1 Title 2 Can we reliably predict plant traits globally? A critical data selection and assessment of 3 modelling uncertainty. 4 5 Running title 6 Reliability of global plant trait predictions 7 8 Abstract 9 Aim: Plant trait data is becoming increasingly available, and global predictions over space or 10 time are in high demand. A necessary first step forward is to assess the reliability of global 11 trait predictions. In this study, we predict community mean plant traits at the global scale, and 12 present a systematic evaluation of their reliability in terms of the model’s accuracy, ecological 13 realism, and modeling uncertainty. 14 15 Location: Global. 16 17 Time period: Present. 18 19 Major taxa studied: Vascular plants. 20 21 Methods: We predicted global distributions of community mean specific leaf area, leaf 22 nitrogen concentration, plant height, and wood density with four modelling techniques using 23 georeferenced, locally measured trait data representative of the plant community. We assessed 24 models’predictive performance, plausibility of predicted trait combinations, effect of data 25 quality, and uncertainty across geographic space due to extrapolation and diverging models’ 26 predictions. 27 28 Results: Models for plant height, specific leaf area, and wood density, had high predictive 29 performance and showed ecologically realistic trait-environment relationships and trait 30 combinations. Leaf nitrogen content could not be predicted. Data quality had a large impact 31 on trait predictability, where consideration of intra-specific trait variation and a representative 32 species sample resulted in highest predictability. Predictions were mostly within the 33 applicability domain, except for the Arctic and in deserts. Different modelling techniques 34 varied in their predictive performance per trait and lead to divergent predictions in some 35 regions. 36 37 Main conclusions: Plant traits can be reliably predicted at the global scale when data quality 38 is high, but prediction accuracy differs per trait and model, and varies over space. More high- 39 quality data and improved geographic coverage is needed to further increase reliability of 40 global trait predictions. We recommend the use of ensemble forecasting to account for the 41 diverse performance of statistical methods, and to more routinely assess the reliability of trait 42 predictions. 43 44 Keywords 45 ensemble forecasting, environmental filtering, height, intra-specific trait variation, leaf 46 nitrogen concentration, specific leaf area, trait model, trait-environment relationships, wood 47 density 48 1 | Introduction 49 Global trait-based models have proliferated in the last years due to the increasing availability 50 of plant trait data (Jens Kattge, 2019). Fitting and projecting trait-environment relationships 51 over large spatial scales is becoming increasingly common to study trait trade-offs (e.g. 52 Bruelheide et al., 2018; Díaz et al., 2016; Wright et al., 2004), trait relationships with 53 environmental gradients (e.g. Moles et al., 2009; Wright et al., 2005), and describe geographic 54 patterns of plant traits (e.g. Yang et al., 2016; Madani et al., 2018). Such models can not only 55 increase our understanding of trait-environment relationships, but also allow us to estimate 56 how plant traits might respond to global environmental change (Bjorkman et al., 2018; 57 Wullschleger et al., 2014). Traits are indeed considered particularly useful for predicting the 58 impact of environmental change on vegetation (Webb, Hoeting, Ames, Pyne, & LeRoy Poff, 59 2010), as they allow to directly link plant fitness to environmental filters like climate, soil 60 properties, and disturbance (Joner, Anand, & Pillar, 2012; Keddy, 1992). 61 Recent attempts to model global plant trait distributions as a function of environmental 62 conditions have yielded different trait patterns so far (e.g. Butler et al., 2017; Madani et al., 63 2018; Moreno-Martínez et al., 2018; Van Bodegom, Douma, & Verheijen, 2014; Wright et 64 al., 2017). For example, Butler et al. (2017) and Moreno-Martínez et al. (2018) predicted 65 specific leaf area to be low in the west of Canada and high in the Northern Russia and East of 66 Brazil, while Van Bodegom et al. (2014) and Madani et al. (2018) predicted the opposite. 67 Such discrepancies among existing global trait models may arise from a variety of reasons. 68 These reasons include differences in (i) the underlying trait data originating from various 69 sources (floras and measurements in natural areas, manipulated field experiments, botanical 70 gardens, and greenhouses), (ii) the representativeness of the sampled species towards the 71 entire natural plant community, (iii) the selection of environmental predictors, and (iv) the 72 techniques for model fitting. 73 The first discrepancy translates to the use of global species trait averages and a mismatch of 74 trait and environmental data, while the second and third combined translate to different spatial 75 patterns of uncertainty due to extrapolations of trait-environment relationships (Thuiller, 76 Brotons, Araujo, & Lavorel, 2004), and the fourth may translate to considerable differences 77 among predictions (Thuiller, 2007). Additionally, the ecological realism of the combination of 78 predicted plant traits has so far not been tested against observed trait combinations. Finally, 79 while all studies reported the variance explained by the trait models, the predictability of 80 independent samples has not been assessed, yet. To further increase macroecological insights 81 on global environment-trait relationships with potential application for conservation 82 assessments, e.g. climate change impact (Lavorel & Garnier, 2002), or when trait predictions 83 are used as input for further modelling step, e.g. Dynamic Global Vegetation Models 84 (Sakschewski et al., 2015), a necessary step forward is to perform a thorough assessment of 85 the reliability of global trait predictions. 