dataesr/scientific-paragraphs-categorization huggingface dataset:
7C ). This procedure does not allow to access the respective fabric strength of each class, but the number of grains remains significant for most categories and we see how the J index evolves by adding new grains to the growing dataset (see the 'Method' section for further details). In Fig. 7 , our method confirms a significant increase of J index -or M index (see supp. Fig. 4 )-with increasing equivalent diameter, except below 8 µm where the J index drops drastically. The density overestimation threshold is here estimated to be ∽500 grains. To better document the dependency of the fabric strength on grain size, we compiled datasets from several EBSD maps acquired over a larger shear band in grade 5 (Fig. 8  and supp. Fig. 5 ). For each map in Fig. 8A , the J index has been calculated as a function of grain size considering categories with a cumulative number of grains, as described in Fig.
7C  and the 'Method' section. We further checked for density overestimations through calculation of the J and M indices based on the same number of grains for each category, but selecting grains randomly-rather than sorted by size-in the same dataset (see the 'Method' section). This gives rise to a threshold number of grains above which the fabric strength remains quasi-unchanged, and below which J and M depend on the number of discrete data, as exemplified for map #5 in Fig. 8B. Only data above the density overestimation thresholds have been therefore considered and plotted in Fig. 8C , where a dependency of the fabric strength on grain size is documented for most aggregates of the shear band, particularly in maps #5 and #7. However, this dependency is differently pronounced and non-systematic, as shown in maps #1, #8 and #9 for which no dependency is observed (Fig.
J and M are calculated for a cumulative number of grains either sorted by ascending grain size or randomly selected in the same dataset (randomly sorted). This graph exemplifies our procedure to define the threshold number of grains (here 100 grains) above which J and M are relevant, i. e. , independent on density overestimations (see the 'Method' section). The dashed line refines the threshold value by applying a zero-phase digital filtering to J and M based on randomly sorted data. (C) Texture (J) index versus number of grains extracted from all maps shown in (A). J is calculated for a cumulative number of grains sorted by ascending grain size. Only data above the density overestimation threshold have been considered. Symbols give the J index and number of grains for grain size (GS) populations lower than 10, 15, 20 and 30 μm.
While backscattered electron images have been acquired using a Gemini I field Emission Gun from Zeiss available in Orléans (ISTO/BRGM, France), a TESCANx MIRA 3 XMU equipped with an EDAX Pegasus system, also available at the ISTO/BRGM, has been used to get EBSD data. SEM observations and EBSD analyzes have been performed at an accelerating voltage of 15 and 20 kV, and a working distance of 10 and 15 mm, respectively. The size of micro-pores has been estimated by contouring their area-subsequently converted in equivalent diameter-using the open-access software 'imageJ' (version 1. 51; https:// imagej. nih. gov/ ij) on SEM images. EBSD acquisitions have been performed on thin sections tilted at 70°. EBSD mapping. Data acquisition and post-analyzing cleaning have been performed using the TSL-OIM softwares (OIM data collection and OIM analysis version 7.
1; https:// www. edax. com/ produ cts/ ebsd/ oim-analy sis) with map "cleaning" procedure described in Précigout et al. 9, 10. We used a step size of 1 micron for each map, except for the maps shown in Fig. 4  where we applied a step size of a ¼ micron. The data were then treated and plotted using the open-source MTEX toolbox  54, 55  (version 5. 7; https:// mtex-toolb ox. github. io) for MATLAB. The minimum angles of lattice misorientation to define high-angle (grain) and low-angle (sub-grain and inner) boundaries have been respectively set to 10° and 2°, and each grain contains a minimum of five consecutive pixels on several rows. While continuous low-angle boundaries are referred to as sub-grain boundaries, the discontinuous ones are referred to as inner boundaries. Whereas the crystal symmetry for quartz is trigonal 32 (point group 321), we chose to use a hexagonal symmetry (point group 622) to avoid artefacts related to dauphine twins, some of them being artificially produced during data acquisition; dauphine twins can be merged with parent grains, but even so, they significantly change the mean orientation of grains  29.
