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% Supplementary Information

# Supplementary methods
We developed the equation of $\alpha_{c,f} = \alpha_{0,f} + \alpha_r \, t_f + \alpha_i \, t_c + \alpha_s \, \vert t_c-t_f \vert$ along with the basal area of each competitive species in the competition index to show the parameters are directly related to community weighted means of the different traits variables as:
\begin{equation} \label{alphaBA}
\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} + \alpha_r \, t_f \, B_{i,tot} + \alpha_i \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}
\end{equation}

Where:

$B_{i,tot} = \sum_{c=1}^{C_p} {B_{i,c,p,s}}$,

$B_{i,t_c} = \sum_{c=1}^{C_p} {t_c \times B_{i,c,p,s}}$,

$B_{i,\vert t_c - t_f \vert} = \sum_{c=1}^{C_p} {\vert t_c - t_f \vert \times B_{i,c,p,s}}$,

and $C_p$ is the number of species on the plot $p$.

## Details on sites

### Panama

- Data set name: Panama
- Data type: LPP
- Plot size: 1 to 50 ha
- Dbh threshold: 1 cm
- Number of plots: 42
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: R. Condit (conditr@gmail.com)
- Comments: The data used include both the 50 ha lot of BCI and the network of 1 ha plots from Condit et al. (2013). The two first census of BCI plot were excluded.
- References: 
	- Condit, R. (1998). Tropical forest census plots. Springer, Berlin, Germany.
	- Condit, R., Engelbrecht, B.M.J., Pino, D., Perez, R., Turner, B.L., (2013).  Species distributions in response to individual soil nutrients and seasonal drought across a community of tropical trees. Proceedings of the National Academy of Sciences 110: 5064-5068.
	- Wright, S.J., Kitajima, K., Kraft, N.J.B., Reich, P.B., Wright, I.J., Bunker, D.E., Condit, R., Dalling, J.W., Davies, S.J., Díaz, S., Engelbrecht, B.M.J., Harms, K.E., Hubbell, S.P., Marks, C.O., Ruiz-Jaen, M.C., Salvador, C.M. & Zanne, A.E. (2010) Functional traits and the growth-mortality trade-off in tropical trees. Ecology 91: 3664-3674.


### Japan

- Data set name: Japan
- Data type: LPP
- Plot size: 0.35 to 1.05 ha
- Dbh threshold: 2.39 cm
- Number of plots: 16
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: M. I. Ishihara (moni1000f_networkcenter@fsc.hokudai.ac.jp)
- Comments: 
- References: 
	- Yakushima Forest Environment Conservation Center, Ishihara, M.I., Suzuki, S.N., Nakamura, M., Enoki, T., Fujiwara, A., Hiura, T., Homma, K., Hoshino, D., Hoshizaki, K., Ida, H., Ishida, K., Itoh, A., Kaneko, T., Kubota, K., Kuraji, K., Kuramoto, S., Makita, A., Masaki, T., Namikawa, K., Niiyama, K., Noguchi, M., Nomiya, H., Ohkubo, T., Saito, S., Sakai, T., Sakimoto, M., Sakio, H., Shibano, H., Sugita, H., Suzuki, M., Takashima, A., Tanaka, N., Tashiro, N., Tokuchi, N., Yoshida, T., Yoshida, Y., (2011). Forest stand structure, composition, and dynamics in 34 sites over Japan. Ecological Research 26: 1007-1008. 


### Puerto Rico

- Data set name: Luquillo
- Data type: LPP
- Plot size: 16 ha
- Dbh threshold: 1 cm
- Number of plots: 1
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: J. Zimmerman (esskz@ites.upr.edu)
- Comments: 
- References: 
	- Thompson, J., N. Brokaw, J. K. Zimmerman, R. B. Waide, E. M. Everham III, D. J. Lodge, C. M. Taylor, D. GarciaMontiel, and M. Fluet. (2002). Land use history, environment, and tree composition in a tropical forest. Ecological Applications 12: 1344-1363.
	- Swenson, N.G., J.C. Stegen, S.J. Davies, D.L. Erickson, J. Forero-Montana, A.H. Hurlbert, W.J. Kress, J. Thompson, M. Uriarte, S.J. Wright and J.K. Zimmerman. (2012). Temporal turnover in the composition of tropical tree communities: functional determinism and phylogenetic stochasticity. Ecology 93: 490-499.


