High plant diversity is needed to maintain ecosystem services. Year. A B Function. Year. A B Function

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1 doi:38/nture08 High plnt diversity is needed to mintin ecosystem services Forest Isbell, Vincent Clcgno,AndyHector, John Connolly 3,W.StnleyHrpole 4, Peter B. Reich 5,6, Michel Scherer-Lorenzen 7, Bernhrd Schmid, Dvid Tilmn 8, Jsper vn Ruijven 9,AlexndrWeigelt 0, Brin J. Wilsey 4,ErikS.Zvlet &MichelLoreu Biodiversity is rpidly declining worldwide, nd there is consensus tht this cn decrese ecosystem functioning nd services 7.It remins uncler, though, whether few 8 or mny 9 of the species in n ecosystem re needed to sustin the provisioning of ecosystem services. It hs been hypothesized tht most species would promote ecosystem services if mny times, plces, functions nd environmentl chnges were considered 9 ; however, no previous study hs considered ll of these fctors together. Here we show tht 84% of the 47 grsslnd plnt species studied in 7 biodiversity experiments promoted ecosystem functioning t lest once. Different species promoted ecosystem functioning during different yers, t different plces, for different functions nd under different environmentl chnge scenrios. Furthermore, the species needed to provide one function during multiple yers were not the sme s those needed to provide multiple functions within one yer. Our results indicte tht even more species will be needed to mintin ecosystem functioning nd services thn previously suggested by studies tht hve either () considered only the number of species needed to promote one function under one set of environmentl conditions, or () seprtely considered the importnce of biodiversity for providing ecosystem functioning cross multiple yers 0 4, plces 5,6, functions 4,7,8 or environmentl chnge scenrios,9. Therefore, lthough species my pper functionlly redundnt when one function is considered under one set of environmentl conditions 7, mny species re needed to mintin multiple functions t multiple times nd plces in chnging world. Arguments for biodiversity conservtion re often bsed on ecosystem services, but it remins uncler whether few 8 or mny 9 species re needed to mintin ecosystem services. Determining how mny species provide ecosystem services will require synthesis of severl res of biodiversity reserch (Fig. ). Biodiversity ecosystem functioning studies hve often considered single functionl context nd found tht multiple, but not ll, study species promoted ecosystem functioning 5 7 (Fig. ). We define functionl context (henceforth context) s the mesurement of one function, t one time nd plce, under one environmentl chnge scenrio. Severl relted biodiversity studies hve explored whether more species promote ecosystem functioning when more thn one context is considered. For exmple, biodiversity ecosystem stbility (tht is, the invribility of productivity) studies hve found tht more species re needed to provide ecosystem functioning t lrger sptio-temporl scles becuse different species promote productivity t different times 0 4 (Fig. b) or plces 5,6. Biodiversity ecosystem multifunctionlity studies hve found tht more species re needed to provide multiple functions becuse different species promote different functions 4,7,8 (Fig. c). Biodiversity globl chnge studies hve found tht more species re needed to provide ecosystem functioning in chnging world becuse different species promote ecosystem functioning under different environmentl chnge scenrios. Here, for the first time to our knowledge, we consider ll of these reltionships together. We included dt from 7 grsslnd biodiversity experiments tht considered multiple times, plces, functions or environmentl chnge scenrios (Supplementry Tble nd Supplementry Dt). To test whether different species promoted ecosystem functioning during different yers, we included studies tht plnted replicte plots (sme species compositions) during consecutive yers 3 or mde repeted mesurements of ecosystem functions cross yers 7,9,,,4,5. To test whether different species promoted ecosystem functioning t different plces, we included studies tht plnted replicte plots (sme species compositions, with one exception 5 ) t multiple sites cross Europe 6 or multiple sptil blocks within site 7,3,5. To test whether different c Do multiple species promote ecosystem functioning within prticulr context? b Do different species promote ecosystem functioning during different yers? No Yes No Yes Do different