Yoann Le Bagousse-Pinguet

Santiago Soliveres
email: santiagosoliverescodina@gmail.com

Nicolas Gross
email: nicolas.gross@inra.fr

Rubén Torices

Miguel Berdugo

Fernando T Maestre

Phylogenetic, functional, and taxonomic richness have both positive and negative effects on ecosystem multifunctionality

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

species on the multifunctionality of 123 drylands from six continents. Our results highlight the importance of the phylogenetic and functional attributes of subordinate species as key drivers of multifunctionality. In addition to a higher taxonomic richness, we found that simultaneously increasing the richness of early diverging lineages and the functional redundancy between species increased multifunctionality. In contrast, the richness of most recent evolutionary lineages and the functional and phylogenetic attributes of dominant plant species (mass-ratio effects) were weakly correlated with multifunctionality. However, they were important drivers of individual nutrient cycles. By identifying which biodiversity attributes contribute the most to multifunctionality, our results can guide restoration efforts aiming to maximize either multifunctionality or particular nutrient cycles, a critical step to combat dryland desertification worldwide.

Significance

Biodiversity is declining globally, but its different taxonomic, functional and evolutionary attributes are doing so at a different pace. Understanding how these attributes influence ecosystem functioning is crucial to better predict the ecological consequences of biodiversity loss. Based on a survey of 123 drylands worldwide, our results highlight the phylogenetic and functional attributes of subordinate species as key drivers of the provision of multiple ecosystem functions simultaneously (multifunctionality). Our study expands our understanding of the relationship between biodiversity and multifunctionality by identifying the diversity of early diverging lineages and functional redundancy as important biodiversity attributes to prioritize in conservation and restoration programs aimed at promoting dryland multifunctionality worldwide.

Key-words

Functional diversity │ Mass-ratio hypothesis │ Nutrient cycling │ Phylogenetic diversity │ Taxonomic diversity. \body

Introduction

Understanding the relationship between biodiversity and the capacity of ecosystems to perform multiple functions simultaneously (multifunctionality) has been a core ecological research topic in the last decade [START_REF] Gamfeldt | Multiple functions increase the importance of biodiversity for overall ecosystem functioning[END_REF][START_REF] Isbell | High plant diversity is needed to maintain ecosystem services[END_REF][START_REF] Maestre | Plant species richness and ecosystem multifunctionality in global drylands[END_REF][START_REF] Soliveres | Biodiversity at multiple trophic levels is needed for ecosystem multifunctionality[END_REF]. In recent years, considerable research efforts have been devoted to explore how the biodiversityecosystem multifunctionality relationship (B-EMF relationship hereafter) is contingent upon the number and identity of ecosystem functions considered (e.g., refs. [START_REF] Meyer | Biodiversity-multifunctionality relationships depend on identity and number of measured functions[END_REF][START_REF] Gamfeldt | Revisiting the biodiversity-ecosystem multifunctionality relationship[END_REF]). In contrast, how multiple attributes of biodiversity such as the richness and abundance of species (taxonomic diversity), the diversity of evolutionary lineages (phylogenetic diversity) and that of the traits related to resource-use strategy (functional diversity) simultaneously influence ecosystem functioning remains poorly investigated [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity--ecosystem-function relationships[END_REF][START_REF] Cadotte | Phylogenetic diversity promotes ecosystem stability[END_REF][START_REF] Naeem | Biodiversity as a multidimensional construct : a review , framework and case study of herbivory ' s impact on plant biodiversity[END_REF][START_REF] Craven | Multiple facets of biodiversity drive the diversity-stability relationship[END_REF][START_REF] Roger | Effects of multiple dimensions of bacterial diversity on functioning, stability and multifunctionality[END_REF], particularly at the global scale. Since these biodiversity attributes do not necessarily correlate [START_REF] Brum | Global priorities for conservation across multiple dimensions of mammalian diversity[END_REF][START_REF] Tucker | On the relationship between phylogenetic diversity and trait diversity[END_REF], assessing how they simultaneously influence multifunctionality is not only crucial to expand our fundamental understanding of the B-EMF relationships, but also to prioritize relevant biodiversity attributes in global conservation programs, and to improve management actions to preserve and restore terrestrial ecosystems [START_REF] Brum | Global priorities for conservation across multiple dimensions of mammalian diversity[END_REF][START_REF] Balvanera | Linking biodiversity and ecosystem services: Current uncertainties and the necessary next steps[END_REF]. While most B-EMF studies have focused on species richness (1-3), functional diversity is also a key driver of multifunctionality [START_REF] Mouillot | Functional structure of biological communities predicts ecosystem multifunctionality[END_REF][START_REF] Valencia | Functional diversity enhances the resistance of ecosystem multifunctionality to aridity in Mediterranean drylands[END_REF][START_REF] Gross | Functional trait diversity maximizes ecosystem multifunctionality[END_REF]. Higher functional diversity could enhance multifunctionality either because co-occurring species with contrasting trait values increase the overall resource utilization [START_REF] Naeem | Declining biodiversity can alter the performance of ecosystems[END_REF] or by including species that strongly affect ecosystem functioning ("sampling effect"; ref. [START_REF] Tilman | Plant diversity and ecosystem productivity[END_REF]). The phylogenetic diversity of plant communities can also influence ecosystem functions such as biomass production [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity--ecosystem-function relationships[END_REF][START_REF] Cadotte | Phylogenetic diversity promotes ecosystem stability[END_REF]. However, how phylogenetic diversity influences the B-EMF relationships remains unclear [START_REF] Cadotte | Explaining ecosystem multifunction with evolutionary models[END_REF], and we do not know whether early diverging vs. recent evolutionary events ultimately influence ecosystem functioning [START_REF] Harmon | Evolutionary diversification in stickleback affects ecosystem functioning[END_REF]. Phylogenetic diversity is a key biodiversity attribute when it effectively encompasses unmeasured biological traits that are relevant for ecosystem functioning [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity--ecosystem-function relationships[END_REF][START_REF] Venail | Species richness, but not phylogenetic diversity, influences community biomass production and temporal stability in a re-examination of 16 grassland biodiversity studies[END_REF].