86 Here, we predict community mean plant traits at the global scale, and present a systematic 87 evaluation of their reliability in terms of the model’s accuracy, ecological realism, and 88 modeling uncertainty. We systematically selected data focusing on four widely studies plant 89 traits (specific leaf area, leaf nitrogen concentration, height, and wood density). These traits 90 reflect global spectra in plant form and function, are responsive to the abiotic environment, 91 and show physical tradeoffs (Díaz et al., 2016; Lavorel & Garnier, 2002). For each of the 92 traits we calculated the community mean trait value per cell and modeled the trait patterns at 93 the global scale. Then we proceeded by evaluating the three main components. First, we 94 evaluated the predictive performance of the models. Second, we assessed the ecological 95 plausibility of the models in terms of the trait-environment relationships, and correlations and 96 combinations of individually predicted trait values (Díaz et al., 2016; Lavorel & Garnier, 97 2002). Third, we evaluated the effect of various sources of modelling uncertainty: (i) the 98 effect of data quality in terms of representativeness of the sampled species towards the entire 99 natural plant community and the use of global trait averages vs. local trait measurements; (ii) 100 the uncertainty across geographic space due to extrapolating traits outside the environmental 101 coverage of the data; and (iii) the uncertainty across geographic space due to discrepancies in 102 the predictions of four different modelling techniques. We build upon this assessment to 103 provide guidelines for the further development, interpretability and usability of global plant 104 trait-environment models. 105 106 2 | Methods 107 2.1 | Plant functional traits 108 We selected four plant functional traits: specific leaf area (SLA; mm2.mg-1), leaf nitrogen 109 concentration per leaf mass (LNC; mg.g-1), height (m), and wood density (mg.mm-3). The leaf 110 traits SLA and LNC are both linked to photosynthetic capacity and nutrient investment, where 111 a high SLA and high LNC represent a fast return on investment on the expense of a shorter 112 life-span (Wright et al., 2004). Plant height is considered to be indicative of initial species 113 responses to climate change and its competitive ability (Guittar, Goldberg, Klanderud, 114 Telford, & Vandvik, 2016; Moles et al., 2009). Last, wood density is a measure of carbon 115 investment representing a trade-off between growth (e.g. to overcome light limitation) and 116 strength (e.g. mechanical support and drought tolerance), with higher wood density reflecting 117 slower growth but increased strength (Chave et al., 2009). 118 The selected traits have the advantage of being easily measured, according to a standardized 119 measurement procedure (Perez-Harguindeguy et al. 2013). This facilitates the integration of 120 data from multiple datasets and reduces trait variation caused by seasonal changes 121 (Bloomfield et al., 2018). To increase our dataset, we allowed for slightly different measures 122 per trait, including measurements for SLA on shade-leaves instead of sun-leaves (but see 123 Keenan & Niinemets, 2016), for wood density on sapwood instead of heartwood, and for 124 height on generative instead of vegetative plant organs (also done by e.g. Siefert et al., 2015). 125 126 2.2 | Data collection and selection procedure 127 Our main source for plant trait data was the TRY database (J. Kattge et al., 2011), from which 128 we received 964,464 trait records on 85,437 species from 168 datasets. We also obtained data 129 from the Tundra Trait Team (TTT) database (Bjorkman et al., 2018), and various other 130 datasets, both published (Bloomfield et al., 2018; Cornelissen et al., 2003; Gleason, Butler, 131 Ziemińska, Waryszak, & Westoby, 2012; Kraft, Valencia, & Ackerly, 2008; Meir, Levy, 132 Grace, & Jarvis, 2007; Simpson, Richardson, & Laughlin, 2016; van der Sande et al., 2017, 133 2018; Van Der Sande et al., 2016) and unpublished (Schamp, B.; Santini, L.). For the 134 additional datasets, we standardized all species names using The Plant List (2013) to make 135 data comparable to the data from TRY. Then, we selected trait observations based on the 136 following six criteria. First, we only included georeferenced observations in order to enable a 137 meaningful link with environmental covariates. Second, we only considered actual 138 measurements of plant traits (i.e. no species-level averages) in order to include intra-specific 139 trait variation which can substantially contribute to the trait variation within and between 140 communities (Albert et al., 2010; Bloomfield et al., 2018; Siefert et al., 2015). Third, we only 141 considered measurements obtained from natural vegetation, to minimize influences of local 142 management practices and legacy effects of historical land-use (Perring et al., 2017). Fourth, 143 we only included observations from studies that measure all or the most abundant species 144 present in the entire plant community or in the dominant vegetation structure in order to 145 account for the representativeness of the sampled species towards the local, natural 146 vegetation. This is in line with previous studies on this topic (e.g. Poorter et al. (2017); Wüest 147 et al. (2017)) and in accordance with the biomass ratio hypothesis (Grime, 1998). Fifth, we 148 only included observations from studies that targeted all life-stages and/or size-classes and 149 from studies that targeted only adults. We, thus, excluded observations from studies focusing 150 only on early-successional plant communities and studies measuring only seedlings or 151 juveniles in a more established vegetation. This reduces confounding effects of ontogeny (e.g. 152 Thomas & Bazzaz, 1999) and succession (e.g. Purschke et al., 2013). Sixth, we only included 153 measurements conducted from 1980 onwards, in order to link up with the environmental 154 covariate data, which spans from 1979 till 2013. We excluded trait observations for which the 155 listed criteria could not be checked. The Supplementary Information contains an overview of 156 the number of datasets excluded per criterion (Appendix S1) as well as an overview of the 157 datasets and studies from the TRY and the TTT database we included in our final database 158 (Appendix S2). In total, we removed 63.1% of all the datasets we originally received from 159 TRY and 54.5% of all datasets in the TTT database. 