species promote different functions? No Yes Species pool d Do different species provide ecosystem stbility nd ecosystem multifunctionlity? No Yes Figure Some of the wys tht biodiversity cn be importnt for ecosystem functioning. Ech of the eight symbols represents species. Species shown in the bivrite plots re those tht promoted ecosystem functioning within ech functionl context (for exmple, context A might be boveground biomss mesured during 00). Although this figure defines contexts in two dimensions for simplicity, we considered four dimensions (Fig. 3). Previous studies hve considered () one context, or (b, c) one dimension of contexts (b, ecosystem stbility studies; c, ecosystem multifunctionlity studies). Figure tests the question in d, by compring the one-dimensionl overlp (for exmple, between A nd A) with the two-dimensionl overlp (for exmple, between A nd B) nd three-dimensionl overlp (tht is, pir of contexts tht differs in three wys; not shown). Our results reject ech of the null hypotheses shown on the left in d. Deprtment of Biology, McGill University, Montrel, Quebec, H3, Cnd. Institute of Evolutionry Biology nd Environmentl Studies, University of Zurich, CH-8057 Zurich, Switzerlnd. 3 UCD School of Mthemticl Sciences, University College Dublin, Dublin 4, Irelnd. 4 Deprtment of Ecology, Evolution, nd Orgnisml Biology, Iow Stte University, Ames, Iow 500, USA. 5 Deprtment of Forest Resources, University of Minnesot, St Pul, Minnesot 5508, USA. 6 Hwkesbury Institute for the Environment, University of Western Sydney, Richmond, New South Wles 753, Austrli. 7 Fculty of Biology, University of Freiburg, Geobotny, D-7904 Freiburg, Germny. 8 Deprtment of Ecology, Evolution, nd Behvior, University of Minnesot, St Pul, Minnesot 5508, USA. 9 Nture Conservtion nd Plnt Ecology, Wgeningen University, 6700 AA Wgeningen, The Netherlnds. 0 Institute of Biology I, University of Leipzig, 0403 Leipzig, Germny. Environmentl Studies Deprtment, University of Cliforni, Snt Cruz, Cliforni 95064, USA. 0 Mcmilln Publishers Limited. All rights reserved 00 MONTH 0 VOL 000 NATURE

2 RESEARCH LETTER species promoted different functions, we included studies tht mesured severl functions 4,7,, such s biomss production nd nutrient uptke. Mny of these functions re considered to be supporting ecosystem services becuse other types of ecosystem services depend on them 4,7. To test whether different species promoted ecosystem functioning under different environmentl chnge scenrios, we included studies tht pplied environmentl chnge tretments, such s nutrient nd CO enrichment 9, precipittion chnges or lnd use chnges such s livestock grzing nd hying 0. We begn by identifying the sets of study species tht influenced ecosystem functioning within ech context. Species were considered to promote ecosystem functioning in prticulr context if they hd effects in the direction tht would usully be considered desirble from n ecosystem services perspective 7. Positive effects were considered desirble for ll functions except for soil inorgnic nitrogen nd light vilbility t ground level, where negtive effects re consistent with lower levels of unconsumed resources 7. We did not use seprte definitions of desirble effects for different species (for exmple, positive effects of legumes on soil nitrogen might be considered desirble) to be consistent with previous studies 7,8, to be conservtive nd becuse it my not be possible to mnge simultneously for both positive nd negtive effects. We found tht pproximtely 7% of the study species promoted ecosystem functioning within ny prticulr context, regrdless of the size of the study species pool (Fig. ). Note tht if mny species were functionlly redundnt, or if only the most common species promoted ecosystem functioning, then we would expect sturting reltionship in Fig.. Insted, our results suggest tht even rre species cn promote ecosystem functioning. After identifying the sets of species tht promoted ecosystem functioning in ech context, we tested whether different sets of species promoted ecosystem functioning in different contexts. We used Sørensen s similrity index to quntify overlp between species sets 7. All comprisons were mde within studies so tht differences between pirs of contexts were not due to smpling from multiple species pools. First, we quntified one-dimensionl overlp between ll pirs of contexts tht differed in only one wy (Fig. b, c). For exmple, multi-yer overlp ws quntified between ech pir of contexts tht