As such, considering simultaneously phylogenetic diversity, which often grasps traits that are not typically measured (e.g. those related to plant-pathogen or plant-mycorrhiza interactions [START_REF] Gilbert | Phylogenetic signal in plant pathogen-host range[END_REF][START_REF] Montesinos-Navarro | Evidence for phylogenetic correlation of plant-AMF assemblages?[END_REF], and measured traits could better account for the many dimensions of trait diversity exhibited by plant species [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity--ecosystem-function relationships[END_REF][START_REF] Tucker | On the relationship between phylogenetic diversity and trait diversity[END_REF]. Therefore, doing so could provide greater insights on how the multidimensionality of biodiversity influences multifunctionality.

No matter the taxonomic, phylogenetic or functional attribute of biodiversity we look at, focusing solely on richness ignores the overwhelming effect that dominant species may have on ecosystem functioning [START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF][START_REF] Garnier | Plant Functional Markers Capture Ecosystem Properties[END_REF]. According to the mass-ratio hypothesis [START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF], the effect of plant species on ecosystem functioning is directly proportional to their biomass (mass-ratio effects), and thus is relatively insensitive to the richness of subordinate species [START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF]. This hypothesis was originally framed for individual functions related to biomass production and carbon cycling [START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF][START_REF] Garnier | Plant Functional Markers Capture Ecosystem Properties[END_REF][START_REF] Smith | Dominant species maitain ecosystem function with non-random species loss[END_REF]. However, the importance of the dominant species seems less clear when focusing on multifunctionality [START_REF] Lyons | Rare species and ecosystem functioning[END_REF][START_REF] Soliveres | Locally rare species influence grassland ecosystem multifunctionality Locally rare species influence grassland ecosystem multifunctionality[END_REF], as it may depend on the attribute of biodiversity or the function considered.