160 161 2.3 | Data processing 162 We checked and corrected for possible errors in our database by doing the following: 1) we 163 removed duplicate entries, which are defined by having the same coordinates and references 164 or the same coordinates and trait values but different dataset identification numbers; 2) for 165 observations not located on land, we checked the original reference and corrected coordinates 166 according to the site description; 3) we excluded obvious errors in trait observations (e.g. SLA 167 = 0); and 4) we evaluated outliers in trait values against values of the same species reported 168 by other studies in our database and/or external sources (local floras), and corrected them 169 when appropriate (adjustment of decimal separator). We then calculated location-specific 170 community means per trait and per study to represent the mean response of the plant 171 community to the local environment (Ackerly & Cornwell, 2007). The main reason for using 172 unweighted community means was that previous studies did not provide a conclusive answer 173 to which is better to use, and since >50% of our data did not include species abundances 174 unweighted means were the better compromise (see Supplementary Information Appendix S4 175 for further discussion and comparison between the two approach).Then, we averaged the 176 location-specific community means to 0.5 degree grid cells (~ 55×55km at the equator, with 177 an median of 22 communities per grid cell) in order to describe large-scale patterns in traits. 178 This is a common resolution used in previous studies modeling traits globally (Butler et al., 179 2017; Van Bodegom et al., 2014) and a good compromise accounting for the effect of climatic 180 filtering on plant traits, resolution of global biodiversity models for conservation (Pollock, 181 Thuiller, & Jetz, 2017), coordinate uncertainty of data collection, and uncertainty related to 182 interpolated climatic variables (Stoklosa, Daly, Foster, Ashcroft, & Warton, 2015). These 183 community means represent the average trait values of the entire vegetation in a grid cell, 184 making values not directly transferable to a specific species or a class of species. The final 185 dataset used as input for model fitting included community mean trait values based on data 186 from 76 studies and 8,955 species averaged to 486 grid cells, including 361 grid cells for 187 SLA, 338 for LNC, 217 for height, and 125 for wood density (Figure 7). 188 189 2.4 | Environmental data 190 We considered environmental variables that are expected to affect plant performance (e.g. 191 Varela et al., 2015), including climate, and soil properties. This allowed us to check the 192 ecological plausibility of the resulting trait-environment relationships. Based on ecological 193 relevance, we selected bioclimatic variables from CHELSA version 1.2 (Karger et al., 2017) 194 and soil characteristics from SoilGrids250m (Hengl et al., 2017). For the latter, we averaged 195 data to a depth of 30 cm, which we considered most relevant for plant establishment. As an 196 additional predictor, we calculated the aridity index as the mean annual precipitation divided 197 by the mean annual potential evapotranspiration (Zomer et al. 2008). To avoid collinearity, 198 we reduced the number of predictors based on Variance Inflation Factors (VIF < 4), while 199 ensuring a combination of different environmental factors (i.e. both climatic and soil 200 characteristics) (Franklin, Serra-Diaz, Syphard, & Regan, 2016). The final selection included 201 six predictors: minimum temperature of the coldest month (Tmin; °C), aridity index 202 (dimensionless), precipitation in the driest quarter (mm), precipitation seasonality (coefficient 203 of variation based on monthly precipitation; dimensionless), soil cation exchange capacity 204 (CEC; cmol+ kg-1), and soil pH (-log(H+)). As lower values of the aridity index indicate 205 higher aridity, for clarity we will refer to this predictor as ‘humidity index’ from now on. 206 All environmental covariates were resampled to a resolution of 0.5 degrees in order to match 207 the resolution of the plant community mean trait data. 208 209 2.5 | Model fitting and validation 210 To quantify the relationships between the plant traits and environmental variables, we fitted 211 four different models per trait: two statistical models (Generalized Linear Models (GLMs) 212 and Generalized Additive Models (GAMs)) and two machine learning models (Random 213 Forest (RF) and Boosted Regression Trees (BRT)). An overview of the model 214 parameterization is provided in the Supplementary Information Appendix S5. We validated 215 all models by running a 10-fold cross-validation using a split-sampling procedure (80-20%) 216 and evaluated the models’ predictive performance (cross-validated pseudo-R2) by regressing 217 the predicted and observed trait values from all repetitions of the cross-validation. 218 To quantify the relative importance of each predictor in a consistent way across the models, 219 we predicted traits using permuted values for the predictor of concern, and correlated those 220 predictions with predictions of the model using the original data, and quantified relative 221 variable importance as 1 minus the correlation coefficient (Thuiller, Lafourcade, Engler, & 222 Araújo, 2009). 223 224 2.6 | Testing sensitivity to data quality 225 To test the effect of data quality, we created four different datasets with trait values for the 226 same communities, but that differed in terms of trait values, i.e. intra-specific trait variation 227 versus species-specific trait values, and in terms of representativeness, i.e. a representative 228 sample of species versus an specific selection of species in the plant community (Figure 1). 