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 kunstler committed Jul 17, 2015 1 2 \documentclass[a4paper,11pt]{article} \usepackage{lmodern} kunstler committed Aug 04, 2015 3 \usepackage{amsmath} kunstler committed Jul 17, 2015 4 5 6 7 8 9 10 11 12 \usepackage{ifxetex,ifluatex} \usepackage{fixltx2e} % provides \textsubscript \ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \else % if luatex or xelatex \ifxetex \usepackage{mathspec} \usepackage{xltxtra,xunicode} kunstler committed Aug 04, 2015 13 \else kunstler committed Jul 17, 2015 14 15 16 17 18 19 20 21 \usepackage{fontspec} \fi \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} \newcommand{\euro}{€} \fi \usepackage{ms} % use upquote if available, for straight quotes in verbatim environments \IfFileExists{upquote.sty}{\usepackage{upquote}}{} kunstler committed Aug 04, 2015 22 23 % % use microtype if available % \IfFileExists{microtype.sty}{% Kunstler Georges committed Sep 25, 2015 24 % \usepackage{microtype} kunstler committed Aug 04, 2015 25 26 % \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts % }{} kunstler committed Jul 17, 2015 27 kunstler committed Jul 17, 2015 28 \usepackage[numbers,super,sort&compress]{natbib} kunstler committed Jul 17, 2015 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 \ifxetex \usepackage[setpagesize=false, % page size defined by xetex unicode=false, % unicode breaks when used with xetex xetex]{hyperref} \else \usepackage[unicode=true]{hyperref} \fi \hypersetup{breaklinks=true, bookmarks=true, pdfauthor={Kunstler}, pdftitle={Methods}, colorlinks=true, citecolor=blue, urlcolor=blue, linkcolor=magenta, pdfborder={0 0 0}} \urlstyle{same} % don't use monospace font for urls \setlength{\parindent}{0pt} \setlength{\parskip}{6pt plus 2pt minus 1pt} \setlength{\emergencystretch}{3em} % prevent overfull lines \setcounter{secnumdepth}{0} \usepackage{fancyhdr} \pagestyle{fancy} \rhead{Methods} kunstler committed Sep 04, 2015 54 \title{Methods} kunstler committed Jul 17, 2015 55 56 57 58 59 60 61 62 63 64 65 \date{} \begin{document} \maketitle \section{Model and analysis}\label{model-and-analysis} To examine the link between competition and traits we used a neighbourhood modelling framework\citep{Canham-2006, Uriarte-2010, Ruger-2012, Kunstler-2012, Lasky-2014} to model the growth of a focal tree of species $$f$$ as a product of its kunstler committed Sep 04, 2015 66 maximum growth (determined by its traits and size) together with kunstler committed Jul 17, 2015 67 reductions due to competition from individuals growing in the local kunstler committed Sep 04, 2015 68 neighbourhood (see definition below). Specifically, we assumed a relationship of the form kunstler committed Jul 17, 2015 69 70 \label{G1} kunstler committed Sep 04, 2015 71 G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_i} {-\alpha_{c,f} B_{i,c,p,s}}\right), kunstler committed Jul 17, 2015 72 73 74 75 76 77 78 where: \begin{itemize} \itemsep1pt\parskip0pt\parsep0pt \item kunstler committed Sep 04, 2015 79 $$G_{i,f,p,s,t}$$ and $$D_{i,f,p,s,t}$$ are the the annual basal area kunstler committed Jul 17, 2015 80 growth and diameter at breast height of individual $$i$$ from species kunstler committed Sep 04, 2015 81 $$f$$, plot or quadrat (see below) $$p$$, data set $$s$$, and census $t$, kunstler committed Jul 17, 2015 82 \item kunstler committed Sep 04, 2015 83 $$G_{\textrm{max} \, f,p,s}$$ is the maximum basal area growth for species $$f$$ on plot or quadrat $$p$$ in data set $$s$$, i.e.~in kunstler committed Jul 17, 2015 84 85 86 87 absence of competition, \item $$\gamma_f$$ determines the rate at which growth changes with size for species $$f$$, modelled with a normally distributed random effect of kunstler committed Aug 04, 2015 88 89 90 91 species $$\varepsilon_{\gamma, f}$$ {[}as $$\gamma_f = \gamma_0 + \varepsilon_{\gamma, f}$$ where $$\varepsilon_{\gamma, f} \sim \mathcal{N} (0,\sigma_{\gamma})$$ -- a normal distribution of mean 0 and standard deviation $\sigma_{\gamma}${]} kunstler committed Jul 17, 2015 92 93 94 95 \item $$\alpha_{c,f}$$ is the per unit basal area effect of individuals from species $$c$$ on growth of an individual