To better understand the functional consequences of biodiversity changes occurring worldwide, we gathered data from 123 dryland ecosystems from six continents, including steppes, savannas and shrublands (SI Appendix, Fig. S1), to investigate how multiple plant diversity attributes simultaneously influence multifunctionality. We used eight complementary biodiversity metrics that account for changes in the taxonomic, phylogenetic (early diverging and recent lineages) and functional diversity of plant communities (see methods; SI Appendix, Fig. S2, Tables S1 andS2). Within this framework, our selection included metrics that were weighted and non-weighted by species abundance to disentangle the effect of dominant (massratio effects) vs. that of subordinate (richness effects) plant species on multifunctionality. After controlling for important climatic, soil and geographic variables, we related multiple biodiversity metrics to four indices of multifunctionality using the multiple thresholds approach [START_REF] Byrnes | Investigating the relationship between biodiversity and ecosystem multifunctionality: Challenges and solutions[END_REF]. The four indices were: 1) multifunctionality (based on 11 weakly correlated functions), 2) carbon cycling (C; including organic carbon concentration; pentose content and aboveground plant productivity), 3) nitrogen cycling (N; including nitrate concentration, dissolved organic nitrogen, protein content and potential nitrification) and 4) phosphorus cycling (P; including available, inorganic and total phosphorus, and phosphatase enzymatic activity) (SI Appendix, Table S3). We tested the core hypothesis that considering multiple biodiversity attributes simultaneously increases the strength of biodiversity effects on multifunctionality.

Results

The biodiversity metrics studied were strongly related to multifunctionality, even after accounting for the strong influence of geographic, climate and soil properties on ecosystem functioning (Fig. 1). Biodiversity attributes explained up to 18% of multifunctionality (total variance), and up to 25%, 22% and 27% of the variation in the indices derived for C, N and P cycling, respectively. While species richness alone explained on average ~ 5% of variation in multifunctionality and up to 8% for C cycling, the inclusion of multiple biodiversity attributes enhanced the effect of biodiversity on multifunctionality by three-fold. Functional, phylogenetic and taxonomic biodiversity attributes were all selected in the most parsimonious models as significant predictors of multifunctionality, indicating that they have complementary effects on C, N and P cycling.

Richness effects [the sum of explained variance of species richness and of non-weighted functional (FDIS) and phylogenetic (PSV, MNTD) metrics] explained between 76-100% of the biotic effects on multifunctionality (Fig. 2a). In contrast, the importance of dominant species through mass-ratio effects (i.e. the metrics weighted by the abundance of the species) increased when considering each nutrient cycle individually (Fig. 2b,c,d). Mass-ratio effects contributed, on average, to 51%, 41% and 63% of the explained variance for C, N and P cycling, respectively. Mass-ratio effects were mostly related to the functional identity (CWM-SLA and CWM-H) of dominant species rather than to their functional/phylogenetic diversities. In summary, richness effects due to subordinate species were the strongest predictors of multifunctionality, while mass-ratio effects better explained C, N and P cycling separately.

The net relationship between biodiversity and multifunctionality was generally positive, although weak, and even null when high multifunctionality thresholds were considered (Fig. 3a). This result was consistent regardless of the number of biodiversity attributes considered (Fig. 4) but varied with the nutrient studied. Thus, despite the larger amount of variance explained (Fig. 1), the net effect of biodiversity on ecosystem functioning was not stronger when multiple biodiversity attributes were included (Fig. 4). The inconsistency between variance explained and the net effect observed was mainly caused by contrasting effects of individual biodiversity attributes on different nutrient cycles taken separately and on overall multifunctionality.

When evaluating the sets of functions separately, we observed positive relationships between biodiversity and C and P cycling (Fig. 3b andd), which turned negative in the case of N cycling (Fig. 3c). In addition, we observed contrasting relationships depending on the biodiversity attribute considered (Fig. 5). Species richness and phylogenetic diversity (PSV) were positively related to multifunctionality (Fig. 5a), and to C, N and P cycling (Fig. 5b,c,d).

However, FDIS (describing the dispersion of functional trait values observed within communities) was negatively related to multifunctionality, C and N cycling. These results highlight that particular combinations of biodiversity attributes are needed to maximize either targeted nutrient cycles or overall multifunctionality.