229 The community mean trait values excluding intra-specific trait variation were calculated by 230 averaging trait values per species for all data we originally gathered (see Appendix S6), and 231 replacing the original trait values with these species averages. Datasets where species 232 representativeness of the entire plant community was not considered was simulated by 233 randomly selecting one plant species from each community, and replicating this process 10 234 times. This one-species-sample mimicks common practice where data from the Global 235 Biodiversity Information Facility (GBIF) or of studies targeting a single species is included in 236 a dataset. For each dataset, community means were then calculated as described in section 237 2.3. To ensure pure effects of trait values and species representativeness, and not of sample 238 size effects or differences in applicability domain, we only adjusted communities that are 239 present in the dataset with the actual community means. These actual community means are 240 the ones that included the intra-specific trait variation and had species representative of the 241 entire plant community. Thus, plot 1 in Figure 3 is the actual community mean dataset, plot 2 242 is representative but has local trait values replaced with species means, for plot 3 species were 243 removed, and for plot 4 species were removed and local trait values were replaced with 244 species means. To ensure sample size would not change when removing species, we retained 245 a minimum of one species per community. 246 For each dataset (N=102), we ran the parameter selection for the four different models for 247 each of the four traits, ran all models with the selected parameters, and evaluated each model 248 by confronting predictions of the cross-validation with community mean trait values from the 249 dataset with the actual community means (Appendix S6). 250 251 2.7 | Spatial predictions and their assessment 252 To derive spatial predictions per trait, we used an ensemble forecasting procedure, which 253 averages the predictions of the four algorithms weighted by their cross-validated pseudo-R2 254 values (Marmion, Parviainen, Luoto, Heikkinen, & Thuiller, 2009). Similarly, we estimated 255 ensemble variable importance and partial response curves. To quantify model uncertainty, i.e. 256 the variability in predictions across algorithms, the coefficient of variation was calculated as 257 the weighted difference of each of the four individual models’ predictions compared to the 258 ensemble prediction (see Supplementary Information Appendix S7 for further explanation). 259 To identify geographic areas outside the environmental domain covered by our data, we 260 calculated and mapped the multivariate environmental similarity surface (MESS) as described 261 by Elith et al. (2010). This analysis quantifies the difference of the most extrapolated 262 environmental predictor in a certain location and the environmental range of that predictor 263 covered by the dataset, while considering the distribution of data within the environmental 264 range. 265 Furthermore, we checked if among-trait correlations observed in the data were retained in the 266 predictions by correlating the trait correlation matrix of the dataset (i.e. the 0.5 degree grid 267 cell trait averages used for model fitting) with the trait correlation matrix of the predictions 268 (i.e. across all 0.5 degree grid cells). Additionally, we assessed whether predicted trait 269 combinations were realistic by comparing them with a hypervolume of all trait combinations 270 existing in our dataset. To build the hypervolume, we used the original trait values before 271 calculating community means or grid cell averages, as we want to check if predicted trait 272 combinations can actually occur, and because this ensured enough observations with all four 273 traits measured to build the hypervolume. For this analysis, we used the ‘hypervolume_svm’ 274 function and the ‘hypervolume_inclusion_test’ function of the ‘hypervolume’ R package 275 (Blonder et al. 2014). Note that this test does not necessarily imply that predicted trait 276 combinations do not or cannot exist, but only that they might be unrealistic and should be 277 interpreted with caution. 278 279 3 | Results 280 3.1 | Predicted global plant trait variation 281 The variation explained by the environmental variables clearly varied among traits (Figure 2). 282 Model predictive performance was highest for plant height, followed sequentially by wood 283 density, SLA, and leaf nitrogen concentration (Figure 2). The projected global trait maps 284 revealed low SLA in arid areas and high SLA in temperate climates (Figure 3a), whereas 285 LNC was found to be low in dry tropical regions (Figure 3c). We further found lower plant 286 height at higher latitudes, with the tallest vegetation in wet tropical areas, and shorter 287 vegetation in temperate climates (Figure 3e). Finally, wood density, representing the potential 288 average wood density for all woody vegetation in a location, was predicted particularly low in 289 areas with low precipitation seasonality (Figure 3g). 290 291 3.2 | Ecological assessment 292 3.2.1 | Trait-environment relationships 293 SLA was mostly explained by humidity index and minimum temperature of the coldest month 294 (Figure 4a). As expected, SLA showed a unimodal response to minimum temperature and a 295 monotonic increase with humidity index, but we did not find a response of SLA to soil pH 296 (Table 1, Figure 5). We further found a decrease of SLA with increasing precipitation in the 297 driest quarter of the year and soil CEC, and a small increase of SLA with precipitation 298 seasonality (Figure 5). 299 LNC was mostly explained by minimum temperature of the coldest month (Figure 4b). We 300 expected LNC to decrease with minimum temperature and humidity index, but found a 301 unimodal response of LNC with minimum temperature around 0 °C, and found LNC to 302 increase strongly from very arid to less arid environments after which it declined again (Table 303 1, Figure 5). We further found LNC to decrease with precipitation seasonality (Figure 5). 304 Plant height was mostly explained by the amount of precipitation in the driest quarter of the 305 year (Figure 4c). As expected, height increased with increasing minimum temperature and 306 minimum precipitation, whereas in contrast to our original expectation, we found height to 307 decrease with humidity index, and to increase with precipitation seasonality (Table 1, Figure 308 5). 309 Wood density was mostly explained by minimum temperature of the coldest month (Figure 310 4d). As expected, wood density decreased with humidity (Table 1, Figure 5). Contradicting 311 our expectations, wood density increased with minimum temperature, and showed a unimodal 312 response to soil CEC (Table 1, Figure 5). Furthermore, we found no response of wood density 313 with changing precipitation in the driest quarter of the year, precipitation seasonality, or soil 314 pH (Figure 5). 