study organisms. In cases where R2 was in a single study reported for different years, habitats, or different experimental designs we included only the highest R2. This is because our aim was to explore the best explanatory power that different diversity indices can achieve, rather than comparing average R2 across studies. We found 16 studies reporting relationships between multivariate functional diversity and ecosystem functioning (see Table below). All but one study focused on terrestrial plants or algae and none of them studied terrestrial animals. Furthermore, the majority of these studies (10 out of 16) were experimental. Some data-sets have been used repeatedly in different publications to test functional diversity and ecosystem functioning relationships, e.g., data from the BIODEPTH project and the Cedar Creek experiment. The most commonly investigated ecosystem functions were above- or below-ground biomass (13 studies), decomposition (5 studies), and carbon storage (3 studies). Some studies investigated more than one ecosystem function. Multi-trait functional diversity had significant positive effects on ecosystem functioning in 41% and negative in 38% of cases. A majority of the studies that tested for effects of both single- and multi- trait diversity indices found that selected single-trait indices performed better than multi-trait indices in predicting ecosystem functioning (73%). Species richness and abundances were generally poor at predicting ecosystem functioning (highest R2 = 0.37), while

2 highest explanatory power for single-trait indices was R = 0.54 for CWMx (Schumacher &

2 Roscher 2009), and for multi-trait indices R = 0.69 for FRdendr (Thompson et al. 2005). The most common significant multi-trait predictors measured functional divergence (FDdiv) and functional dispersion (FDrao, FDdis), with less prevalent effects of functional richness indices (FRdendr,

FRminvol). Note that for single-trait measures (CWM, Fdvar-s, FRO, Range, FDRao-s,FDqs, ) the direction of the effect is not included because it is highly variable depending on the traits investigated and only the highest R2 is reported. If the authors did not report explained variation

(R2) for single-variable models (SVM) we present the multi-variable model (MVM) with highest

R2. Explained variation and slopes for the best model/variable corresponds to the ecosystem function in the same row. For structural equation models (SEM) only variables with direct links to the ecosystem function are presented. References Study Experiment Tested Index-Ecosystem SVM Slope MVM R2 organis /Field index* function R2 1. Griffin et al. 2009 Oikos Macroam Experimentstudy FAD Primary productivity 0.10 n.s lgae 4 Species Primary productivity 0.79 identity 6 2. Butterfield & Suding 2013 Plants Field study FRO Aboveground biomass EV+CWM+Range (R2= 0.48) Journal of Ecology 2 CWM Soil organic carbon CWM+Stot/b (R = 0.12)

Range Net ecosystem service EV+CWM+Range (R2= 0.38) level

Fdvar-s

FRminvol

FDeve

FDdiv

Stot/b

EV

2 3. Conti & Diaz 2013 Journal of Plants Field study Individual Aboveground biomass Fdvar-s+CWM (R = 0.73) Ecology abundances( IA) 2 CWM Aboveground litter Fdvar-s+IA (R = 0.89) carbon 2 Fdvar-s Soil organic carbon FDdiv (negative)+CWM+IA (R = 0.86) 2 FDdiv Total ecosystem carbon Fdvar-s, CWM, IA(R = 0.87)

4. Scherer-Lorenzen 2008 Plants Experiment Srich Functional Ecology (BIODEPTH) FGR Cotton decomposition positiv e

FDRao-m Cotton decomposition 0.15 positiv e

FDRao-m Wood decomposition 0.12 positiv e

FDRao-m Litter decomposition 0.38 positiv e FGR Litter decomposition positiv e

5. Thompson et al. 2005 Plants Field study Srich Aboveground biomass 0.17 negati Functional Ecology 5 ve FGR Aboveground biomass 0.10 negati 1 ve Mean plant Aboveground biomass 0.20 trait 2

FDdendr Aboveground biomass 0.69 negati ve

6. Mouillot et al. 2011 PlosOne Plants Experiment Srich Cotton decomposition PCoA+ FDeve (negative) + FDdiv (BIODEPTH) (positive) (R2= 0.42)

Seve Litter decomposition Seve (negative)+ PCoA+ FDdiv (positive) (R2= 0.69)

Functional Aboveground biomass Srich (positive)+PCoA+FDdiv identity (positive) (R2= 0.82) (PCoA) FRminvol Nitrogen pool size PCoA+FRminvol(positive)+ FDdiv (positive) (R2 =0.84) 2 FDeve Multifunctionality PCoA+FDdiv (positive) (R =0.80)

FDdiv

7. Cadotte et al. 2009 PlosOne Plants Experiment Srich Aboveground biomass 0.36 positiv 9 e *Index abbreviations:

FDdendrTotal branch length of functional dendrogram (Petchey & Gaston 2002, 2006) FDdendr/abun Traits weighted by individual species abundances (Clark et al. 2012) FDdendr/joint.abun Distance weighted by the joint abundances of pairs of species (Clark et al. 2012) FDdendr/cv Trait axes scaled by variance (Clark et al. 2012) FDdendr/cv.abun Combination of FDrich_pg/abun and FDrich_pg/cv (Clark et al. 2012) FDdendr/cv.joint.abun Combination of FDrich_pg/joint.abun and FDrich_pg/cv (Clark et al. 2012) Hull Minimum volume circumscribed by species in multidimensional trait-space (Cornwell et al. 2006) Hull/abun Traits weighted by individual species abundances (Clark et al. 2012) Hull/cv Trait axes scaled by variance (Clark et al. 2012) Hull/cv.abun Combination of Hull/abun and Hull/cv (Clark et al. 2012) FDRao-s, FDRao-m single and multiple trait Rao’s quadratic entropy (Rao 1982, Botta-Dukát 2005, Mouillot et al. 2005, Ricotta 2005, Leps et al. 2006) FDRao/d,FDRao/b quadratic diversity of Rao without weights, densitiy-weighted, biomass- weighted, respectively; Weigelt et al. 2008) FDRao-m/cv variance-weighted Rao’s quadratic entropy (Clark et al. 2012) FDeve Evenness of abundance distribution in the minimum spanning tree (Villéger et al. 2008) FDdiv Divergence of abundance distributions relative to the community centroid (Villéger et al. 2008) FDdis Mean distance of individual species to the community centroid (Laliberté & Legendre 2010) Sobs Observed species richness Strt Treatment species richness FGRobs Observed functional group richness FRGtrt Treatment functional group richness FAD functional attribute diversity (Walker et al. 1999) FRO functional regularity index (Mouillot et al. 2005) FDminvol functional richness (Villéger et al. 2008) Srich species richness FGR functional group richness Seve species evenness according to Smith & Wilson 1996 or Pielou index (Legendre & Legendre 1998), or Simpson’s evenness index PD phylogenetic diversity (Faith 1992, Cadotte et al. 2008) Simpson’s diversity (Maguuran 2004) SI Species identity CWM (Garnier et al. 2004, Violle et al. 2007) Range maximum trait value minus the minimum trait value of species within community (not weighted) Fdvar-s,Fdvar-m single and multiple trait functional diversity index (Mason et al. 2003) Stot/a Stot/b total numerical and total biomass abundabces IA Individual abundances Mean plant trait (not weighted) (Thompson et al. 2005) Functional identity (PCoA)-axes produced by Principal coordinate analysis on the trait matrix (Mouillot et al. 2011) Trait variation -coefficient of variation in trait values (Cadotte et al. 2009) NMDS -axes produced by Nonmetric multidimensional scaling performed on the trait matrix (Cadotte et al. 2009)

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