Discussion

We investigated how multiple biodiversity attributes (taxonomic, phylogenetic and functional richness and mass-ratio effects) simultaneously influenced the multifunctionality of 123 drylands worldwide. Together, these attributes explained up to 27% of variation in multifunctionality across a wide range of geographic contexts, climatic and soil conditions. The simultaneous effect of multiple biodiversity attributes on multifunctionality stresses the need to move from a single taxonomic to a more multidimensional perspective of biodiversity to better grasp its complex effects on the functioning of terrestrial ecosystems. The importance of considering multiple biodiversity attributes has been recently shown for biomass production and its temporal variability, or for N availability [START_REF] Naeem | Biodiversity as a multidimensional construct : a review , framework and case study of herbivory ' s impact on plant biodiversity[END_REF][START_REF] Craven | Multiple facets of biodiversity drive the diversity-stability relationship[END_REF][START_REF] Roger | Effects of multiple dimensions of bacterial diversity on functioning, stability and multifunctionality[END_REF][START_REF] García-Palacios | Climate mediates the biodiversity-ecosystem stability relationship globally[END_REF]. Our results expand this research by highlighting how multiple biodiversity attributes differentially impact both multifunctionality and major nutrient cycles at the global scale.

Our study helps to reconcile two influential hypotheses on the effects of biodiversity on ecosystem functioning [START_REF] Tilman | Plant diversity and ecosystem productivity[END_REF][START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF]. Mass-ratio effects (i.e., the abundance-weighted metrics considered, accounting for the effect of the most dominant species) were the strongest predictors related to individual nutrient cycles, but were weakly correlated with multifunctionality. As such, the Mass-ratio hypothesis may not apply when considering multiple functions simultaneously (see also ref. [START_REF] Lyons | Rare species and ecosystem functioning[END_REF]. In contrast, richness effects (those mainly driven by subordinate species) were the almost exclusive biotic drivers of multifunctionality in the drylands studied. Our results show that richness effects increase in importance when aiming at maximizing multiple ecosystem functions simultaneously. This matches the common view that species are unique, i.e. that a high number of co-occurring subordinate species can promote different functions at different times and places, therefore maximising the performance of multiple functions simultaneously [START_REF] Gamfeldt | Multiple functions increase the importance of biodiversity for overall ecosystem functioning[END_REF][START_REF] Isbell | High plant diversity is needed to maintain ecosystem services[END_REF][START_REF] Meyer | Biodiversity-multifunctionality relationships depend on identity and number of measured functions[END_REF][START_REF] Gamfeldt | Revisiting the biodiversity-ecosystem multifunctionality relationship[END_REF]. Our study extends the view of taxonomic diversity to the phylogenetic and functional attributes of subordinate species as important predictors of multifunctionality in terrestrial ecosystems.

Biodiversity had an overall positive effect on multifunctionality when considering multiple biodiversity attributes simultaneously. However, and contrarily as hypothesized, this effect was relatively weak (Fig. 3a; Fig. 4). The observed weak B-EMF relationship resulted first from contrasting relationships among the sets of functions relating to different biogeochemical cycles (Fig. 3b, c andd). Also, we observed contrasting effects among the studied biodiversity attributes (Fig. 5). As a result, biodiversity effects on multifunctionality did not increase when considering multiple biodiversity attributes simultaneously (Fig. 4).

These contrasting effects match with recent evidences reporting the occurrence of diverse (positive, neutral and negative) biodiversityecosystem functioning relationships in real world ecosystems, especially when considering ecosystem functions other than plant biomass [START_REF] Soliveres | Biodiversity at multiple trophic levels is needed for ecosystem multifunctionality[END_REF][START_REF] Roger | Effects of multiple dimensions of bacterial diversity on functioning, stability and multifunctionality[END_REF][START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF][START_REF] Jiang | On the importance of the negative selection effect for the relationship between biodiversity and ecosystem functioning[END_REF]. Our findings highlight that B-EMF relationships do not only depend on the combination of functions studied (e.g., ref. [START_REF] Gamfeldt | Revisiting the biodiversity-ecosystem multifunctionality relationship[END_REF]), but also on the identity of biodiversity attributes considered.