### Central African Republic

- Data set name: M'Baiki
- Data type: LPP
- Plot size: 4 ha
- Dbh threshold: 10 cm
- Number of plots: 10
- Traits: Wood density, SLA, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: G. Vieilledent (ghislain.vieilledent@cirad.fr)
- Comments: 
- References: 
	- Ouadraogo, D.-Y., Mortier, F., Gourlet-Fleury, S., Freycon, V., and Picard, N. (2013). Slow-growing species cope best with drought: evidence from long-term measurements in a tropical semi-deciduous moist forest of Central Africa. Journal of Ecology 101: 1459-1470.
	- Gourlet-Fleury, S., V. Rossi, M. Rejou-Mechain, V. Freycon, A. Fayolle, L. Saint-André, G. Cornu, J. Gerard, J. M. Sarrailh, and O. Flores. (2011). Environmental Filtering of Dense-Wooded Species Controls above-Ground Biomass Stored in African Moist Forests. Journal of Ecology 99: 981-90.


### Taiwan

- Data set name: Fushan
- Data type: LPP
- Plot size: 25 ha
- Dbh threshold: 1 cm
- Number of plots: 1
- Traits: Wood density, SLA, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: I-F. Sun (ifsun@mail.ndhu.edu.tw)
- Comments: 
- References: 
	- Lasky, J.R., Sun, I., Su, S.-H., Chen, Z.-S., and Keitt, T.H. (2013). Trait-mediated effects of environmental filtering on tree community dynamics. Journal of Ecology 101: 722-733.


### French Guiana

- Data set name: Paracou
- Data type: LPP
- Plot size: 6.25 ha
- Dbh threshold: 10 cm
- Number of plots: 15
- Traits: Wood density, SLA, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: B. Herault (bruno.herault@cirad.fr)
- Comments: 
- References: 
	- Herault, B., Bachelot, B., Poorter, L., Rossi, V., Bongers, F., Chave, J., Paine, C.E., Wagner, F., and Baraloto, C. (2011). Functional traits shape ontogenetic growth trajectories of rain forest tree species. Journal of Ecology 99: 1431-1440.
	- Herault, B., Ouallet, J., Blanc, L., Wagner, F., and Baraloto, C. (2010). Growth responses of neotropical trees to logging gaps. Journal of Applied Ecology 47: 821-831.
	- Baraloto, C, P.C.E. Timothy, L. Poorter, J. Beauchene, D. Bonal, AM Domenach, B. Hérault, S. Patińo, JC Roggy, and Jerome Chave. (2010). Decoupled Leaf and Stem Economics in Rain Forest Trees. Ecology Letters 13: 1338-47.


### France

- Data set name: France
- Data type: NFI
- Plot size: 0.017 to 0.07 ha
- Dbh threshold: 7.5 cm
- Number of plots: 41503
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: G. Kunstler (georges.kunstler@gmail.com)
- Comments: The French NFI is based on temporary plot, but 5 years tree radial growth is estimated with short core. All trees with dbh > 7.5 cm, > 22.5 cm and > 37.5 cm were measured within a radius of 6 m, 9 m and 15 m, respectively. Plots are distributed over forest ecosystems on a 1-km 2 cell grid
- References: 
	- IFN. (2011). Les resultats issus des campagnes d'inventaire 2006, 2007, 2008, 2009, 2010 et 2011. Inventaire Forestier National, Nogent-sur-Vernisson, FR.
	- http://inventaire-forestier.ign.fr/spip/spip.php?rubrique153


### Spain

- Data set name: Spain
- Data type: NFI
- Plot size: 0.0078 to 0.19 ha
- Dbh threshold: 7.5 cm
- Number of plots: 49855
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: M. Zavala (madezavala@gmail.com)
- Comments: Each SFI plot included four concentric circular sub-plots of 5, 10, 15 and 25-m radius. In these sub-plots, adult trees were sampled when diameter at breast height (d.b.h.) was 7.5-12.4 cm, 12.5-22.4 cm, 22.5-42.5 cm and >= 42.5 cm, respectively.
- References: 
	- Villaescusa, R. & Diaz, R. (1998) Segundo Inventario Forestal Nacional (1986-1996), Ministerio de Medio Ambiente, ICONA, Madrid.
	- Villanueva, J.A. (2004) Tercer Inventario Forestal Nacional (1997-2007). Comunidad de Madrid.  Ministerio de Medio Ambiente, Madrid.
	- http://www.magrama.gob.es/es/desarrollo-rural/temas/politica-forestal/inventario-cartografia/inventario-forestal-nacional/default.aspx


