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\rhead{Traits and trees competition}
\title{Plant functional traits have globally consistent effects on competition}

\author[1,2,3]{Georges Kunstler}
\author[3]{Daniel Falster}
\author[4]{David A. Coomes}
\author[5]{Francis Hui}
\author[3,6]{Robert M. Kooyman}
\author[7]{Daniel C. Laughlin}
\author[8]{Lourens Poorter}
\author[9]{Mark Vanderwel}
\author[10]{Ghislain Vieilledent}
\author[11]{S. Joseph Wright}
\author[12]{Masahiro Aiba}
\author[13,14]{Christopher Baraloto}
\author[15]{John Caspersen}
\author[16]{J. Hans C. Cornelissen}
\author[10]{Sylvie Gourlet-Fleury}
\author[17,18]{Marc Hanewinkel}
\author[19]{Bruno Herault}
\author[20,21]{Jens Kattge}
\author[12,22]{Hiroko Kurokawa}
\author[23]{Yusuke Onoda}
\author[24,25]{Josep Peñuelas}
\author[26]{Hendrik Poorter}
\author[27]{Maria Uriarte}
\author[28]{Sarah Richardson}
\author[29,30]{Paloma Ruiz-Benito}
\author[31]{I-Fang Sun}
\author[32]{Göran Ståhl}
\author[33]{Nathan G. Swenson}
\author[34,35]{Jill Thompson}
\author[32]{Bertil Westerlund}
\author[36,21]{Christian Wirth}
\author[30]{Miguel A. Zavala}
\author[15]{Hongcheng Zeng}
\author[35]{Jess K. Zimmerman}
\author[37]{Niklaus E. Zimmermann}
\author[3]{Mark Westoby}

\affil[1]{Irstea, UR EMGR, 2 rue de la Papeterie BP-76, F-38402, St-Martin-d'Hères, France \\ \url{georges.kunstler@irstea.fr}}
\affil[2]{Univ. Grenoble Alpes, F-38402 Grenoble, France}
\affil[3]{Department of Biological Sciences, Macquarie University NSW 2109, Australia}
\affil[4]{Forest Ecology and Conservation Group, Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK}
\affil[5]{Mathematical Sciences Institute, Australian National University, Canberra, Australia}
\affil[6]{National Herbarium of New South Wales, Royal Botanic Gardens and Domain Trust, Sydney, NSW, Australia}
\affil[7]{Environmental Research Institute, School of Science, University of Waikato, Hamilton, New Zealand}
\affil[8]{Forest Ecology and Forest Management Group, Wageningen University, Wageningen, The Netherlands}
\affil[9]{Department of Biology, University of Regina, 3737 Wascana Pkwy, Regina, SK, S4S 0A2, Canada}
\affil[10]{Cirad, UPR BSEF, F-34398 Montpellier, France}
\affil[11]{Smithsonian Tropical Research Institute, Apartado 0843–03092, Balboa, Republic of Panama}
\affil[12]{Graduate School of Life Sciences, Tohoku University, Sendai 980-8578, Japan}
\affil[13]{INRA, UMR Ecologie des Forêts de Guyane, BP 709, 97387 Kourou Cedex, France}
\affil[14]{International Center for Tropical Botany, Department of Biological Sciences, Florida International University, Miami, FL, USA}
\affil[15]{Faculty of Forestry, University of Toronto, 33 Willcocks Street, Toronto, Ontario, M5S 3B3, Canada}
\affil[16]{Systems Ecology, Department of Ecological Science, VU University, Amsterdam, 1081 HV, The Netherlands}
\affil[17]{Swiss Federal Research Inst. WSL, Forest Resources and Management Unit, CH-8903 Birmensdorf, Switzerland}
\affil[18]{University of Freiburg, Chair of Forestry Economics and Planning, D-79106 Freiburg, Germany}
\affil[19]{Cirad, UMR Ecologie des Forêts de Guyane, Campus Agronomique, BP 701, 97387 Kourou, France}
\affil[20]{Max Planck Institute for Biogeochemistry, Hans Knöll Str. 10, 07745 Jena, Germany}
\affil[21]{German Centre for Integrative Biodiversity Research (iDiv), Halle-Jena-Leipzig, Deutscher Platz 5e 04103 Leipzig, Germany}
\affil[22]{Forestry and Forest Products Research Institute, Tsukuba, 305-8687 Japan (current address)}
\affil[23]{Graduate School of Agriculture, Kyoto University, Kyoto, Japan}
\affil[24]{CSIC, Global Ecology Unit CREAF-CSIC-UAB, Cerdanyola del
  Vallès 08193, Catalonia, Spain}
\affil[25]{CREAF, Cerdanyola del Vallès, 08193 Barcelona, Catalonia, Spain}
\affil[26]{Plant Sciences (IBG-2), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany}
\affil[27]{Department of Ecology, Evolution and Environmental Biology, Columbia University, New York, NY 10027, United States of America}
\affil[28]{Landcare Research, PO Box 40, Lincoln 7640, New Zealand}
\affil[29]{Biological and Environmental Sciences, School of Natural Sciences, University of Stirling, FK9 4LA, Stirling, UK}
\affil[30]{Forest Ecology and Restoration Group, Department of Life Sciences, Science Building, University of Alcala, Campus Universitario, 28805 Alcalá de Henares (Madrid), Spain}
\affil[31]{Department of Natural Resources and Environmental Studies, National Dong Hwa University, Hualien 97401, Taiwan}
\affil[32]{Department of Forest Resource Management, Swedish University of Agricultural Sciences (SLU), Skogsmarksgränd, Umeå, Sweden}
\affil[33]{Department of Biology, University of Maryland, College Park, Maryland, United States of America}
\affil[34]{Centre for Ecology and Hydrology−Edinburgh, Bush Estate, Penicuik, Midlothian EH26 0QB United Kingdom}
\affil[35]{Department of Environmental Sciences, University of Puerto Rico, Río Piedras Campus P.O. Box 70377 San Juan, Puerto Rico 00936-8377, USA}
\affil[36]{Institute for Systematic, Botany and Functional Biodiversity, University of Leipzig, Johannisallee 21 04103 Leipzig, Germany}
\affil[37]{Swiss Federal Research Inst. WSL, Landscape Dynamics Unit, CH-8903 Birmensdorf, Switzerland}
\date{}