differed only in which yer ecosystem functioning ws mesured (tht is, sme plce, function nd environmentl chnge scenrio in both contexts). A multi-yer overlp vlue of one or zero would respectively indicte tht completely identicl or completely unique sets of species promoted ecosystem functioning during different yers, independent of the other sources of vrition. We found overlp vlues between these two extremes, which indictes tht somewht different sets of species promoted ecosystem functioning during different yers, t different plces, for different functions nd under different environmentl chnge scenrios (Fig. b). After considering these sources of vrition independently, we quntified multi-dimensionl overlp between pirs of contexts tht differed in two or three wys (Fig. d). Agin, ll comprisons were mde within studies. We found tht the verge overlp between pirs of contexts decresed s the number of differences between contexts incresed (Fig. b nd Supplementry Fig. ). This mens tht, for exmple, the identities of the dditionl species needed to provide one function during multiple yers were not the sme s the identities of the dditionl species needed to provide multiple functions during one yer (Fig. d). Additionlly, species sets did not simply vry independently of context ttributes (permuttion test P, 0 for one-, two- nd three-dimensionl overlp) (Fig. b). Thus, our results indicte tht even more species will be needed to mintin ecosystem functioning nd services thn previously suggested by studies tht hve either () considered only the number of species needed to promote one function under one set of environmentl conditions, or () seprtely considered the importnce of biodiversity for providing ecosystem functioning cross multiple yers 0 4, plces 5,6, functions 4,7,8 or environmentl chnge scenrios,9. Future studies could more completely consider the consequences of biodiversity declines for ecosystem functioning nd services by similrly considering the multidimensionlity of ecosystem functioning both in experimentl nd nturl communities. Next, we quntified the extent to which the number of species promoting ecosystem functioning incresed s more yers, plces, functions or environmentl chnge scenrios were considered within ech study. In other words, we quntified the ccumultion of species cross ech of the four dimensions of contexts tht we considered (Fig. ). We found tht greter proportion of species promoted 5.0 b Differences between contexts s (Y) Number of species promoting n ecosystem function per context Species overlp between pirs of contexts 0. Plces (P) Ecosystem functions (F) Environmentl chnges (C) Y nd P Y nd F Y nd C Number of study species 3 Number of differences between contexts P nd F F nd C Y nd P nd F Y nd F nd C Figure Sets of study species tht promoted ecosystem functioning.,the men number of species tht promoted ecosystem functioning within ech context incresed linerly (t , P, 0, R ) with the size of the species pool, such tht pproximtely 7% (men, 95% confidence intervls for slope: 0.7, 0.30) of the study species promoted ecosystem functioning within ech context. Error brs for ech study indicte 95% generlized liner model confidence intervls. b, Different sets of species promoted ecosystem functioning in different contexts (overlp, ), nd overlp between pirs of contexts decresed s the number of differences between contexts incresed (see Fig. ). Symbols indicte mens for ech specific type of overlp; horizontl dotted lines show 6 95% permuttion test confidence intervls; error brs for symbols nd brs indicte 95% bootstrp confidence intervls. Supplementry Dt indictes numbers of contexts for ech study. NATURE VOL MONTH 0 0 Mcmilln Publishers Limited. All rights reserved

3 RESEARCH Proportion of species promoting ecosystem functioning b.0 0. c.0 0. d Number of yers Number of plces Figure 3 The proportion of study species tht promoted ecosystem functioning incresed when more () yers, (b) plces, (c) ecosystem functions nd (d) environmentl chnge scenrios were independently considered. Solid blue lines indicte generlized liner model fits for ech study; dshed red line indictes grnd men generlized liner model fitted ecosystem functioning when more yers, plces, functions or environmentl chnge scenrios were considered (Fig. 3). These reltionships result from different species promoting ecosystem functioning in different contexts (Fig. b). Note tht if the one-dimensionl overlp vlues corresponding to ech pnel in Fig. 3 were