### Switzerland

- Data set name: Swiss
- Data type: NFI
- Plot size: 0.02 to 0.05 ha
- Dbh threshold: 12 cm
- Number of plots: 2665
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: N. E. Zimmermann (niklaus.zimmermann@wsl.ch)
- Comments: All trees with dbh > 12 cm and > 36 cm were measured within a radius of 7.98 m and 12.62 m, respectively.
- References: 
	- http://www.lfi.ch/index-en.php


### Sweden

- Data set name: Sweden
- Data type: NFI
- Plot size: 0.0019 to 0.0314 ha
- Dbh threshold: 5 cm
- Number of plots: 22904
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: G. Stahl (Goran.Stahl@slu.se)
- Comments: All trees with dbh > 10 cm, were measured on circular plots of 10 m radius.
- References: 
	- Fridman, J., and Stahl, G. (2001). A three-step approach for modelling tree mortality in Swedish forests. Scandinavian Journal of Forest Research 16: 455-466.


### USA

- Data set name: US
- Data type: NFI
- Plot size: 0.0014 to 0.017 ha
- Dbh threshold: 2.54 cm
- Number of plots: 97434
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: M. Vanderwel (Mark.Vanderwel@uregina.ca)
- Comments: FIA data are made up of cluster of 4 subplots of size 0.017 ha for tree dbh > 1.72 cm and nested in each subplot sapling plots of 0.0014 ha for trees dbh > 2.54 cm. The data of the four subplot were lumped together.
- References: 
	- http://www.fia.fs.fed.us/tools-data/


### Canada

- Data set name: Canada
- Data type: NFI
- Plot size: 0.02 to 0.18 ha
- Dbh threshold: 2 cm
- Number of plots: 15019
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: TRY
- Contact of person in charge of data formatting: J. Caspersen (john.caspersen@utoronto.ca)
- Comments: The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plot are 10 m in radius in this Province.
- References: 


### New Zealand

- Data set name: NZ
- Data type: NFI
- Plot size: 0.04 ha
- Dbh threshold: 3 cm
- Number of plots: 1415
- Traits: Wood density, SLA, Maximum height, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: D. Laughlin (d.laughlin@waikato.ac.nz)
- Comments: Plots are 20 x 20 m.
- References: 
	- Wiser, S.K., Bellingham, P.J. & Burrows, L.E. (2001) Managing biodiversity information: development of New Zealand's National Vegetation Survey databank. New Zealand Journal of Ecology, 25: 1-17.
	- https://nvs.landcareresearch.co.nz/


### Australia

- Data set name: NSW
- Data type: NFI
- Plot size: 0.075 to 0.36 ha
- Dbh threshold: 10 cm
- Number of plots: 30
- Traits: Wood density, Maximum height, and Seed mass
- Source trait data: local
- Contact of person in charge of data formatting: R. M. Kooyman (robert@ecodingo.com.au)
- Comments: Permanents plots established by the NSW Department of State Forests or by RMK
- References: 
	- Kooyman, R.M. and Westoby, M. (2009) Costs of height gain in rainforest saplings: main stem scaling, functional traits and strategy variation across 75 species. Annals of Botany 104: 987-993.
	- Kooyman, R.M., Rossetto, M., Allen, C. and Cornwell, W. (2012) Australian tropical and sub-tropical rainforest: phylogeny, functional biogeography and environmental gradients. Biotropica 44: 668-679.

