% 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: $$\label{alphaBA} \sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} + \alpha_r \, t_f \, B_{i,tot} + \alpha_i \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}$$ 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 {r kable, echo = FALSE, results="asis"} library(plyr) dat <- read.csv('../../data/metadata/sites/sites_description.csv', check.names=FALSE, stringsAsFactors=FALSE) # reorder so references column is last i <- match("References", names(dat)) dat <- dat[,c(seq_len(ncol(dat))[-c(i)], i)] dat <- dat[,c(2,1,3:ncol(dat))] refs <- read.csv('../../data/metadata/sites/references.csv', check.names=FALSE, stringsAsFactors=FALSE) refs$citation <- iconv(refs$citation, "ISO_8859-2", "UTF-8") replace_refs <- function(x){ ids <- as.numeric(unlist(strsplit(x,","))) if(length(ids>0)) ret <- paste0("\n\t- ", refs$citation[match(ids, refs$id)], collapse="") else ret <- "" } dat$References <- sapply(dat$References, replace_refs) paste_name_data <- function(df){ sprintf("### %s\n\n%s\n\n", df[["Country"]], paste0( llply(names(df)[-c(1)], function(x) sprintf("- %s: %s", x, df[[x]])), collapse="\n") ) } list.t <- dlply(dat, 1, paste_name_data) writeLines(unlist(list.t[dat[["Country"]]]))  ## References for the data extracted from the TRY database used in this analysis {r refs data, echo = FALSE, results='asis'} data.refs <-read.csv(file.path("../..", 'output', 'refsTRYtidy.csv'), stringsAsFactors = FALSE) list.t <- lapply(as.list(data.refs$refs), function(x) paste("- ",x)) writeLines(unlist(list.t))  # Supplementary discussion ## Trait effects and potential mechanisms The most important driver of individual growth was individual tree size with a positive effect on basal area growth (see Extended data Table 3). This is unsurprising as tree size is known to be a key drivers of tree growth[@stephenson_rate_2014; @enquist_allometric_1999]. Then there was a consistent negative effect of the total basal area of neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height > 10cm), agree well with the idea that facilitation processes are generally limited to the regeneration phase rather than at the adult stage [@callaway_competition_1997]. In term of traits effects, 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 (confidence intervals spanned zero except for temperate rain forest and taiga), 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