in species $$f$$, and \item kunstler committed Sep 04, 2015 96 97 98 99 100 101 102 103 104 105 106 107 108 $$B_{i,c,p,s}= 0.25\, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s,t}^2$$ is the sum of basal area of all individuals competitor trees $$j$$ of the species $$c$$ within the local neighbourhood of the tree $i$ in plot $$p$$, data set $$s$$ and census $t$, where $$w_j$$ is a constant based on neighboorhood size for tree $j$ depending on the data set (see below). Note that $$B_{i,c,p,s}$$ include all trees of species $c$ in the local neighbourhood excepted the tree $$i$$, \item $$N_i$$ is the number of competitor species in the local neighbourhood of focal tree $i$. kunstler committed Jul 17, 2015 109 110 111 112 113 114 115 116 117 \end{itemize} Values of $$\alpha_{c,f}> 0$$ indicate competition, whereas $$\alpha_{c,f}$$ \textless{} 0 indicates facilitation. Log-transformation of eq. \ref{G1} leads to a linearised model of the form \label{logG1} kunstler committed Sep 04, 2015 118 \log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s,t}} + \sum_{c=1}^{N_i} {-\alpha_{c,f} B_{i,c,p,s}}. kunstler committed Jul 17, 2015 119 120 Kunstler Georges committed Sep 18, 2015 121 122 123 To include the effects of traits on the parameters of the growth model we build on previous studies that explored the role of traits for tree performances and tree competition\citep{Uriarte-2010, Kunstler-2012, Lasky-2014}. We modelled the effect of trait, one trait at a time. The effect of a focal species' trait value, $$t_f$$, on its maximum growth was include as: kunstler committed Jul 17, 2015 124 125 \label{Gmax} Kunstler Georges committed Sep 21, 2015 126 \log{G_{\textrm{max} \, f,p,s}} = m_{0} + m_1 \, t_f + m_2 \, MAT + Kunstler Georges committed Sep 25, 2015 127 m_3 \, MAP + \varepsilon_{G_{\textrm{max}}, f} + \varepsilon_{G_{\textrm{max}}, p} + \varepsilon_{G_{\textrm{max}}, s}. kunstler committed Jul 17, 2015 128 129 130 Here $$m_0$$ is the average maximum growth, $$m_1$$ gives the effect of Kunstler Georges committed Sep 21, 2015 131 132 the focal species trait, $m_2$ and $m_3$ of mean annual temperature $MAT$ and sum of annual precipitation $MAP$ respectively, and $$\varepsilon_{G_{\textrm{max}}, f}$$, kunstler committed Aug 04, 2015 133 $$\varepsilon_{G_{\textrm{max}}, p}$$, $$\varepsilon_{G_{\textrm{max}}, s}$$ kunstler committed Jul 17, 2015 134 135 are normally distributed random effect for species $$f$$, plot or quadrat $$p$$ (see below), and data set $$s$$ {[}where kunstler committed Aug 04, 2015 136 137 $$\varepsilon_{G_{\textrm{max}, f}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, f}})$$; $$\varepsilon_{G_{\textrm{max}, p}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, p}})$$ kunstler committed Jul 17, 2015 138 and kunstler committed Aug 04, 2015 139 $$\varepsilon_{G_{\textrm{max}, s}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, s}})$${]}. kunstler committed Jul 17, 2015 140 Kunstler Georges committed Sep 18, 2015 141 142 143 144 145 Previous studies have proposed different decomposition of the competition parameter into key trait-based processes\footnote{There has been different approach to model $\alpha$ from traits. In one of the first study Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha = \alpha_0 + \alpha_s \vert t_f-t_c \vert$. Then Kunstler et al.\citep{Kunstler-2012} used two different models: $\alpha = \alpha_0 + \alpha_s \vert t_f-t_c \vert$ or $\alpha = \alpha_0 + \alpha_h ( t_f-t_c )$. Finally, Lasky et al.\citep{Lasky-2014} developped one single model inculding multiple-processes as $\alpha = \alpha_0 + \alpha_t t_f +\alpha_h ( t_f-t_c ) + \alpha_s \vert t_f-t_c \vert$. In this study, we extended this last model by considering that it was more clear to split Kunstler Georges committed Sep 25, 2015 146 $\alpha_h (t_f - t_c)$ in $\alpha_t t_f + \alpha_e t_c$, which is equivalent to the hierarchical distance if $\alpha_t = - \alpha_e$ (thus avoiding replication of $t_f$ effect through both $\alpha_h$ and $\alpha_t$), and splitting $\alpha_0$ in intra- and inter-specific competition.