one or zero, then these reltionships would be horizontl or linerly incresing, respectively 7. Our results re between these two extremes. After compring contexts within studies, dt from ll studies were combined to consider how the totl number of species tht promoted ecosystem functioning incresed with the totl number of contexts. We quntified the number of species tht promoted ecosystem functioning in rndom subset of ll possible combintions of our observed contexts (tht is, 00 pirs, 00 groups of three, etc.). The lrge increse in the number of species tht promoted ecosystem functioning s more contexts were considered (Fig. 4) is the result of different species promoting ecosystem functioning during different yers, t different plces, for different functions, under different environmentl chnge scenrios nd in different species pools. Considering ll of these fctors together suggests tht mny species will be needed to mintin ecosystem multifunctionlity t lrge sptio-temporl scles in chnging world. Consequently, the extinction (or decresed locl occurrence) of lmost ny of these species is expected to decrese ecosystem functioning nd services in t lest some contexts. Further study is needed to identify the processes tht explin why different species promoted ecosystem functioning in different contexts. The specific mechnisms involved probbly differed cross contexts, but previous results from these nd other biodiversity experiments 8 suggest tht complementrity (in time, spce, functionl effect trits nd functionl response trits) is generl explntion for this pttern. Our results revel new opportunities nd chllenges for prioritizing conservtion efforts nd predicting consequences of biodiversity declines. According to the precutionry principle, ll species should be conserved becuse we cnnot be certin which species ctully provide ecosystem services 9. Our results offer further support for the precutionry principle becuse most of the studied species were importnt t lest once, nd species exhibited context-dependent effects tht will be difficult to predict. If it is impossible or imprcticl to conserve ll species, then future studies could dditionlly consider how often (Supplementry Fig. nd Supplementry Dt) nd how much species influenced ecosystem functioning to determine which species re most importnt for mintining ecosystem functioning nd services. This will require creful considertion of mny contexts, becuse it is not possible to mke generl predictions or conclusions by considering few context-dependent phenomen 30. Future studies could determine whether some species consistently promote ecosystem functioning under environmentl conditions tht Number of ecosystem functions Number of environmentl chnges cross ll studies. Box plots summrize observed dt: blck bnd, medin; bottom nd top of boxes respectively correspond to lower nd upper qurtiles; error brs, 6.5 times the interqurtile rnge. See Supplementry Dt for the specific yers, plces, functions nd environmentl chnge scenrios considered in ech study. re currently common, or under environmentl chnge scenrios tht will probbly become incresingly common. Note tht even species tht hve smll effects could be importnt for mintining ecosystem functioning nd services if they hve lrge cumultive desirble effect cross mny contexts. For exmple, Eriochlo serice hd the smllest desirble effect on bove-ground biomss in the irrigted plots t the MEND Irrigtion experiment during 009, but promoted ecosystem functioning in 75% of the contexts in which it ws included. Future studies could lso determine which species promote ecosystem functioning in prticulr contexts tht re highly vlued by stkeholders. Note tht even species tht rrely promote (or often decrese) ecosystem functioning could be most importnt for mintining ecosystem functioning nd services within some contexts. For exmple, lthough Pscopyrum smithii only promoted ecosystem functioning in % of the contexts in which it ws included, it promoted soil crbon more thn ny other species in the Cedr Creek Biodiversity experiment during 004. Furthermore, note tht declines in locl diversity, which re fr more common thn globl extinctions, will lso decrese ecosystem functioning nd services within some contexts. Finlly, even the few species tht never promoted ecosystem functioning in these studies (Supplementry Fig. ) could promote ecosystem functioning Number of species promoting ecosystem functioning Number of functionl contexts Figure 4 The number of study species tht promoted ecosystem functioning incresed with the number of contexts considered cross ll studies. The points re the number of species tht promoted ecosystem functioning when 557 contexts were smpled from ll 557 contexts. The dshed line indictes the totl number of studied species (47), which restricts the upper limit for these vlues. The x xis includes vrition cross yers, plces, functions, environmentl chnge scenrios nd species pools. 0 Mcmilln Publishers Limited. All rights reserved 00 MONTH 0 VOL 000 NATURE 3