315 316 3.2.2 | Combinations of predicted traits 317 The predicted trait values largely preserved the global trait correlations present in the training 318 data (r=0.83). Further, for 99.9% of all grid cells, the predicted trait combination of 319 community means does not violate the trait combinations found in individual plants or 320 species. Locations with unrealistic predicted trait combinations are presented in the 321 Supporting Information Appendix S8, Figure S8. 322 323 3.3 | Modelling uncertainty assessment 324 3.3.1 | Data quality 325 Predictive accuracy of traits on average reduced by 9% when intra-specific trait variation was 326 excluded (Figure 6; Appendix S6 Table S6). Predictably, the representativeness of the species 327 sample towards the community also reduced the predictive accuracy on average by 19% 328 (Figure 6). The combination of not considering intra-specific trait variation and using a non- 329 representative species sample amplified the negative effects and reduced the predictive 330 accuracy of traits by 31% (Figure 6). Yet, the decrease in predictability was not as 331 pronounced as expected. 332 333 3.3.2 | Applicability domain 334 Despite a lack of trait data in large areas of the world (e.g. India, Asian Russia and Africa; 335 Figure 7), the data covered a large part of the global environmental space (Figure 7; Appendix 336 S9 Figure S9), indicating that predictions were mostly within the applicability domain of the 337 models. However, deserts, tropical islands, and some parts of the Arctic were out of the 338 environmental domain covered by the trait data, meaning that predictions for these areas 339 should be interpreted carefully. 340 341 3.3.3 | Model selection 342 Predictive performance differed between models per trait, where the random forest technique 343 showed the highest predictive performance for SLA, LNC, and wood density, while the 344 generalized linear model best predicted height (Figure 2). The consistency in the predictions 345 among the four modelling techniques varied geographically (Figure 3b,d,f,h), where 346 uncertainty across geographic space due to model selection was highest for plant height. The 347 coefficient of variation of SLA was mostly low apart from some areas in Africa. LNC had 348 overall low coefficient of variation except for the Sahara. Plant height showed a shifting 349 pattern of high and low coefficients of variation over the globe. And wood density had an 350 overall low coefficient of variation but was predicted with more uncertainty in parts of Africa 351 and most of the Arctic. 352 353 4 | Discussion 354 In this study, we established global plant trait models based on locally measured trait data 355 representative of natural vegetation, and used these models to make global-scale trait 356 predictions. We assessed these trait predictions by models’ predictive performance, ecological 357 realism, data quality, the applicability domain for predictions, and model choice uncertainty. 358 Our results showed that models for SLA, plant height, and wood density could predict trait 359 variation well. The trait-environment relationships were mostly as hypothesized, and our trait 360 predictions preserved the observed among-trait correlations and combinations. Furthermore, 361 we showed that most of the global environmental variation was covered by the available trait 362 data that met our criteria for quality, that including intra-specific trait variation and having a 363 representative species sample improved the predictability of traits at the resolution and extent 364 applied here, and that different modelling techniques demonstrated different predictive 365 performances for different traits. Overall, this suggests that global predictions aimed at 366 describing broad geographic plant trait patterns are reliable with the data currently available, 367 but caution is needed for certain traits and areas. 368 369 4.1 | Global trait patterns 370 The performance of our models in predicting trait values along environmental gradients is 371 comparable with other global or large-scale trait-based studies (Van Bodegom et al., 2014; 372 Yang et al., 2016; Butler et al., 2017; Madani et al., 2018). Predicted spatial patterns were 373 also consistent with those predicted by previous studies for some areas. For example, we 374 found lower SLA values in central Australia compared to the coast (Figure 3a), which shows 375 the leaf adaptation to dryer conditions (Butler et al., 2017; Madani et al., 2018; Moreno- 376 Martínez et al., 2018; Van Bodegom et al., 2014). Similarly, we found lower SLA values in 377 the Amazon compared to the South American Cerrado (Figure 3a), which was also found 378 before (Butler et al., 2017; Moreno-Martínez et al., 2018). Further, we found that vegetation 379 in tropical climates was taller than in temperate climates (Figure 3e), similar to Madani et al. 380 (2018). 381 On the contrary, in some areas SLA, LNC, and wood density predictions were inconsistent 382 with previous studies. For example, we predicted higher SLA values for boreal forests 383 compared to desert areas, similar to Van Bodegom et al. (2014), whereas Butler et al. (2017) 384 predicted the opposite. Additionally, predicted patterns for LNC and wood density did not 385 coincide with other maps (Figure 3; Butler et al., 2017; Moreno-Martínez et al., 2018; Van 386 Bodegom et al., 2014). 387 When trait predictions disagree, it is difficult to conclude which predictions are more reliable. 388 One option is to validate global trait predictions against regional trait maps. For example, we 389 found wood density to be higher in the East of the Amazon region compared to the North 390 West and South West (Figure 3g), as was found by Baker et al. (2004). However, the paucity 391 of regional trait maps makes this validation method impractical. Another option is to consider 392 model predictive performances and the applicability domain to infer reliability of predictions. 393 Unfortunately, the lack of quantification and indication of these in previous studies makes it 394 difficult to conclude which predictions are more accurate. Nevertheless, our models for LNC 395 had poor predictive accuracy, making LNC predictions unreliable (Figure 2). 