}, here we extended the approach of the most recent study\citep{Lasky-2014}. As presented in Fig. 1, competitive kunstler committed Jul 17, 2015 147 148 149 150 151 152 interactions were modelled using an equation of the form\footnote{For fitting the model the equation of $$\alpha_{c,f}$$ was developped with species basal area in term of community weighted mean of the trait, see Supplementary methods for more details.}: \label{alpha} Kunstler Georges committed Sep 25, 2015 153 \alpha_{c,f}= \alpha_{0,f,intra} \, CON + \alpha_{0,f,inter} \, (1-CON) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert kunstler committed Jul 17, 2015 154 155 156 157 158 159 160 where: \begin{itemize} \itemsep1pt\parskip0pt\parsep0pt \item Kunstler Georges committed Sep 25, 2015 161 $\alpha_{0,f,intra}$ and $\alpha_{0,f,inter}$ are respectively intra- and interspecific trait independent competition for the focal kunstler committed Jul 17, 2015 162 species $$f$$, modelled with a normally distributed random effect of Kunstler Georges committed Sep 25, 2015 163 species $$f$$ and each with normally distributed random effect of data set kunstler committed Jul 17, 2015 164 $$s$$ {[}as kunstler committed Aug 04, 2015 165 166 $$\alpha_{0,f} = \alpha_0 + \varepsilon_{\alpha_0, f}+ \varepsilon_{\alpha_0, s}$$, where $$\varepsilon_{\alpha_0, f} \sim \mathcal{N} (0,\sigma_{\alpha_0, f})$$ and Kunstler Georges committed Sep 25, 2015 167 $$\varepsilon_{\alpha_0, s} \sim \mathcal{N} (0,\sigma_{\alpha_0, s})$${]}. And $CON$ is a binary variable taking the value one for $f=c$ (conspecific) and zero for $f \neq c$ (heterospecific), kunstler committed Jul 17, 2015 168 \item kunstler committed Jul 17, 2015 169 $$\alpha_t$$ is the \textbf{tolerance of competition} of the focal kunstler committed Jul 17, 2015 170 171 172 species, i.e.~change in competition tolerance due to traits $$t_f$$ of the focal tree with a normally distributed random effect of data set $$s$$ included kunstler committed Aug 04, 2015 173 {[}$$\varepsilon_{\alpha_t,s} \sim \mathcal{N} (0,\sigma_{\alpha_t})$${]}, kunstler committed Jul 17, 2015 174 175 176 177 \item $$\alpha_{e}$$ is the \textbf{competitive effect}, i.e.~change in competition effect due to traits $$t_c$$ of the competitor tree with a normally distributed random effect of data set $$s$$ included kunstler committed Aug 04, 2015 178 {[}$$\varepsilon_{\alpha_i,s} \sim \mathcal{N} (0,\sigma_{\alpha_i})$${]}, and kunstler committed Jul 17, 2015 179 180 181 182 183 \item $$\alpha_s$$ is the effect of \textbf{trait similarity}, i.e.~change in competition due to absolute distance between traits $$\vert{t_c-t_f}\vert$$ with a normally distributed random effect of data set $$s$$ included kunstler committed Aug 04, 2015 184 {[}$\varepsilon_{\alpha_s,s} \sim \mathcal{N} (0,\sigma_{\alpha_s})${]}. kunstler committed Jul 17, 2015 185 186 \end{itemize} Kunstler Georges committed Sep 25, 2015 187 Estimating different $\alpha_0$ for intra- and interspecific competition allow to account for trait independant differences in interactions with conspecific or with heterospecific. Kunstler Georges committed Sep 21, 2015 188 Kunstler Georges committed Sep 25, 2015 189 We also explored a simpler version of the model where only one $\alpha_0$ was include in the model of $\alpha_{c,f}$ as most previous studies have generally not make this distinction which may lead into an overestimation of the trait similarity effect. In this alternative model the equation was: Kunstler Georges committed Sep 21, 2015 190 Kunstler Georges committed Sep 28, 2015 191 \label{alpha2} Kunstler Georges committed Sep 25, 2015 192 \alpha_{c,f}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert Kunstler Georges committed Sep 21, 2015 193 194 Kunstler Georges committed Sep 25, 2015 195 This results are presented in Supplementary Results. Kunstler Georges committed Sep 21, 2015 196 kunstler committed Jul 17, 2015 197 Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of kunstler committed Sep 04, 2015 198 199 growth based on change in diameter between census $t$ and $t+1$ (respectively at year $y_t$ and $y_{t+1}$), given by kunstler committed Jul 17, 2015 200 kunstler committed Sep 04, 2015 201 202 \label{logGobs} G_{i,f,p,s,t} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right)/(y_{t+1} - y_t). kunstler committed Jul 17, 2015 203 204 205 206 207 208 209 To estimate standardised coefficients (one type of standardised effect size)\citep{Schielzeth-2010}, response and explanatory variables were standardized (divided by their standard deviations) prior to analysis. Trait and diameter were also centred to facilitate convergence. The models were fitted using $$lmer$$ in lme4\citep{Bates-2014} kunstler committed Sep 04, 2015 210 in the R statistical environment\citep{RTeam-2014}. We fitted two versions of this model. In the first kunstler committed Jul 17, 2015 211 212 version parameters $$m_{0}, m_1, \alpha_0,\alpha_t,\alpha_i,\alpha_s$$ were estimated as constant across all biomes. In the second version, we kunstler committed Sep 04, 2015 213 repeated the same analysis as in the first version but allowed kunstler committed Jul 17, 2015 214 different fixed estimates of these parameters for each biome. This kunstler committed Sep 04, 2015 215 216 enabled us to explore variation among biomes. Because some biomes had few observations, we merged those with biomes with similar climates. Tundra was kunstler committed Jul 17, 2015 217 218 merged with taiga, tropical rainforest and tropical seasonal forest were merged into tropical forest, and deserts were not included in this final Kunstler Georges committed Sep 21, 2015 219 220 221 222 analysis as too few plots were available. To evaluate if our results were robust to the random effect structure we also explored a model with a single effect constant across biomes but with a random effect for the parameters with both the data set and a local ecoregion using Kunstler Georges committed Sep 25, 2015 223 224 the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see Supplementary Results). kunstler committed Jul 17, 2015 225 Kunstler Georges committed Sep 28, 2015 226 \subsection{Estimating the effect of traits on the mean ratio of intra- \textit{vs.} inter-specific competition}\label{rho} Kunstler Georges committed Sep 25, 2015 227 Kunstler Georges committed Sep 28, 2015 228 The ratio of inter- \textit{vs.} intra-specific competition is generally considered as key in controlling species coexistence. For instance, recent studies\citep{Kraft-2015, Godoy-2014} have recently proposed to analyse the link between traits and $\rho$ defined as the geometric mean of the ratio of interspecific competition over intraspecific competition to understand traits effects on coexistence. This is based on a method developed by Chesson\citep{Chesson-2012} which demonstrates that $\rho$ can be used to quantify the stabilising niche difference between pairs of species (this estimates the strength processes favouring the establishment of a species as rare invader in the population of an other species already established, see an example based on the Lotka-Volterra model based on Godoy \& Levine\citep{Godoy-2014} in the Supplementary Methods). In this approach $\rho$ is defined as $\rho = \sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}}$, where $\alpha'_{ij}$ represent the population level competitive effect of species $j$ on species $i$. Even if our model estimate competition effect only on the individual basal area growth, and not on the population growth, it is interesting to quantify how this ratio of inter- \textit{vs.} intra-specific competition is influenced by traits. The competitive effect of species $j$ on species $i$ can be defined in the tree basal area growth model (see equ. \ref{logG1}) as the reduction of growth of species $i$ by one unit of basal area of competitors of the species $j$ ( thus as $\alpha'_{ij} = \frac{1}{e^{-\alpha_{ij}}}$, with $\alpha_{ij}$ defined by equ. \ref{alpha}). $\rho$ can then be related to the estimated parameters of eqn. \ref{alpha} as: Kunstler Georges committed Sep 25, 2015 229 Kunstler Georges committed Sep 28, 2015 230 \label{rhoequ} Kunstler Georges committed Sep 25, 2015 231 232 233 234 235 \rho = \sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}} = e^{(\alpha_{0,inter} - \alpha_{0,intra} + \alpha_s \vert t_j - t_i \vert)} The stabilising niche