4 RESEARCH LETTER in other contexts, or be conservtion priority for other (for exmple, ethicl, esthetic) resons. Therefore, we encourge creful considertion of mny contexts when mking conservtion decisions nd predicting the consequences of biodiversity declines. METHODS SUMMARY Identifying the species tht promoted ecosystem functioning. For ech context, we modelled ecosystem functioning response vribles s function of the presence or bsence of ech study species t the plot level. We used bckwrdelimintion multiple regression to identify minimlly dequte model, bsed on the Akike informtion criterion (AIC) 7. This procedure ws performed with the stepaic function in the MASS pckge of R.. (see Methods). Species were considered to promote ecosystem functioning in context if they were included in the minimlly dequte model nd hd effects in the direction tht would usully be considered desirble from n ecosystem services perspective 7. Compring sets of species between pirs of contexts. We used Sørensen s similrity index to quntify the overlp between the sets of species tht promoted ecosystem functioning in pirs of contexts within ech study 7. This llowed us to test whether identicl (overlp 5 ), unique (overlp 5 0) or somewht different (0, overlp, ) sets of species promoted ecosystem functioning in different contexts. We lso tested whether overlp decresed s the number of differences between contexts incresed (Fig. ). Accumultion of species cross cross contexts. We quntified the ccumultion of species cross ech of the four dimensions of contexts tht we considered (Methods; Fig. ). A qusi-binomil generlized liner model ws fitted to determine how the proportion of species tht promoted ecosystem functioning incresed with the number of yers (or plces, functions, environmentl chnges), including study s fctor. This llowed us to describe the men trends within nd cross studies. We lso rndomly smpled combintions (tht is, 00 pirs, 00 groups of three, nd so on) of ll 557 contexts to determine how the number of species promoting ecosystem functioning incresed when ll of these fctors were considered together. Full Methods nd ny ssocited references re vilble in the online version of the pper t Received 8 Mrch; ccepted 0 June 0. Published online 0 August 0.. Butchrt, S. H. M. et l. Globl biodiversity: indictors of recent declines. Science 38, (00).. Loreu, M. et l. Biodiversity nd ecosystem functioning: current knowledge nd future chllenges. Science 94, (00). 3. Hooper, D. U. et l. Effectsof biodiversity on ecosystem functioning: consensus of current knowledge. Ecol. Monogr. 75, 3 35 (005). 4. Blvner, P. et l. Quntifying the evidence for biodiversity effects on ecosystem functioning nd services. Ecol. Lett. 9, (006). 5. Crdinle, B. J. et l. Effects of biodiversity on the functioning of trophic groups nd ecosystems. Nture 443, (006). 6. Neem, S., Bunker, D. E., Hector, A., Loreu, M. & Perrings, C. Biodiversity, Ecosystem ing, nd Humn Wellbeing: An Ecologicl nd Economic Perspective (Oxford Univ. Press, 009). 7. Crdinle, B. J. et l. The functionl role of producer diversity in ecosystems. Am. J. Bot. 98, (0). 8. Ridder, B. Questioning the ecosystem services rgument for biodiversity conservtion. Biodivers. Conserv. 7, (008). 9. Duffy, J. E. Why biodiversity is importnt to the functioning of rel-world ecosystems. Front. Ecol. Environ 7, (009). 0. McNughton, S. J. Diversityndstbilityofecologicl communities: comment on the role of empiricism in ecology. Am. Nt., (977).. Ychi, S. & Loreu, M. Biodiversity nd ecosystem productivity in fluctuting environment: the insurnce hypothesis. Proc. Ntl Acd. Sci. USA 96, (999).. Crine, J. M. et l. The role of plnt species in biomss production nd response to elevted CO nd N. Ecol. Lett. 6, (003). 3. Tilmn, D., Reich, P. B. & Knops, J. M. H. Biodiversity nd ecosystem stbility in decde-long grsslnd experiment. Nture 44, (006). 