Therefore, ignoring the variety of attributes that biodiversity encompasses, such as taxonomic, phylogenetic and functional diversity, or the influence of subordinate vs. dominant species may largely bias our ability to predict the consequences of biodiversity loss for the functioning of terrestrial ecosystems.

In opposition to the positive effect of species richness on multifunctionality and on C, N and P cycling, functional richness (FDIS: the trait dispersion within communities) was negatively related to multifunctionality, C and N cycling (Fig. 5). This negative effect of FDIS is in line with previous observed negative effects of trait dispersion on dryland multifunctionality [START_REF] Gross | Functional trait diversity maximizes ecosystem multifunctionality[END_REF], as well as on the production and stability of biomass in several ecosystems [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity--ecosystem-function relationships[END_REF][START_REF] Craven | Multiple facets of biodiversity drive the diversity-stability relationship[END_REF][START_REF] García-Palacios | Climate mediates the biodiversity-ecosystem stability relationship globally[END_REF]. The contrasting effect between species richness and FDIS highlights the importance of functional redundancy within the studied communities to maintain high multifunctionality levels. This may be particularly true for communities experiencing strong abiotic stress such as dryland plant communities. Maximizing functional redundancy between species in drylands (31) may limit the inclusion of mal-adapted plant strategies particularly under drier conditions, which in turn may alter plant-soil feedbacks and accelerate land degradation and desertification processes [START_REF] Valencia | Functional diversity enhances the resistance of ecosystem multifunctionality to aridity in Mediterranean drylands[END_REF][START_REF] Gross | Functional trait diversity maximizes ecosystem multifunctionality[END_REF][START_REF] Ochoa-Hueso | Soil fungal abundance and plant functional traits drive fertile island formation in global drylands[END_REF].

Phylogenetic diversity played a significant role as driver of multifunctionality even after controlling for taxonomic and functional diversity, confirming the importance to consider this attribute in future B-EMF research. Phylogenetic diversity may reflect additional axes of functional specialization that are neither captured by maximum plant height nor by SLA, two fundamental traits reflecting plant resource-use strategies [START_REF] Díaz | The global spectrum of plant form and function[END_REF]. Phylogenetic diversity may effectively take into account "hidden traits" that are particularly relevant for the functioning of drylands (e.g. traits related to pathogen infection, pollination rates or mycorrhizal associations [START_REF] Gilbert | Phylogenetic signal in plant pathogen-host range[END_REF] or to plant demographic strategies [START_REF] Salguero-Gómez | The compadre Plant Matrix Database: An open online repository for plant demography[END_REF]) and thus are required to properly model B-EMF relationships. Dryland multifunctionality increased with a higher diversity of evolutionary lineages (PSV). The coexistence of species from both quaternary and tertiary periods are commonly observed in arid regions as a consequence of facilitative interactions [START_REF] Valiente-Banuet | Facilitation can increase the phylogenetic diversity of plant communities[END_REF]. Also, PSV had opposite effects on multifunctionality compared to FDIS, indicating that maximizing both the phylogenetic distinctiveness and functional redundancy within species-rich communities are complementary drivers of higher ecosystem multifunctionality. Our results also reflect that evolutionary distinct lineages shared similar maximum plant height and SLA attributes (see also [START_REF] Cornwell | Functional distinctiveness of major plant lineages[END_REF]). This pattern may arise from both species filtering with suitable trait values and the adaptive evolution of traits in local lineages. A deeper understanding of the role of these processes could shed light on the importance of natural selection and convergent evolution as key evolutionary processes involved in the functioning of dryland ecosystems.

To further understand the linkages between the diversity of evolutionary lineages and multifunctionality, we investigated such relationships both at the most recent evolutionary events (tip level: MNTD) and across the whole tree (PSV). This approach revealed that both MNTD and PSV are related to ecosystem functioning in drylands worldwide (Figs. 1 and5).