difference is then defined as $1-\rho$. kunstler committed Jul 17, 2015 236 237 238 239 240 241 \section{Data}\label{data} \subsection{Growth data}\label{growth-data} Our main objective was to collate data sets spanning the dominant forest biomes of the world. Data sets were included if they (i) allowed both kunstler committed Sep 04, 2015 242 growth of individual trees and the local abundance of competitors kunstler committed Jul 17, 2015 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 to be estimated, and (ii) had good (\textgreater{}40\%) coverage for at least one of the traits of interest (SLA, wood density, and maximum height). The data sets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter were sampled in a network of small plots (often on a regular grid) covering the country (references of NFI data used\citep{-b, Kooyman-2012, -e, Wiser-2001, -c, Villaescusa-1998, Villanueva-2004, Fridman-2001, -a, -d}); (2) large permanent plots (LPP) ranging in size from 0.5-50ha, in which the x-y coordinates of all trees above a given diameter were recorded (references of LPP data used\citep{Condit-2013, Condit-1993, Lasky-2013, Ishihara-2011, Thompson-2002, Ouedraogo-2013, Herault-2010, Herault-2011} ). These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that were identified as a plantations, or overlapping a forest edge. kunstler committed Sep 04, 2015 258 259 Finally, we randomly selected only two consecutive census dates per plot or quadrat to kunstler committed Jul 17, 2015 260 avoid having to account for repeated measurements, as less than a third Kunstler Georges committed Sep 25, 2015 261 of the data had repeated measurements. Because human and natural disturbances are present in all these forests (see Supplementary Methods), they probably all experience successional dynamics (as shown by the forest age distribution available in some of these sites in Supplementary Methods). See the Supplementary Methods and kunstler committed Jul 17, 2015 262 263 264 Extended Data Table 1 for more details on the individual data sets. Basal area growth was estimated from diameter measurements recorded kunstler committed Sep 04, 2015 265 between the two census. For the French NFI, these data were kunstler committed Jul 17, 2015 266 267 268 obtained from short tree cores. For all other data sets, diameter at breast height ($$D$$) of each individual was recorded at multiple census dates. We excluded trees (i) with extreme positive or negative diameter kunstler committed Sep 04, 2015 269 growth measurements, following criteria developed at the BCI site kunstler committed Jul 17, 2015 270 271 272 273 274 275 276 277 278 279 280 281 282 283 \citep{Condit-1993} (see the R package \href{http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/}{CTFS R}), (ii) that were a palm or a tree fern species, or (iii) that were measured at different height in two consecutive censuses. For each individual tree, we estimated the local abundance of competitor species as the sum of basal area for all individuals \textgreater{} 10cm diameter within a specified neighbourhood. For LPPs, we defined the neighbourhood as being a circle with 15m radius. This value was selected based on previous studies showing the maximum radius of interaction to lie in the range 10-20m\citep{Uriarte-2004, Uriarte-2010}. To avoid edge effects, we also excluded trees less than 15m from the edge of a plot. To account for variation of abiotic conditions within the LPPs, we kunstler committed Sep 04, 2015 284 285 divided plots into regularly spaced 20x20m quadrats and included in a random quadrat effect (see above). kunstler committed Jul 17, 2015 286 287 288 289 290 291 292 For NFI data coordinates of individual trees within plots were generally not available, thus neighbourhoods were defined based on plot size. In the NFI from the United States, four sub-plots of 7.35m located within 20m of one another were measured. We grouped these sub-plots to give a single estimate of the local competitor abundance. Thus, the neighbourhoods used in the competition analysis ranged in size from kunstler committed Sep 04, 2015 293 294 295 10-25 m radius, with most