\begin{document}
\maketitle


\section{Main text}

% (235/max 300 but rather 200)
\textbf{Phenotypic traits and their associated trade-offs have been shown to have globally consistent
effects on individual plant physiological
functions\citep{Westoby-2002, Wright-2004, Chave-2009}, but
it has remained unclear how these effects scale up to
influence competition -- a key driver of
community assembly in terrestrial
vegetation\citep{Keddy-1989}. Here we use growth data, from
more than 3 million trees in more than 140000 plots across the world, to show how three key functional traits -- wood density, specific leaf area
and maximum height -- consistently influence competitive interactions.
Fast maximum growth of a species was correlated negatively with its
wood
density in all biomes and positively with its specific leaf area in most biomes. Low wood density
was also correlated with a low ability to tolerate competition and a
low competitive impact on neighbours (competitive effect), while high
specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with \emph{vs.} without
competition, a fundamental ingredient in the classical hypothesis
that coexistence of plant species is enabled via differentiation in
their successional strategies\citep{Rees-2001}. Competition within species was
stronger than between species, but an increase in trait dissimilarity
between species had little influence in weakening competition. No
benefit of dissimilarity was detected for specific leaf area or wood density and
only a weak benefit for maximum height. Our trait-based approach to
modelling competition makes generalisation possible across the forest
ecosystems of the globe and their highly diverse species composition.}


% \section{Main text}\label{main-text}
% (1554/max 1500)
Phenotypic traits are considered fundamental drivers of community
assembly and thus species diversity \citep{Westoby-2002, Adler-2013}. The effects of traits on individual
plant physiologies and functions are increasingly understood, and have been shown to be underpinned
by well-known and globally consistent trade-offs
\citep{Westoby-2002, Wright-2004, Chave-2009}.
For instance, traits such as wood density and specific leaf area capture
trade-offs between the construction cost and longevity or strength of
wood and leaf tissues\citep{Wright-2004, Chave-2009}.
In contrast, we still have limited understanding of how such trait-based trade-offs translate into
competitive interactions between species,
particularly for long-lived organisms such as trees. Competition is a key
filter through which ecological and evolutionary success is
determined\citep{Keddy-1989}. A long-standing hypothesis is that the intensity of competition decreases as two species diverge
in trait values\citep{MacArthur-1967} (trait dissimilarity). The few
studies\citep{Uriarte-2010, Kunstler-2012, HilleRisLambers-2012, Lasky-2014, Kraft-2015, Mayfield-2010}
that have explored links between traits and competition have shown
that linkages were more complex than this, as particular trait values may also
confer competitive advantage independently from trait dissimilarity\citep{Mayfield-2010, Kunstler-2012, Kraft-2014}. This
distinction is fundamental for species coexistence and the
local mixture of traits. If neighbourhood competition is driven
mainly by trait dissimilarity, this will favour a wide spread of trait
values at a local scale. In contrast, if neighbourhood interactions are mainly
driven by the competitive advantage associated with particular trait
values, those trait values should be strongly selected at the local
scale, with coexistence operating at larger spatial or temporal
scales\citep{Mayfield-2010, Adler-2013}. Empirical investigations have
been limited so far to a few particular
locations, restricting our ability to find general mechanisms that link traits and competition in the main vegetation types
of the world.