## References for the data extracted from the TRY database used in this analysis

-  Ackerly & Cornwell 2007 Ecology Letters 10:135-145
-  Castro-Diez et al. 1998 Oecologia 116:57-66
-  Chave et al. 2009 Ecology Letters 12:351-366
-  Cornelissen 1996 Journal of Ecology 84:573-582
-  Cornelissen et al. 1996 Journal of Ecology 84:755-765
-  Cornelissen et al. 1997 Oecologia 111:460-469
-  Cornelissen et al. 2003 Journal of Vegetation Science 14:311-322
-  Cornelissen et al. 2003 Journal of Vegetation Science 14:311-322
-  Cornelissen et al. 2003 Journal of Vegetation Science 14:311-322
-  Cornelissen et al. 2004 Functional Ecology 18:779-786
-  Cornwell & Ackerly 2009 Ecological Monographs 79:109-126
-  Cornwell et al. 2006 Ecology 87:1465-1471
-  Cornwell et al. 2007 Functional Ecology 21:1063-1071
-  Cornwell et al. 2007 Functional Ecology 21:1063-1071
-  Cornwell et al. 2008 Ecology Letters 11:1065-1071
-  Díaz et al. 2004 Journal of Vegetation Science 15:295-304
-  Fonseca et al. 2000 Journal of Ecology 88:964-977
-  Fortunel et al. 2009 Ecology 90:598-611
-  Freschet et al. 2010 Journal of Ecology 98:362-373
-  Freschet et al. 2010 New Phytologist 186:879-889
-  Garnier et al. 2007 Annals of Botany 99:967-985
-  Green 2009 http://bricol.net/downloads/data/PLANTSdatabase 
-  Gutiérrez & Huth  2012 Perspect. Plant Ecol. Evol. Syst.
-  Han et al. 2005 New Phytologist 168:377-385
-  He et al. 2006 New Phytologist 170:835-848
-  He et al. 2008 Oecologia 155:301-310
-  Hoof et al. 2008 Biotropica 40:113-118
-  Hoof et al. 2008 Biotropica 40:113-118
-  Kattge et al. 2009 Global Change Biology 15:976-991
-  Kleyer et al. 2008 Journal of Ecology 96:1266-1274
-  Laughlin et al. 2010 Functional Ecology 24:493-501.
-  Martin et al. 2007 Oecologia 151:387-400
-  Martin et al. 2007 Oecologia 151:387-400
-  McDonald et al. 2003 Functional Ecology 17:50-57
-  Medlyn & Jarvis 1999 Ecological Modelling 124:69-83
-  Medlyn et al. 1999 Plant, Cell and Environment 22:1475-1495
-  Medlyn et al. 2001 New Phytologist 149:247-264
-  Messier et al. 2010 Ecology Letters 13:838-848
-  Moles et al. 2004 Journal of Ecology 92:384-396
-  Moles et al. 2004 Journal of Ecology 92:384-396
-  Moles et al. 2005 PNAS 102:10540-10544
-  Moles et al. 2005 Science 307:576-580
-  Niinemets 1999 New Phytologist 144:35-47
-  Niinemets 2001 Ecology 82:453-469
-  Ogaya & Penuelas 2003 Environmental and Experimental Botany 50:137-148
-  Ogaya & Penuelas 2006 Biologia Plantarum 50:373-382
-  Ogaya & Penuelas 2007 Plant Ecology 189:291-299
-  Ogaya & Penuelas 2008 Acta Oecologica 34:331-338
-  Onoda et al. 2011 Ecology Letters 14:301-312
-  Ordonez et al. 2010 American Naturalist 175:225-239
-  Ordonez et al. 2010 Ecology 91:3218-3228
-  Pakeman et al. 2008 Journal of Ecology 96:355-366
-  Pakeman et al. 2009 Journal of Vegetation Science 20:148-159
-  Penuelas et al. 2010 Global Change Biology 16:2171-2185
-  Penuelas et al. 2010 Journal of Chemical Ecology 36:1255-1270
-  Poorter & Bongers 2006 Ecology 87:1733-1743
-  Poorter 2009 New Phytologist 181:890-900
-  Poorter et al. 2009 New Phytologist 182:565-588
-  Preston et al. 2006 New Phytologist 170:807-818
-  Pyankov et al. 1999 New Phytologist 143:131-142
-  Quested 2003 et al. Ecology 84:3209-3221
-  Reich et al. 2008 Ecology Letters 11:793-801
-  Reich et al. 2009 Oecologia 160:207-212
-  Sack 2004 Oikos 107:110-127
-  Sack et al. 2005 New Phytologist 167:403-413
-  Sack et al. 2006 American Journal of Botany 93:829-839
-  Sardans et al. 2008 Forest Science 54:513-522
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-  Wilson, K. B., D. D. Baldocchi, and P. J. Hanson. 2000. Tree Physiology 20:565-578.
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-  Zanne et al. 2009 Dryad 