plots 10-15 m radius. We included variation in neighbourhood size in the constant $w_j$ to compute competitors basal area in $m^2/ha$. kunstler committed Jul 17, 2015 296 297 298 299 300 We extracted mean annual temperature (MAT) and mean annual sum of precipitation (MAP) from the \href{http://www.worldclim.org/}{worldclim} data base \citep{Hijmans-2005}, using the plot latitude and longitude. MAT and MAP data were then used to classify plots into kunstler committed Jul 17, 2015 301 biomes, using the diagram provided by Ricklefs\citep{Ricklefs-2001} kunstler committed Jul 17, 2015 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 (after Whittaker). \subsection{Traits}\label{traits} Data on species functional traits were extracted from existing sources. We focused on wood density, species specific leaf area (SLA) and maximum height, because these traits have previously been related to competitive interactions and are available for large numbers of species \citep{Wright-2010, Uriarte-2010, Ruger-2012, Kunstler-2012, Lasky-2014} (see Extended data Table 2 for traits coverage). Where available we used data collected locally (References for the local traits data used in this analysis\citep{Wright-2010, Swenson-2012, Gourlet-Fleury-2011, Lasky-2013, Baraloto-2010}); otherwise we sourced data from the \href{http://www.try-db.org/}{TRY} trait data base \citep{Kattge-2011} (References for the data extracted from the TRY database used in this analysis\citep{Ackerly-2007, Castro-Diez-1998, Chave-2009, Cornelissen-1996, Cornelissen-1996a, Cornelissen-1997, Cornelissen-2004, Cornelissen-2003, Cornwell-2009, Cornwell-2006, Cornwell-2007, Cornwell-2008, Diaz-2004, Fonseca-2000, Fortunel-2009, Freschet-2010, Freschet-2010a, Garnier-2007, Green-2009, Han-2005, He-2006, He-2008, Hoof-2008, Kattge-2009, Kleyer-2008, Kurokawa-2008, Laughlin-2010, Martin-2007, McDonald-2003, Medlyn-1999a, Medlyn-1999, Medlyn-2001, Messier-2010, Moles-2005b, Moles-2005a, Moles-2004, Niinemets-2001, Niinemets-1999, Ogaya-2003, Ogaya-2006, Ogaya-2007, Ogaya-2007a, Onoda-2011, Ordonez-2010, Ordonez-2010a, Pakeman-2008, Pakeman-2009, Penuelas-2010, Penuelas-2010a, Poorter-2006, Poorter-2009, Poorter-2009a, Preston-2006, Pyankov-1999, Quested-2003, Reich-2008, Reich-2009, Sack-2004, Sack-2005, Sack-2006, Sardans-2008, Sardans-2008a, Shipley-2002, Soudzilovskaia-2013, Willis-2010, Wilson-2000, Wright-2007, Wright-2006, Wright-2010, Wright-2004, Zanne-2010}). Local data were available for most tropical sites and species (see Supplementary methods). Several of the NFI data kunstler committed Jul 17, 2015 317 sets also provided tree height measurements, from which we computed a kunstler committed Jul 17, 2015 318 319 320 321 322 323 324 325 326 327 328 329 330 331 species' maximum height as the 99\% quantile of observed values (for France, US, Spain, Switzerland). For Sweden we used the estimate from the French data set and for Canada we used the estimate from the US data set. Otherwise, we extracted measurement from the TRY database. We were not able to account for trait variability within species between sites. For each focal tree, our approach required us to also account for the traits of all competitors present in the neighbourhood. Most of our plots had good coverage of competitors, but inevitably there were some trees where trait data were lacking. In these cases we estimated trait data as follows. If possible, we used the genus mean, and if no genus data was available, we used the mean of the species present in the country. However, we restricted our analysis to plots where (i) the percentage of basal area of trees with no species level trait data was kunstler committed Sep 04, 2015 332 333 334 less than 10\%, and (ii) the percentage of basal area of trees with no species and genus level trait data was less than 5\%. kunstler committed Jul 17, 2015 335 336 337 \newpage \clearpage kunstler committed Aug 04, 2015 338 kunstler committed Jul 17, 2015 339 340 \section{References}\label{references} kunstler committed Jul 17, 2015 341 \bibliographystyle{naturemag} kunstler committed Jul 17, 2015 342 343 344 \bibliography{references} \end{document}