This includes the texture and misorientation indices, which are calculated differently, but provide the same-and very useful-information. However, both indices have been described as depending on the number of discrete data below a certain amount of them  32. To tackle this issue, we here develop a numerical routine that defines the threshold number of grains above which J and M are relevant for a given EBSD map. At first, we calculate each scalar for a cumulative number of grains sorted by ascending grain size. For instance, we select all grains lower than 3 µm and calculate the J and M indices. We then add grains between 3 and 4 µm and calculate both indices again, and so on until considering all grains of the map dataset. Note that the grain size increment is not necessarily 1 µm, but may be adjusted to either refine the transition from one class to another (at small grain size) or avoid oversampling of categories (at large grain size).
To check for density overestimation, we then use the same number of grains in each class, but selecting grains randomly in the map dataset. Through calculation of J and M, which we repeated several times for each category to refine the mean index values, we can define the number of grains above which J and M remain constant, and hence, do not depend on the amount of discrete data anymore. Zero-phase digital filtering ("filtfilt" option in Matlab) has been also applied to fit the J and M values over the full range of data, so that the threshold value is better defined (see example in Fig. 8B ).
(C) Lattice-preferred orientation of quartz for the area shown in (A) and considering the mean orientation of each grain. Distributions of the [0001] c and [1120] a axes are shown in lower-hemisphere, equal-area pole figures using iso-contours and a color bar to highlight multiples of a uniform distribution (MUD). n number of grains; J texture index 56 ; M misorientation index 32. (D) Distribution of misorientation axes across low-angle boundaries shown in (A). As highlighted by multiples of uniform distribution (MUD), most axes concentrate around the [c] axis, indicating dominant prism-<a> dislocation slip-system to produce intra-grain boundaries (see text). n number of axes. (E) Grain size distribution for quartz shown in (A). Grains cut by the map frame are excluded from the dataset. The mode is estimated using a best-fit ('histfit' function in Matlab) log-normal distribution (red curve).
(C) Texture (J) index versus number of grains extracted from all maps shown in (A). J is calculated for a cumulative number of grains sorted by ascending grain size. Only data above the density overestimation threshold have been considered. Symbols give the J index and number of grains for grain size (GS) populations lower than 10, 15, 20 and 30 μm. While most EBSD maps highlight a positive dependency of the fabric strength on grain size, this dependency weakens or even disappears for some of them (see text).
Acknowledgements We thank  Dr. Elena Druguet  to have reviewed a former version of this manuscript. We also thank  Prof. Georges W. Bergantz  and  Dr. Amicia Lee  for correcting the English writing and providing constructive comments. This work has received funding from the  European Research Council  ( ERC RHEOLITH , grant agreement N°  290864 ) and  Agence National de la Recherche (ANR MECAMUSH , grant agreement N°  ANR-19-CE31-0007 ).
g. root depth)  2. As with all plants, the functional biogeography of trees is known to be partly governed by leaf economics  13  , which are critical for light acquisition and water balance, as well as wood and root traits, which are fundamental for structural stability and water transport and nutrient acquisition  6, 23. Traits such as seed characteristics and crown dimensions can be critical drivers of successional trajectories, canopy positioning, and life-history strategies across the landscape  [24] [25] [26]. Identifying the multidimensional trait relationships that integrate these different tree parts is urgently needed to create standardized, systematic metrics of forest functional biodiversity across the globe  12, 27, 28. A key limitation when exploring functional trait relationships is the sparsity inherent in most plant trait databases  5, 17, 29, 30.
To explore relationships between phylogenetically conserved traits and environmentally plastic traits, trait-imputation methods must consider evolutionary history along with the local environmental conditions  32. Given the enormous ontogenetic and environmental variation observed in many important tree traits-including stem size, crown size, leaf geometry, tree height, and root depth  [23] [24] [25]  -incorporating both phylogenetic information and environmental information is particularly important when exploring trait patterns in trees. Here, we use a global trait database  29  comprising nearly 500,000 trait measurements across more than 13,000 tree species to explore relationships among 18 functional traits, reflecting leaf economics, wood structure, bark thickness, tree size and crown size, seed size, and root depth (Fig.