While we observed exclusive effects of PSV on multifunctionality, those of MNTD were even stronger when considering individual nutrient cycles (positive and negative for C and N cycling, respectively). These B-EMF patterns indicate an increase in the importance of early diverging lineages with increasing the number of functions considered, i.e. that the diversity of more ancient lineages increases present-day multifunctionality. Alongside, recent evolutionary events might reflect recent innovations promoting C cycling and productivity (Fig. 5, SI Appendix, Tables S4 andS5) without altering the level of multifunctionality. Our study was not designed to specifically investigate the changes in B-EMF relationships over evolutionary times. Nonetheless, the contrasted B-EMF patterns observed at two phylogenetic scales open new horizons on the importance of species evolutionary history for the emergence of "multifunctional" ecosystems, e.g. for tracking when biodiversity became an important multifunctionality driver.

Our results emphasize the need to consider the multidimensionality of biodiversity to better understand B-EMF relationships. The biodiversity attributes involved in individual nutrient cycles were mostly related to mass-ratio effects. In contrast, richness effects enhanced multifunctionality through the diversity of early diverging lineages and functional redundancy within species-rich communities. In an era of global biodiversity crisis, our results can contribute to shape conservation, restoration and management efforts based on species attributes to prioritize targeted nutrient cycles or overall multifunctionality, and therefore optimizing the limited budgets allocated to maintain ecosystem functioning and associated services in drylands, the Earth´s largest biome.

Methods

Characteristics of the study sites. We obtained field data from 123 sites located in 13 countries (SI Appendix, Fig. S1). These sites (30 m x 30 m) are representative from the major vegetation types found in drylands and differ widely in plant species richness and environmental conditions (see further details in SI Appendix, Fig. S1).

Ecosystem multifunctionality. We assessed ecosystem functioning at each site using 11 variables that provide a comprehensive and balanced design of C (organic C, pentose, plant productivity), N (nitrate, dissolved organic N, proteins, potential N transformation rate) and P (total and available P, activity of phosphatase and inorganic P) cycling and storage. These variables (hereafter functions) are uncorrelated with each other (see details in SI Appendix, Table S3), and together constitute a good proxy for nutrient cycling, biological productivity, and build-up of nutrient pools [START_REF] Maestre | Plant species richness and ecosystem multifunctionality in global drylands[END_REF][START_REF] Whitford | Ecology of desert systems[END_REF][START_REF] Reynolds | Global desertification: building a science for dryland development[END_REF][START_REF] Delgado-Baquerizo | Microbial diversity drives multifunctionality in terrestrial ecosystems[END_REF].

We calculated four indices based either on all measured functions (multifunctionality)

or on different set of functions representing C (three functions), N (four functions) and P (four functions) cycling (SI Appendix, Table S3). We standardized separately the 11 functions measured (F) using the Z-score transformation:

𝑍 -𝑠𝑐𝑜𝑟𝑒 𝑖𝑗 = 𝐹 𝑖𝑗 -𝑀𝑒𝑎𝑛 𝐹 𝑖 𝑆𝐷 𝐹 𝑖 Equation (2);
where Fij is the value of a function i in the community j, Mean Fi and SD Fi are the mean and the standard deviation of the function Fi calculated for the 123 studied communities, respectively. We used a multiple threshold approach to evaluate whether multiple functions are simultaneously performing at high levels [START_REF] Byrnes | Investigating the relationship between biodiversity and ecosystem multifunctionality: Challenges and solutions[END_REF]. In short, this approach counts the number of functions that reach a given threshold (as the % of the maximum value of each of the functions observed in the dataset). This maximum is taken as the top 5% values for each function observed across all study sites [START_REF] Zavaleta | Sustaining multiple ecosystem functions in grassland communities requires higher biodiversity[END_REF]. Considering multiple thresholds allows a better understanding of how biodiversity affects ecosystem functioning, and to account for potential trade-offs between the functions evaluated [START_REF] Byrnes | Investigating the relationship between biodiversity and ecosystem multifunctionality: Challenges and solutions[END_REF]. We considered thresholds between 20% and 80% (every 5%), since care should be taken to avoid over-interpreting results at very high or low thresholds [START_REF] Lefcheck | Biodiversity enhances ecosystem multifunctionality across trophic levels and habitats[END_REF]. Each calculated threshold (T) was smoothed by using a moving average with intervals [T-10%, T+10%]. We used this approach for all functions together, and also for those that only relate to the C, N and P cycling. We also calculated multifunctionality as the average of the standardized values across all functions [START_REF] Maestre | Plant species richness and ecosystem multifunctionality in global drylands[END_REF][START_REF] Mouillot | Functional structure of biological communities predicts ecosystem multifunctionality[END_REF], obtaining results similar to those presented in the main text (SI Appendix, Fig. S3).