396 397 4.2 | Ecological evaluation of global trait predictions 398 Most trait-environment relationships established at the community-scale were found at the 399 global scale, too. In general, we found traits to vary more with climatic factors than with soil 400 characteristics (Figure 4). This may reflect the greater variation in soil characteristics at 401 smaller scales compared to climatic variables, which makes the relative predictor importance 402 scale-dependent. Furthermore, all predicted trait combinations and correlations were found 403 within the composed dataset. 404 Our results mostly showed the hypothesized relationships between SLA and the 405 environmental variables (Table 1, Figure 5). However, we found SLA to decrease with 406 minimum precipitation and increase with precipitation seasonality (Figure 5). This can be 407 explained by the phylogenetic trend where areas with more and more frequent rain have 408 relatively more gymnosperms, which have a low SLA (Díaz et al., 2016). Further, we 409 expected SLA to increase with soil fertility, but found the opposite (Table 1, Figure 5). 410 The expected responses of LNC with the environmental variables were not found (Table 1, 411 Figure 5). The partial responses of LNC showed great variation over small environmental 412 ranges, possibly due the nature of machine learning models to over-fit. Together with the low 413 models’ predictive performance, this might reflect that LNC responds more to small-scale 414 environmental variation or that LNC is too plastic in relation to multiple environmental 415 factors leading to non-universal adaptations (Bloomfield et al., 2018; Reich & Oleksyn, 2004) 416 and different responses when considering intra-specific variation or not (Albert et al., 2010). 417 This plasticity makes it difficult to reliably predict LNC distributions at this resolution. 418 Our results mostly showed the hypothesized relationships between average community height 419 and the environmental variables (Table 1, Figure 5). However, we found mean plant height to 420 decrease with humidity index (Table 1, Figure 5), which, in the absence of a biological 421 explanation, might merely show that more humid environments are dominated by shorter 422 vegetation (e.g. grasses, herbs, and shrubs). The unexpected increase in height with 423 precipitation seasonality (Table 1, Figure 5) can be explained by the fact that many species in 424 areas with seasonal rainfall can shed leaves, which makes deciduous vegetation less 425 vulnerable to cavitation compared to evergreen vegetation. Furthermore, taller plants are 426 better able to reach the water from the previous rain season due to deeper root systems 427 (Canadell et al., 1996). 428 Our results mostly conflicted with the hypothesized relationships between wood density and 429 the environmental variables (Table 1, Figure 5). The unexpected higher wood densities with 430 minimum temperature (Table 1, Figure 5) can be an effect of decreased xylem vulnerability 431 for cavitation. However, it could also be a phylogenetic trend where colder areas are more 432 dominated by soft-wooded gymnosperms, and warmer areas are dominated by angiosperms 433 with generally denser wood (Swenson & Enquist, 2007). We expected a decrease in wood 434 density with soil CEC as higher soil fertility can sustain increased growth rates. Nevertheless, 435 the unexpected increase in wood density at the lower end of the CEC spectrum can be 436 explained as the result of extreme limitation to soil nutrients. As no global relationships have 437 been described for wood density with different environmental factors (Moles, 2018), these 438 patterns should be investigated further. 439 Literature reports that some trends between traits and environmental factors at the local scale 440 may vary with leaf habit, plant growth forms, and photosynthetic pathway (e.g. Šímová et al., 441 2018), and likewise, that trends are affected by other factors, such as land-use type, and 442 disturbance (e.g. Chen et al., 2018). However, we expect that this variation will not create 443 great deviations in results, since we model at the global scale community mean values 444 estimated from local measurements in natural vegetation. At this scale, environmental 445 filtering effects on species traits are expected to be much less confounded by variation in 446 biotic interactions and not-considered disturbances than at a smaller scale. 447 448 4.3 | Modelling uncertainty evaluation 449 4.3.1 | Data quality 450 We found that considering intra-specific trait variation contributed to the predictability of 451 traits (Figure 6; Supplementary Information Appendix S6, Table S6). This improvement of 452 the accuracy of trait predictions at the global scale highlights the importance of considering 453 intra-specific trait variation over and above the conclusion made by previous small-scale 454 studies that intra-specific trait variation contributes largely to community trait variation 455 (Albert et al., 2010; Bloomfield et al., 2018; Poorter, Castilho, Schietti, Oliveira, & Costa, 456 2018; Siefert et al., 2015). Additionally, we show that the representativeness of the selected 457 species towards the entire plant community also affected the predictibility of traits, and that 458 the combination of not considering intra-specific trait variation and using unrepresentative 459 species samples led to even lower trait predictability. The relatively small change between 460 predictive performance of datasets with a representative and non-representative species 461 sample is a reflection of the fact that our dataset contained not only communities where all 462 species were sampled, but also communities where only representative species were sampled. 463 When randomly selecting a species from a representative species sample, the community 464 mean trait value might not be that different from the actual community trait value. 465 Though our analysis quantifies the difference of using different quality datasets, also 466 conceptually it leads to different results. Including or excluding intra-specific trait variation 467 leads to results that represent actual community dynamics or potential trait values, 468 respectively (Poorter et al., 2018). Using the same line of reasoning, using data representative 469 of the local vegetation captures environmental trait filtering better than using community 470 means estimated from a random sample of plants. Thus, both statistically and theoretically, 471 including intra-specific trait variation and, more importantly, including data that is 472 representative of the local vegetation should be preferred when the aim is community mean 473 trait predictions. 