1b ). To overcome the data sparsity and focus on relationships across all 18 traits, we develop a series of non-parametric machine-learning models that provide spatially-explicit estimates of trait expression of an individual tree in a given location, as a function of its evolutionary history and the local environmental conditions. Using the resulting dataset, we ask: (1) Which traits and environmental variables best capture overall variation in tree trait expression? and (2) What is the dimensionality of trait space and the dominant multi-trait clusters that capture the full breadth of tree form and function at the global scale? Our expectation was that traits underpinning the leafeconomic spectrum would continue to emerge as a key driver of trait relationships, primarily reflecting the broad differences in leaf morphology and physiology between angiosperms and gymnosperms  5.
1b , Supplementary Fig. 2 ). Across all species, 423 had more than 10 unique traits measured, and two species (Picea abies and Pinus sylvestris) had measurements for all 18 traits. In general, there was highly consistent coverage across taxonomic orders and traits (Supplementary Fig. 1 ), with gymnosperms being slightly overrepresented (comprising 3. 1 ± 6. 8% of measurements in the database versus ~1% of all known tree species  34, 35  , Fig. 1a ), in part reflecting the wider geographic range of many gymnosperms relative to angiosperms  36. To explore relationships in functional traits at the individual level, we used random-forest machine-learning models to estimate missing trait values for each individual tree as a function of its environment and phylogenetic history. We also conducted a second set of analyses where trait expression was estimated using phylogenetic information only, which allowed us to include additional non-georeferenced data (Fig.
4c , Supplementary Figs. 6, 9 ), these results can aid in the selection of representative traits from each cluster, depending on the intended question or application (e. g. by selecting environmentally sensitive traits such as crown size, vs. more phylogenetically conserved traits such as maximum tree height). Such insight can help with the adoption of a standardized set of tree traits that allow for consistent quantification and comparison of forest biodiversity on a global scale. The 18 physiological and morphological traits used here were selected in part due to their representation in prior trait analyses, their functional uniqueness, their relevance to tree structure and architecture, and the data quality. Thus, as with all functional trait analyses, there are additional traits and metrics not considered here which may capture complementary aspects of tree form and function.
For example, various allometric relationships (e. g. the ratio of tree height to stem diameter) may better capture energetic allocation in trees than do physiological traits  76  by reflecting unique aspects of tree morphology (see Supplementary Figs. 24, 25 for analysis exploring allometric ratios). Alternatively, belowground traits such as root architecture and chemistry remain particularly underrepresented for trees, despite capturing potentially unique aspects of tree form and function  74, 75. Increasing the representation of such traits in trait databases is an important next step, and critical for quantifying the multi-functionality of forest biodiversity. Here, by focusing on trees, we have significantly higher specieslevel representation compared to kingdom-wide analyses, encompassing more than 20% of known tree species and 22% of all trait-by-species combinations (Supplementary Fig.
By including environmental variation alongside phylogenetic information, our approach should better incorporate these non-taxonomic drivers of trait expression than approaches which do not allow for intraspecific variation. Yet including high-resolution microsite data and stand-level information in existing trait databases will be critical for gaining a more nuanced understanding of the drivers of tree trait expression. Here, by quantifying the full dimensionality of trait space, this work can serve as a baseline for such research, helping to identify the dominant traits that underpin the functional biodiversity of forests. Collectively, this work reveals key relationships and trait clusters governing tree form and function worldwide. We show that tree functional traits predominantly reflect two major functional axes: one representing leaf-level photosynthetic capacity and resource economies, and the other representing competition for light via tree and crown size.