Plant diversity attributes and biodiversity metrics. Biodiversity effects on ecosystem

functioning can arise from 1) dominant plant species through mass-ratio effects (25), and 2) subordinate species through richness effects [START_REF] Tilman | Plant diversity and ecosystem productivity[END_REF]. Both mass-ratio and richness effects can encompass taxonomic, phylogenetic and functional attributes (SI Appendix, Fig. S2). To account for all these possible biodiversity effects, we included eight metrics that reflect the full spectrum of the attributes considered in our framework (SI Appendix, Figs. S2 andS4, and Table S1). These metrics were weakly correlated among themselves (Spearman´s correlation coefficient < 0.6) and did not induce multicollinearity issues in our analyses (SI Appendix, Table S2). Studied metrics included taxonomic (species richness), functional [community-weighted mean for height and SLA (CWM.H and CWM.SLA), weighted and non-weighted functional dispersion (w.FDIS and FDIS)] and phylogenetic [phylogenetic species variability (PSV), weighted and non-weighted Mean Nearest Taxon Distance (w.MNTD and MNTD)] diversity (full methodological details in SI Appendix, Figs. S2 andS4).

The use of these metrics also allowed us to assess mass-ratio (i.e. the functional identity and diversity of dominant species; sensu ref. [START_REF] Grime | Benefits of plant diversity to ecosystems: Immediate, filter and founder effects[END_REF]) vs. richness effects by comparing abundanceweighted vs. non-weighted metrics. Considering MNTD and PSV allowed us to investigate whether ecosystem functioning relates to recent vs. early diverging evolutionary events, respectively [START_REF] Graham | Phylogenetic scale in ecology and evolution[END_REF]. Finally, we must note that species evenness was not included in the present study due to its strong correlation with w.FDIS (r > 0.8, SI Appendix, Table S1).

Environmental and spatial variables considered. Mean annual temperature (MAT), mean annual precipitation (MAP) and precipitation seasonality (PS: coefficient of variation of 12 monthly rainfall totals) were obtained from Worldclim (www.worldclim.org), a high resolution (30 arc seconds or ~ 1km at equator) global database [START_REF] Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF]. These variables are major determinants of ecosystem structure and functioning in drylands worldwide (see [START_REF] Maestre | It is getting hotter in here: Determining and projecting the impacts of global environmental change on drylands[END_REF] for a review), were not highly correlated between them in our sites and provide a comprehensive representation of climatic conditions.

We summarized local edaphic parameters at each site using soil sand content and pH. These variables, measured as described in Maestre et al. [START_REF] Maestre | Plant species richness and ecosystem multifunctionality in global drylands[END_REF], play key roles in the availability of water and nutrients in drylands [START_REF] Loik | A multi-scale perspective of water pulses in dryland ecosystems: climatology and ecohydrology of the western USA[END_REF], and are major drivers of the composition and diversity of plant and microbial communities [START_REF] Delgado-Baquerizo | Microbial diversity drives multifunctionality in terrestrial ecosystems[END_REF][START_REF] Bagousse-Pinguet | Testing the environmental filtering concept in global drylands[END_REF]. Clay and silt contents were not used in our analyses due to their correlation with sand content (r = -0.52 and -0.55, respectively). By doing so we avoided over-parameterizing our models and kept the number of environmental and biotic predictors of multifunctionality balanced in our analyses. We also considered the latitude and longitude of the study sites in our analyses to account for spatial autocorrelation in our data [START_REF] Maestre | Plant species richness and ecosystem multifunctionality in global drylands[END_REF][START_REF] Gross | Functional trait diversity maximizes ecosystem multifunctionality[END_REF][START_REF] García-Palacios | Climate mediates the biodiversity-ecosystem stability relationship globally[END_REF][START_REF] Bagousse-Pinguet | Testing the environmental filtering concept in global drylands[END_REF] (see also SI Appendix, Fig. S5).