474 475 4.3.2 | Applicability domain 476 The strict selection criteria we set greatly reduced the amount of available data 477 (Supplementary Information Appendix S1, Table S1). Nevertheless, despite the limited 478 coverage of geographic space, our dataset still covered the major part of the global terrestrial 479 environmental space indicating that predictions can be made without extrapolation for most 480 areas (Figure 7). However, predictions for wood density are extrapolated for a larger part of 481 the terrestrial world compared to the other traits. A reason for the fewer wood density 482 community mean data points is that species mean values are generally considered appropriate 483 for most studies since inter-specific variation in wood density is larger than the intra-specific 484 variation, and so new wood density data are rarely collected in the field (Siefert et al., 2015). 485 However, wood density does show variation even within a species (Siefert et al., 2015). 486 Additionally, most wood density measures available were collected before 1980, meaning that 487 taking global species averages of wood density does not consider any evolutionary responses 488 as it does not match the current local environment. Another reason for the environmental and 489 geographical bias in wood density community mean data points is that measurements of wood 490 density on small shrubs and other woody vegetation with low height (i.e. in the Artic regions) 491 is difficult and maybe imprecise, making that this data is almost never reported (Perez- 492 Harguindeguy et al., 2013). 493 494 4.3.3 | Model selection 495 The selection of a specific modelling technique greatly affected the ability to predict traits 496 (Figure 2). As predictive performance differed among both modelling techniques and traits, 497 we could not identify a single ‘best’ technique. Though the predictive performance is one of 498 the major aspects, besides the applicability domain, to assess the reliability of trait 499 predictions, it can be biased: machine learning models tend to have higher predictive 500 performances but are also more prone to overfitting. The ensemble forecasting approach as 501 employed here can be used to retrieve a single prediction relying mostly on the best 502 performing models, while considering the variability in model predictions between similarly 503 supported models. Areas with high variation in values predicted by different models, like the 504 Sahara and the North of India for plant height, can then be assumed to not provide reliable 505 predictions. Thus, though ensemble forecasting might not necessarily be better in predicting 506 traits compared to a single best model, it reduces the uncertainty due to subjective model 507 technique selection and enables the quantification and mapping of the uncertainty due to 508 divergent model predictions. Finally, it allows for one general modelling approach for 509 multiple traits. 510 511 4.4 | Reliability of global plant trait predictions 512 We conclude that plant traits can reliably be predicted at the global scale with high quality 513 data, but predictions are more accurate for some traits than others, and certainty varies over 514 space. Higher certainty in predictions is found for traits that have low plasticity to small-scale 515 differences in predictors and primarily respond to large-scale environmental factors. The 516 results of our trait models can improve the mechanistic understanding of global plant trait- 517 environment relationships and adds to the central question in functional ecology of the 518 predictability of traits by the environment. Further, our assessment opens a new avenue to test 519 impacts of global change on trait distributions, and, eventually, on community assemblages. 520 Based on our results, we recommend to systematically select data and modelling techniques, 521 and more routinely assess the reliability of trait models based on model predictive 522 performance, applicability domain, model uncertainty, and realism of predicted trait 523 combinations. Such systematic presentation of validation results and applicability domain in 524 studies presenting predictions of spatial patterns of community traits will enhance our ability 525 to build upon previous modelling attempts and eventually improve our understanding on trait- 526 environment relationships. Moreover, the results of global trait models are contingent on the 527 quality and distributions of the trait data. 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Agriculture, Ecosystems and Environment, 126, 67–80. 765 http://doi.org/10.1016/j.agee.2008.01.014 766 767 Data accessibility statement 768 Community trait mean data used in this paper are provided in the supplementary information. 769 Due to regulations of the major trait database used, the raw data cannot be openly shared. The 770 predicted trait distributions maps generated in this study are provided as raster objects in the 771 supplementary information. Furthermore, the Rscripts for model parameter selection and of 772 the final models are provided in the supplementary information. 773 Table and figure legends 774 Table 1. Hypotheses on environmental variables impact on plant performance, and how this 775 affects traits. 776 Figure 1. Overview of data quality types. 777 Figure 2. Model performance for different models and different traits. 778 Figure 3. Global plant trait predictions. 779 Figure 4. Relative predictor importance. 780 Figure 5. Partial response curves. 781 Figure 6. Models performances of different quality datasets. 782 Figure 7. Trait observations and their environmental coverage. 