Methods Trait information. Trait data were obtained from the TRY plant trait database 29 v. 5. 0. Data were cleaned by converting all traits to standardized units and by matching species names to The Plant List (TPL) database v1. 1 (http://www. theplantlist. org, accessed June 2020) using the Taxonstand package in R v3. 6. 0  80. Synonyms were replaced with accepted names, when available. The phylogenetic tree was taken from the seed plant phylogeny of Smith & Brown  81  , and species names were likewise cleaned and harmonized using the TPL database. To limit our analysis to tree functional traits only, we used the BGCI GlobalTreeSearch database v1. 3  35, 82  , containing a comprehensive list of ca. 60,000 tree species compiled and harmonized from across 500 sources. The BGCI database uses TPL for much of its taxonomic identification, but to ensure consistency among all sources we used the same name harmonization pipeline as with TRY and the seed plant phylogeny.
We constrained the set of traits and the phylogenetic tree to those species that could be matched to the BGCI database (n = 52,255 species matched, excluding monocots), and we likewise trimmed the phylogenetic tree to the set of species matched in TRY For comparison with previous work on trait trade-offs, we focused on physiological and morphological traits directly measured at the individual level, rather than derived traits such as those related to tree allometry (although see Supplementary Figs. 24, 25 and Supplementary Notes). The core set of 18 traits was selected from the TRY database first based on their use in prior global analyses  5  (leaf area, specific leaf area, seed dry mass, maximum tree height, leaf nitrogen, wood density), their importance in the leaf economics spectrum  14, 15, 20, 83  (leaf thickness, density, Vcmax, phosphorous, potassium, and stomatal conductance), their role in tree water transport and access  23, 84  (root depth, stem conduit diameter), and finally, those that are integral components of tree structure  6  (stem diameter, bark thickness, crown height and diameter).
This resulted in a primary set of 18 traits for use in the main analysis (Supplementary Table  3 , Supplementary Data 1). For each trait, we selected sub-categories (as specified by TRY) that denoted comparable measurements and reflected uniform assay conditions (e. g. V cmax measured at 25 °C) (Supplementary Table  3 ). We also obtained an additional 12 traits from the TRY to improve our ability to predict missing trait values via incorporating trait covariation (see model details, below). However, these were not used in the main analysis because they are either auto-correlated with one of the focal traits by definition (e. g. leaf width, leaf length, leaf C/N, leaf N/P, leaf moisture), they encompassed fewer than 150 species (root/shoot ratio, root N per mass, root C/N, and wood N per mass), or because they can vary substantially across measurement protocols or assay conditions but had insufficient metadata (i.
e. lack of incubation temperature) needed for standardization (leaf J max , leaf respiration rate, leaf chlorophyll). Trait values were converted to common units where necessary (e. g. mm to cm), log-transformed, and normalized to have a mean of zero and a standard deviation of one, following standard approaches  5, 15, 29, 30. Trait-imputation models. In order to consider multidimensional trait relationships across all species and all traits, we used a machine-learning model to estimate the missing trait values for each species in each location. Specifically, we used random-forest (RF) models to estimate trait values for each georeferenced species using the ranger package in R  85  , with trait expression modelled as a function of each tree's environment and phylogenetic history. The random-forest algorithm is determined by a specified set of "hyper-parameters", which govern the splitting rules, variable selection, and stopping rules when building each tree in the forest  86, 87.
Preliminary investigation showed that a wide variation in these hyperparameters (e. g. using 1 versus 25 minimum observations per node) led to negligible improvements in model accuracy relative to the default parameters (i. e. <2% increase in out-of-bag R 2 ). Thus, to minimize the risk of overfitting due to a large number of traits and models being considered here, we used the default ranger hyper-parameters for all traits (500 trees per forest; sampling with replacement; the number of variables per split equal to the square root of the number of predictors; a minimum of 5 observations per node; and the split rule determined by maximal variance). In order to minimize the influence of data-recording errors or unit mismatches in the dataset, trait values which occurred outside of the bulk of the trait distribution were investigated as outliers.