Statistical analyses.

Relationships between biodiversity attributes and the four indices of ecosystem functioning used were assessed using multiple linear regression models and sequentially repeated across multifunctionality thresholds ranging from 20% to 80%. The models included the following predictors: (i) geographic variables [Latitude, Longitude (sin) and Longitude (cos)], abiotic variables (MAT, MAP, PS, soil sand content and pH) and biodiversity metrics (species richness, CWM-SLA, CWM-H, FDIS, w.FDIS, PSV, MNTD, w.MNTD). After inspecting the data, a quadratic term was allocated to soil pH to properly model non-linear responses.

We used a model selection procedure for each threshold separately, based on minimizing the corrected Akaike information criterion (AICc), to select the best predictors of the four indices of ecosystem functioning. In a first step, we performed a model simplification using a backward regression procedure with the stepAICc function in R. We subsequently removed non-significant quadratic and interaction terms that did not impact the predictive ability of the model. Then, a model selection procedure based on AICc selection (ΔAICc < 2) was applied on the resulting models to select the best predictors supported by the data. This procedure was performed using the dredge function in the R package MuMIn [START_REF] Bartoń | MuMIn: Multi-model inference[END_REF]. Model residuals were inspected to ensure homoscedasticity and normality. All predictors and response variables were standardized before analyses using the Z-score to interpret parameter estimates on a comparable scale.

We evaluated the importance of the predictors under consideration as drivers of multifunctionality and sets of functions related to C, N and P cycling. For doing so, we expressed the importance of predictors as the percentage of variance they explain, based on the comparison between the absolute values of their standardized regression coefficients and the sum of all standardized regression coefficients from all predictors in the models. This method is similar to a variance partition analysis because we previously transformed all predictors to Z-scores. The following identifiable variance fractions were then examined: i) geography, ii) climate, iii) soil, and iv) each of the different biodiversity metrics considered. We repeated this analysis to identify three variance fractions: the mass-ratio effects through i) the identity (CWM-H and CWM-SLA) and ii) diversity of dominant species (w.FDIS and w.MNTD); and iii) richness effects (all non-weighted metrics).

Net biodiversity effects were calculated as the sum of the standardized regression coefficients of all metrics of biodiversity selected during the model selection procedures. http://CRANR-project.org/package=MuMIn. S4 for the variation of standardized regression coefficients of each predictor along the threshold gradient evaluated.

Figure 1 .

 1 Figure 1. Relative importance of eight uncorrelated biodiversity metrics, geographical, climatic

Figure 2 .

 2 Figure 2. Relative importance of mass-ratio vs. richness effects across multiple

Figure 3 .

 3 Figure 3. Net effects of biodiversity attributes on multifunctionality (a), and on carbon (b),

Figure 4 .

 4 Figure 4. Net effects of biodiversity on multifunctionality depending on the number of

Figure 5 .

 5 Figure 5. Standardized regression coefficients of model predictors and associated 95%

Acknowledgments

We thank all the members of the EPES-BIOCOM network for the collection of field data and all the members of the Maestre lab for their help with data organization and management, and for their comments and suggestions on early stages of the manuscript. We are also grateful to the editor, as well as two anonymous reviewers for valuable comments on earlier versions. This work was funded by the European Research Council (ERC Grant agreements 242658 (BIOCOM) and 647038 [BIODESERT]). F.T.M., M.B. and Y.L.B.P. are supported by the European Research Council (BIODESERT). Y.L.B.P. was also supported by a Marie Sklodowska-Curie Actions Individual Fellowship (MSCA-IF) within the European Program Horizon 2020 (DRYFUN Project 656035). SS was supported by the Spanish Government under a Ramón y Cajal contract (RYC-2016-20604). N.G. was supported by the AgreenSkills+ fellowship programme, which has received funding from the EU's Seventh Framework Programme under grant agreement N° FP7-609398 (AgreenSkills+ contract). This work was supported by The French government IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25).