# Supplementary discussion

## Trait effects and potential mechanisms

Wood density (WD) was strongly negatively associated with maximum growth, in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (in full light conditions) than shade tolerant species[@nock_wood_2009; @wright_functional_2010]. One advantage of low wood density is clearly that it is cheaper to build light than dense wood, thus for the same biomass growth a low wood density species will have a higher basal area increment than a high wood density species[@enquist_allometric_1999]. Other advantages of light wood may include higher xylem conductivity[@chave_towards_2009], though for angiosperms this is a correlated trait rather than an automatic consequence. A countervailing advantage for high wood density species was their better tolerance to competition (less growth reduction per unit of basal area of competitors), which is in line with the idea that these species are more shade tolerant[@chave_towards_2009; @nock_wood_2009; @wright_functional_2010]. This has generally been related to the higher survival associated with high wood density[@kraft_relationship_2010], via resistance to mechanical damage, herbivores and pathogens[@chave_towards_2009; @kraft_relationship_2010], but may also be connected to a lower maintenance respiration[@larjavaara_perspective_2010]. For growth, the lower respiration may lead to a direct advantage in deep shade, but the correlation might also arise through correlated selection for high survival rate and for high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effect, especially in tropical forest where the confidence interval did not span zero. This might possibly have been mediated by larger crowns (both in depth and radius)[@poorter_architecture_2006; @aiba_architectural_2009], casting a deeper shade.

SLA was positively correlated with maximum basal area growth (growth without competition). This agrees well with previous studies that reported a positive correlation between SLA and nitrogen and phosphorus concentration, and gas exchange (the 'leaf economic spectrum'[@wright_worldwide_2004]). As in previous studies[@poorter_are_2008; @wright_functional_2010], this direct effect of SLA was smaller than the effect size of wood density and had wider confidence intervals. Low SLA was also correlated with a stronger competitive effect. This may be related to a longer leaf life span characteristic of low SLA species because leaf longevity leads to a higher accumulation of leaf in the canopy and thus a higher light interception[@niinemets_review_2010].

Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@poorter_architecture_2006; @poorter_are_2008; @wright_functional_2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might be expected to select for slower growth in long-lived plants[@poorter_are_2008]. Maximum height was negatively correlated with tolerance to competition, in line with the idea that sub-canopy trees are more shade-tolerant[@poorter_architecture_2006]. There was however a tendency for species with tall maximum height to have stronger competitive effect (though with wider confidence intervals intercepting zero), that might be explained by greater light interception from taller trees.

Our results raised the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and response are the two central elements of the species competitive ability[@goldberg_competitive_1991]. One may expect that because of intra-specific competition, species with strong competitive effect should have evolved a high tolerance to competition. However, in agreement with previous studies[@goldberg_components_1990; @goldberg_competitive_1991; @wang_are_2010], we found little evidence for such coordination. It was present only for wood density, where high density conferred better competitive response and also stronger competitive effect (but with wide confidence intervals). For SLA there was no clear coordinations. For maximum height as explained above there was a tendency for short maximum height to lead to high tolerance to competition but to low competitive effect. This interesting because a trade-off between competitive tolerance and maximum height has been proposed as fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@kohyama_stratification_2009]. Finally the lack of support for coordination between response and effect is important because it means that competitive interaction is not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_r$ as in @kunstler_competitive_2012; @kraft_functional_2014; @lasky_trait-mediated_2014). Traits of competitors alone or of focal plants alone may convey more information. If traits are strongly linked to either competitive effect or competitive response, this still means that some trait values will have an advantage in competitive interactions.

Given that the effect sizes we report for effects of traits on competitive interaction are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that if traits measured at the individual level were available, rather than species averages, this might strengthen predictive power[@kraft_functional_2014].


## Variations between biomes

Overall most results were rather consistent across biomes (Fig 3 main text), but some exceptions deserve comment.

Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 3 main text). High SLA species tended to be more competition-tolerant (competitive response parameter $\alpha_r$) in temperate forests (confidence interval only marginally intercepted zero) while low SLA species were more competition-tolerant in tropical forests. These different outcomes may trace to the prevalence of deciduous species in temperate forests (see Extended data Table 1), because the link between shade-tolerance and SLA is different for deciduous and evergreen species[@lusk_why_2008]. In tropical forests shade-tolerant species often have long leaf lifespans, associated with low SLA. On the other hand in temperate deciduous forests the length of the growing season is fixed by temperature. Shade tolerant species cannot increase leaf longevity and instead reduce the cost of leaf production (high SLA) to offset the reduced income due to low light availability. The other noticeable difference between biomes was for taiga where the parameter relating wood density to competitive impact was positive, versus negative in the other biomes (Fig 3 main text). We do not have a mechanistic explanation to suggest for this discrepancy, but can observe that taiga has relatively few species many of which are conifers where the range of wood density is narrower than for angiosperms (see Extended data Table 1).


# References