We omitted variables that directly measure plant community composition or biotic factors (e. g. NDVI or % forest cover) so as to ensure the resulting geographic layers solely encompassed nonbiotic factors. Layers were sampled from a previously prepared global composite  90. Briefly, all covariate map layers were resampled and reprojected to a unified pixel grid in EPSG:4326 (WGS84) at 30 arcsec resolution (~1 km 2 at the equator). Layers with a higher original pixel resolution were downsampled using a mean aggregation method; layers with a lower original resolution were resampled using simple upsampling (that is, without interpolation) to align with the higher resolution grid. The set of environmental variables for each trait measurement was obtained by sampling this composite image at each unique latitude and longitude value given in the TRY database.
Note that this amounted to us using the phylogeny-only model for seed dry mass only, and the combined model for all other traits (Supplementary Fig. 6 ). Model performance. Model performance was quantified using buffered leave-oneout cross-validation  46. To avoid overestimating the out-of-fit accuracy, we first estimated the range of spatial and phylogenetic autocorrelation in the raw data, following the approach recommended in Roberts et al. (2017). Specifically, before running any trait-imputation models, we fit a simple linear regression model to the raw data, where trait expression was modelled as a linear function of phylogenetic and environmental variables. We then assessed spatial autocorrelation of the residuals via Moran's I plots using the ncf package in R, which displays the value of spatial autocorrelation (ranging from -1 to 1) as a function of distance  93.
We likewise assessed residual phylogenetic autocorrelation across taxonomic ranks (genus, family, order, group), using the the ape package in R. In general, spatial autocorrelation was low (I < 0. 10) (Supplementary Fig. 3 ), with the exception of leaf phosphorous, which exhibited slight autocorrelation up to ~250 km. The residual phylogenetic correlation was likewise low, and generally only observable at the genus level, apart from crown width and height and conduit diameter, which exhibited residual autocorrelation up to the family level (Supplementary Fig. 4 ). Thus, to be conservative, for all traits except crown size and conduit diameter, we used a genus-level spatial buffer of 250 km to exclude test/training data; and for crown size and conduit diameter we used a family-level buffer at 250 km.
To identify the dominant axes of variation across all 18 traits, we use species-weighted principal component analysis (PCA). This was conducted on the full set of imputed traits using the aroma. light package in R, with observed values used in place of imputed values where available. The weights were set to be inversely proportional to the number of observations for each species, which allowed us to incorporate intraspecific variation while also ensuring that each species had the same overall contribution to trait relationships. Representative vectors for each axis were identified by selecting those that loaded most uniquely on each of the first two principle component axes. Abiotic relationships. To explore the relationships between the primary trait axes and environmental conditions, we used Shapley values from random-forest models.
Shapley values are a game-theoretic metric that partitions the relative influence of each variable on the outcome, for every observation in the dataset  60, 95, 96. It is a machine-learning analog to partial regression, in that it looks to quantify the marginal relationship between predictors and outcome variables, taking into account all other variables in the model. To quantify Shapley values, we used the random forest to model each of the PC axis values as a function of the ten environmental variables. We then used the fastshap package in R to estimate the Shapley values for each variable for each observation using out-of-fit test dataset (15% of data withheld), and we quantified the overall variable importance by taking the sum of the absolute Shapley values. The environmental variables in Fig.
3a , b are ranked by variable importance, and the trends for the three variables with the highest Shapley values are shown in Fig. 3c -h for each axis. We also conducted a second analysis on the full set of 50 covariates to depict the full set of trends across climate, soil, and topography (Supplementary Figs. 17, 18), but note that many of these relationships are redundant due to high correlations between variables. Functional cluster analysis. In order to identify the dimensionality of trait space and identify the dominant functional trait clusters capturing the full variation in tree form and function, we conducted hierarchical clustering on the species-level correlation matrix. First, we calculated species-weighted rank correlations between pairs of traits using the wCorr package in R, which again allowed us to incorporate intraspecific trait variation while ensuring each species contributed equal weight.