4. Zvlet, E. S., Psri, J. R., Hulvey, K. B. & Tilmn, G. D. Sustining multiple ecosystem functions in grsslnd communities requires higher biodiversity. Proc. Ntl Acd. Sci. USA 07, (00). 5. Loreu, M., Mouquet, N. & Gonzlez, A. Biodiversity s sptil insurnce in heterogeneous lndscpes. Proc. Ntl Acd. Sci. USA 00, (003). 6. Griffin, J. N. et l. Sptil heterogeneity increses the importnce of species richness for n ecosystem process. Oikos 8, (009). 7. Hector, A. & Bgchi, R. Biodiversity nd ecosystem multifunctionlity. Nture 448, (007). 8. Gmfeldt, L., Hillebrnd, H. & Jonsson, P. R. Multiple functions increse the importnce of biodiversity for overll ecosystem functioning. Ecology 89, 3 3 (008). 9. Reich, P. B. et l. Plnt diversity enhnces ecosystem responses to elevted CO nd nitrogen deposition. Nture 40, (00). 0. Weigelt, A., Weisser, W. W., Buchmnn, N. & Scherer-Lorenzen, M. Biodiversity for multifunctionl grsslnds: equl productivity in high-diversity low-input ndlowdiversity high-input systems. Biogeosciences 6, (009).. Wilsey, B. J., Teschner, T. B., Dneshgr, P. P., Isbell, F. I. & Polley, H. W. Biodiversity mintennce mechnisms differ between ntive nd novel exotic-dominted communities. Ecol. Lett., (009).. Isbell, F. I. & Wilsey, B. J. Incresing ntive, but not exotic, biodiversity increses boveground productivityin ungrzed ndintensely grzed grsslnds. Oecologi 65, (0). 3. Isbell, F. I., Losure, D. A., Yurkonis, K. A. & Wilsey, B. J. Diversity productivity reltionships intwo ecologicllyrelistic rritynd extinctionscenrios. Oikos 7, (008). 4. Tilmn, D. et l. Diversity nd productivity in long-term grsslnd experiment. Science 94, (00). 5. vn Ruijven, J. & Berendse, F. Long-term persistence of positive plnt diversity productivity reltionship in the bsence of legumes. Oikos 8, 0 06 (009). 6. Kirwn, L. et l. Evenness drives consistent diversity effects in intensive grsslnd systems cross 8 Europen sites. J. Ecol. 95, (007). 7. Millennium Ecosystem Assessment. Ecosystems nd Humn Well-being: Synthesis (Islnd Press, 005). 8. Crdinle, B. J. et l. Impcts of plnt diversity on biomss production increse through time becuse of species complementrity. Proc. Ntl Acd. Sci. USA 04, (007). 9. Ehrlich, P. & Ehrlich, A. Extinction: The Cuses nd Consequences of the Disppernce of Species (Victor Gollncz, 98). 30. Lwton, J. H. Are there generl lws in ecology? Oikos 84, 77 9 (999). Supplementry Informtion is linked to the online version of the pper t Acknowledgements We thnk J. Byrnes, L. Gmfeldt nd M. Emmerson for comments on n erlier version of this mnuscript. We thnk the Swiss SystemsX.ch inititive (IPP-008/3) for supporting this project. The BIODEPTH project ws funded by the Europen Commission within the Frmework IV Environment nd Climte Progrmme (ENV-CT ) nd by the Swiss Federl Office for Eduction nd Science (Project EU-3). TheJenExperimentws fundedbythe DeutscheForschungsgemeinschft (DFG, FOR 456), Friedrich Schiller University of Jen, Mx Plnck Society, University of Zurich, Swiss Ntionl Science Foundtion (300AO-0753) nd ETH Zurich. The Wgeningen experiment ws funded by the Dutch Orgnistion for Scientific Reserch (NWO) within the frmework of the Biodiversity Progrmme. Work on the Agrodiversity experiment ws funded by the EU Commission through COST Action 85 nd Science Foundtion Irelnd (09/RFP/EOB546). The BioCON experiment ws funded by the US Deprtment of Energy (DOE/DE-FG0-96ER69) nd the US Ntionl Science Foundtion (Biocomplexity 03057, LTER DEB 9497, DEB , DEB nd LTREB DEB ). The MEND Irrigtion, BioGEN nd Rrity Extinction experiments were funded by the US Ntionl Science Foundtion (DEB ). The Cedr Creek Biodiversity experiment ws funded by the US Ntionl Science Foundtion. M.L. ws supported by The Nturl Sciences nd Engineering Reserch Council of Cnd (Discovery Grnt) nd the Cnd Reserch Chir progrm. Author Contributions F.I. conceived the project; J.C., A.H., F.I., P.B.R., M.S.-L., B.S., D.T., J.v.R., A.W. nd B.J.W. designed nd conducted experiments; F.I. nd V.C. nlysed the dt, with input from A.H. nd M.L.; F.I. wrote the pper with input from ll uthors. Author Informtion Reprints nd permissions informtion is vilble t The uthors declre no competing finncil interests. Reders re welcome to comment on the online version of this rticle t Correspondence nd requests for mterils should be ddressed to F.I. (forest.isbell@gmil.com). 4 NATURE VOL MONTH 0 0 Mcmilln Publishers Limited. All rights reserved