783 Table 1. How plant performance is affected by environmental variables. Reported trait- 784 environment relationships are significant and/or biologically relevant. ↑ indicates an increase 785 of trait value with an increase in value of the predictor, ↓ indicates a decrease, ‒ indicates that 786 no relationship was found, ˄ indicates a unimodal response, and ᴑ indicates that this 787 relationship has not been discussed in literature. Predictor Rationale Impact Hypothesis Minimum Temperature-induced leaf Leaf habit change and their ˄ SLA1,2 temperature damage affects plant changes to be extreme ↓ Nmass3,4,5 of the coldest performance. temperature tolerant. ↑ Plant height6 month Frost-induced cavitation risk Cavitation risk increases ↓ Wood density7,8,9 (Tmin) increases with decreasing with decreasing wood temperatures. density. Humidity Drought-induced cavitation Drought tolerant leaves ↑ SLA1 index risk increases with Cavitation risk increases ↓ Nmass3 decreasing humidity index. with height10. ↑ Plant height3,11 ↓ Wood density8 Precipitation Drought-induced cavitation Cavitation risk increases ᴑ SLA in the driest risk increases with with height10. ᴑ Nmass quarter of the decreasing precipitation. ↑ Plant height6 year ᴑ Wood density (PrecDryQ) Precipitation Moisture availability affects Leaf-shedding. ‒ SLA12 seasonality plant survival. ‒ Nmass12 (PrecSeas) Stature change. ↓ Plant height6 ᴑ Wood density Soil cation Higher CEC increases soil Less durable structures ‒ SLA3,15 exchange fertility13. can be maintained7,14. ‒ Nmass3,15 capacity ᴑ Plant height (CEC) ↓ Wood density16 Soil pH (pH) Lower pH increases soil Less durable structures ↓ SLA15 fertility. can be maintained7,14. ᴑ Nmass ᴑ Plant height ᴑ Wood density 788 1Wright et al., 2005 789 2Went, 1953 790 3Ordoñez et al., 2009 791 4Reich & Oleksyn, 2004 792 5Reich, Oleksyn, & Tjoelker, 1996 793 6Moles et al., 2009 794 7Chave et al., 2009 795 8Reich, 2014 796 9Swenson & Weiser, 2010 797 10Tyree & Sperry, 1989 798 11Ambrose et al., 2010 799 12Borchert, 1998 800 13Efretuei, 2016 801 14Wright et al., 2004 802 15Maire et al., 2015 803 16Ter Steege et al., 2006 805 806 807 Figure 1. Overview of data quality types. Each plot presents the same plant community, 808 where the individuals selected to sample are displayed in green. These samples are merely an 809 example of how samples can be representative or not representative (as defined in Methods 810 section 2.2, criterion 4). Dashed lines represent species mean values. In plot 1, all individuals 811 in the entire community are selected for sampling, thus a representative sample of the 812 community, and intra-specific trait variation is included. In plot 2, all species from the 813 dominant vegetation type are selected for sampling, thus a representative sample of the 814 community, but intra-specific trait variation is excluded. In plot 3, only saplings are sampled, 815 thus a not representative sample of the community, and intra-specific trait variation is 816 included. In plot 4, only one specific species from the dominant vegetation type is selected, 817 thus a not representative sample of the community, and intra-specific trait variation is 818 excluded. 819 820 Figure 2. Model performance for different traits and different models presented as the cross- 821 validated R2 values. Per trait, the bars represent the predictive performance of the Generalized 822 Linear Model, the Generalized Additive Model, the Random Forest, and the Boosted 823 Regression Trees. 824 825 Figure 3. Global plant trait predictions. The left column presents the ensemble trait 826 predictions, and the right column presents the ensemble coefficient of variation (CV) of 827 different model predictions. The grey margin in each plot depicts the mean latitudinal value. 828 Values in plots (b), (d), (f), (h) indicate the predictive performance of the different models, 829 where glm indicates values of the Generalized Linear Models, gam of Generalized Additive 830 Models, rf of Random Forests, and brt of Boosted Regression Trees. These values indicate 831 how well trait are predicted, while the CV maps only identify locations where predictions are 832 divergent between models with high and/or similar predictive power. For extrapolation areas, 833 see Figure 7. No predictions were made for Greenland, as no soil predictions are available, 834 nor for the south of Egypt, as there is no precipitation seasonality. All predictions report 835 potential trait values, as not all terrestrial world is vegetated or includes woody vegetation. 836 837 Figure 4. Relative predictor importance, calculated as 1 – spearman correlation (see Methods 838 2.5), where high values indicate high importance. The bars represent the ensemble relative 839 predictor importance and the error bars show the ensemble coefficient of variation. Tmin 840 stands for minimum temperature, Humidity for humidity index, PrecDryQ for precipitation in 841 the driest quarter of the year, PrecSeas for precipitation seasonality, and CEC for soil cation 842 exchange capacity. 843 844 Figure 5. Ensemble partial trait responses. Shaded areas are the ensemble coefficients of variation. Predictors are minimum temperature (Tmin; 845 °C), humidity index (Humidity; unitless), precipitation in the driest quarter of the year (PrecDryQ; mm), precipitation seasonality (PrecSeas; -), 846 soil cation exchange capacity (CEC; cmol+ kg-1), and soil pH (-log(H+)). The plotted range of each predictor is the 95th quantile of the global 847 range. Extrapolated trait responses are shown with a dashed line. 848 849 Figure 6. Model performances of different quality datasets. The bars represent the average 850 cross-validated R2 values over the four different models, where the errorbars indicate the 851 minimum and maximum cross-validated R2 value. Datasets including and excluding intra- 852 specific trait variation are indicated with intra and inter, respectively. Species 853 representativeness is indicated with the shade of the bar, where darker shades represent 854 datasets with a representative species sample for the community and lighter bars represent 855 datasets with a non-representative species sample. Thus, per trait, the bars represent plot 1, 3, 2, 856 and 4 of Figure 1. 857 858 Figure 7. Locations of trait observations (black dots). Colors indicate the environmental coverage of trait observations as estimated by the MESS 859 analysis (Elith et al., 2010). Legend: blue, interpolation; red, extrapolation. More intense shades indicate greater similarities (blue) or differences 860 (red) in environmental conditions of the location compared to the environmental conditions covered by the training dataset.