5 RESEARCH METHODS Identifying the species tht promoted ecosystem functioning. For ech context, we modelled ecosystem functioning response vribles s function of the presence or bsence of ech study species t the plot level. We used bckwrdelimintion multiple regression nlysis to identify minimlly dequte model, bsed on the AIC 7. This procedure ws performed with the stepaic function in the MASS pckge of R... Specificlly, for ech context, we strted with full model tht included min effect for ech study species nd n intercept. The stepaic function then removed ech species, one t time, from this full model nd compred the AIC vlues of the resulting simpler models with the AIC vlue of the full model. If the AIC vlue for ny of the simpler models ws smller thn the AIC vlue for the full model, then the vrible whose removl resulted in the lrgest decrese in AIC ws permnently removed from the full model. This bckwrd-deletion process ws repeted until the removl of ny species resulted in model with higher AIC vlue. The minimlly dequte model tht resulted from this process contined the most prsimonious set of species influencing ecosystem functioning. These species were considered to promote ecosystem functioning if they hd effects in the direction tht would usully be considered desirble from n ecosystem services perspective 7. Positive effects were considered desirble for ll functions except for soil inorgnic nitrogen nd light vilbility t ground level, where negtive effects re consistent with lower levels of unconsumed resources 7. We did not use seprte definitions of desirble effects for different species (for exmple, positive effects of legumes on soil nitrogen might be considered desirble) to be consistent with previous studies 7,8, to be conservtive nd becuse it my not be possible to mnge simultneously for both positive nd negtive effects. This modelling pproch is conservtive in severl wys. Previous pproches for determining the number of species tht promoted ecosystem functioning could hve been bised by not llowing species to decrese ecosystem functioning 8 or by not identifying which species ctully influenced ecosystem functioning 4. Furthermore, including species interctions in these or other models would probbly increse the proportion of study species tht promoted ecosystem functioning within ech context,6. For exmple, some species perform poorly in monocultures, but interct positively with other species in mixtures (for exmple, grss legume interctions) 3. Our pproch would underestimte the desirble effects of these species. Also, the presence or bsence model tht we used would be especilly conservtive for experimentl designs tht concentrte on vrying evenness rther thn richness, such s the simplex design used in the Agrodiversity study 6. Additionlly, our results were qulittively similr, but less conservtive, when we used model-verging pproch implemented in the glmulti pckge (version -3) of R 3. To compre the number of species tht promoted ecosystem functioning cross studies, we used qusi-poisson generlized liner model with study s min effect. This procedure ws performed with the generlized liner model function in the stts pckge of R. The qusi-mximum-likelihood version of the Poisson generlized liner model ccounts for over- or under-dispersion in the dt. We used the confint.glm function in the MASS pckge of R to obtin the 95% confidence intervls. To quntify the proportion of study species tht promoted ecosystem functioning, we regressed the men number of species tht promoted ecosystem functioning per context on the number of study species (tht is, the number of plnted species tht were present t lest once in biomss smples) with no intercept. Compring sets of species between pirs of contexts. After identifying the sets of species tht promoted ecosystem functioning in ech context, we quntified the overlp between these sets of species to test whether different sets of species promoted ecosystem functioning in different contexts. All overlp comprisons were mde within studies. Overlp between contexts nd b ws quntified by Sørensen s similrity index 7 : j o~ E \E b j 0:5ðjE jzje b jþ where je j is the number of species tht promoted ecosystem functioning in context nd je \E b j is the number of species tht promoted ecosystem functioning in both contexts. First, one-dimensionl overlp ws quntified between pirs of contexts tht only differed in one wy (Fig. b, c). For exmple, multi-yer overlp ws quntified between ech pir of contexts tht differed only in which yer ecosystem functioning ws mesured (tht is, plce, function nd environmentl chnge scenrios were the sme in both contexts). This llowed us to test whether identicl (overlp 5 ), unique (overlp 5 0) or somewht different (0, overlp, ) sets of species promoted ecosystem functioning in different contexts. Next, multi-dimensionl overlp ws quntified between pirs of contexts tht differed in two or three wys (Fig. d). This llowed us to test whether overlp decresed s the number of differences between contexts incresed (Fig. ). For ech type of overlp, we used non-prmetric bootstrp, with correction for bis 33,34, to build 95% confidence intervls. We re-smpled the observed contexts with replcement to generte ech of,000 bootstrp dt sets. For ech of these bootstrp dt sets, we computed the verge overlp cross ll pirs of contexts tht were relevnt (tht is, for the prticulr type of overlp being considered). We used this bootstrp pproch to control for the non-independence of pirwise comprisons tht hd one context in common. We then used n exct permuttion pproch 34 to test whether the observed overlp vlues differed from the expected null vlue (the null hypothesis being tht overlp vried cross contexts independent of context ttributes: yer, plce, function nd environmentl chnge scenrio). Within ech study, we permuted context dt (tht is, the sequence of ones or zeros indicting whether ech species hd desirble effect or not) with respect to context ttributes. For ech of,000 permuttions, we computed the verge overlp cross ll pirs of contexts tht were relevnt (tht is, for the prticulr type of overlp being considered). We used the null distribution of overlp obtined from these rndom permuttions to test whether the observed vlue ws significntly lower (tht is, in the lowest.5 percentiles) or significntly higher (tht is, in the top.5 percentiles) thn the null. We used this test becuse it does not ssume tht study species hd independent responses to context ttributes, nd thus it should be robust to the presence of functionl groups. Note tht there could be correltions between contexts owing to repeted mesurements cross yers. These correltions could influence overlp estimtes nd tests tht ssume independent observtions. For exmple, positive correltions between repeted mesurements during consecutive yers could led to () overestimtes of multi-yer (Y) overlp, nd () smller estimtes of overlp between two different yers t two different plces thn between two different yers t one plce (tht is, Y nd plces (P) overlp less thn Y overlp). These potentil correltions hd little influence on our results becuse multi-yer overlp estimtes were much less thn, nd Y nd P overlp estimtes were not less thn Y overlp estimtes (Fig. ). Nevertheless, we encourge future studies to consider these correltions when interpreting overlp estimtes. Accumultion of species cross contexts. We quntified the ccumultion of species cross ech of the four dimensions of contexts tht we considered (Fig. ). For exmple, bove-ground biomss ws smpled during 3 yers t the Cedr Creek Biodiversity experiment. To determine the extent to which more species promoted bove-ground biomss s more yers were considered, we smpled ll combintions of these 3 contexts (tht is, ll pirs, groups of three, etc.), nd recorded the number of unique species tht promoted ecosystem functioning, nd the number of unique yers, for ech combintion. This ws repeted for ech function, t ech plce, under ech environmentl chnge scenrio. These results re summrized in Fig. 3. A qusi-binomil generlized liner model ws fitted to determine how the proportion of species tht promoted ecosystem functioning incresed with the number of yers, including study s fctor. This llowed us to describe the men trends within nd cross studies. We lso rndomly smpled combintions (tht is, 00 pirs, 00 groups of three, etc.) of ll 557 contexts to determine how the number of species promoting ecosystem functioning incresed when ll of these fctors were considered together. 3. Nyfeler, D. et l. Strong mixture effects mong four species in fertilized griculturl grsslnd led to persistent nd consistent trnsgressive overyielding. J. Appl. Ecol. 46, (009). 3. Clcgno, V. & de Mzncourt, C. glmulti: n R pckge for esy utomted model selection with (generlized) liner models. J. Stt. Softw. 34, 9 (00). 33. Efron, B. & Tibshirni, R. Bootstrp methods for stndrd errors, confidence intervls, nd other mesures of sttisticl ccurcy. Stt. Sci., (986). 34. Mnly, B. F. J. Rndomiztion, Bootstrp nd Monte Crlo MethodsinBiologynd edn (Chpmn nd Hll, 997). 0 Mcmilln Publishers Limited. All rights reserved