Here we quantify the links between traits and competition, measured as
the influence of neighbouring trees on growth of a focal tree. Our framework is
novel in two important ways: (i) competition is analysed at an
unprecedented scale covering all the major forest biomes on Earth (Fig.
\ref{ilustr}a), and (ii) the influence of traits on competition is
partitioned among four fundamental mechanisms (Fig. \ref{ilustr}b,c) as
follows. A competitive advantage for trees with some trait values compared to
others can arise through: (1) permitting faster maximum growth in the absence
of competition\citep{Wright-2010}; (2) exerting a stronger
competitive
effect\citep{Goldberg-1996, Gaudet-1988},
meaning that competitor species possessing those traits suppress more strongly the
growth of their neighbours; or (3) permitting a better tolerance of
competition (or competitive `response' in
Goldberg\citep{Goldberg-1996}), meaning that growth
of species possessing those traits is less affected by competition
from neighbours. Finally, (4) competition can promote trait
diversification, if increasing trait dissimilarity between species
reduces interspecific competition compared to intraspecific competition \citep{MacArthur-1967}. Here we show how these
four mechanisms are connected to three key traits that describe plant
strategies
worldwide\citep{Westoby-2002, Wright-2004, Chave-2009}. These traits are
wood density (an indicator of a trade-off in stems between growth
and strength), specific leaf area (SLA, an indicator of a trade-off in
leaves between cheap construction cost and leaf longevity), and maximum height
(an indicator of a trade-off between sustained access to light and early
reproduction). We analyse basal area growth (annual increase in the
area of the cross section of tree trunk at 1.3 m height) of more than 3
million trees from more than 2500
species, across all major forested biomes of the earth (Fig. \ref{ilustr}). Species mean trait values were extracted from local
data bases and the global TRY
data base\citep{Kattge-2011} (see Methods). We analysed how basal area growth of each
individual tree was reduced by the abundance of competitors in its local
neighbourhood\citep{Uriarte-2004} (measured as the sum of
basal areas of competitors in m$^2$ ha$^{-1}$), accounting for traits of both
the focal tree and its competitors. This analysis allowed effect sizes
to be estimated for each of the four mechanisms outlined above (Fig. \ref{ilustr}c).

Across all biomes the strongest driver of individual growth was the
total abundance of neighbours,
irrespective of their traits (parameters $\alpha_{0 \, \rm intra}$
and $\alpha_{0 \, \rm inter}$ in Fig. \ref{res1}). Values were strongly
positive, indicating neighbours had competitive rather than facilitative effects. The main effects of traits were that some trait values led
to a competitive advantage compared to others through two main
mechanisms. First, traits of the focal species had influences on its
maximum growth -- \emph{i.e.} in the absence of competition -- (parameter $m_1$ in Fig.
\ref{res1} and Extended Data Table 4). The fastest growing species
had low wood density and high SLA, though the confidence interval on
the trait effect
intercepted zero in two out of five biomes for SLA (Fig. \ref{res1}). This
is in agreement with previous studies\citep{Poorter-2008, Wright-2010} of
adult trees reporting a strong link between maximum growth and wood
density but a weaker link for SLA. Second,
some trait values were associated with species having stronger
competitive effects, or better tolerance of competition (Fig.
\ref{res1}; Extended
Data Table 4). High wood density was correlated with better tolerance of
competition from neighbours and with a stronger competitive effect upon
neighbours, whereas low SLA was correlated only with a stronger
competitive effect. This agrees with studies reporting that high wood density species are
more shade-tolerant\citep{Wright-2010} and have deeper and wider
crowns\citep{Poorter-2006a, Aiba-2009}, hence potentially
higher light interception (further detail in Supplementary Discussion). The
shorter leaf lifespan associated with high SLA results in lower
leaf mass fraction\citep{Niinemets-2010}. The low competitive effect
associated with high SLA species could thus result from a lower light
interception but few data are available on this link\citep{Niinemets-2010}. Maximum height was weakly
negatively correlated with tolerance to competition in three out of
five biomes, supporting the idea that sub-canopy trees are more
shade-tolerant\citep{Poorter-2006a}. We found however no correlation
between maximum height and competitive effect. Current height of an
individual has of course an influence on light interception, a key
process in competition\citep{Mayfield-2010}. But maximum
height of a species reflects its long-term strategy and
would possibly have stronger effects on long-term
population level competition outcomes than it did on short-term basal area
growth\citep{Adams-2007}.

After separating trait-independent differences between intraspecific \textit{vs.} interspecific competition, trait dissimilarity
had little effect on competition between species
(Fig. \ref{res1}). Only dissimilarity in maximum height between focal and
neighbour species led to a weak, but consistent, decrease in competitive suppression of
tree growth (Fig. \ref{res1}). Mechanisms explaining this effect are
poorly understood, but could possibly result from complementary
crown architectures\citep{Sapijanskas-2014, Jucker-2015}. The average differences in strength of interspecific \textit{vs.} intraspecific competition between two species -- a key indicator of processes that could stabilise coexistence -- were thus
only weakly related to trait dissimilarity (Extended Data Fig.
3). Trait dissimilarity effects are widely considered to be a key
mechanism by which traits affect competition\citep{Mayfield-2010}, but our analysis shows at
global scale that trait dissimilarity effects are weak or
absent. It remains unclear why the trait-independent competitive effects are higher within species than
between species. Higher loads of shared specialised
pathogens\citep{Bagchi-2014} could plausibly contribute. Other traits or combinations of traits (see Kraft \textit{et al.}\citep{Kraft-2015}) may show stronger trait dissimilarity effects, but we
currently lack the trait data to capture such effects.

Analyses allowing for different effects among biomes did not show
any particular biome behaving consistently
differently from the others (Fig. \ref{res1}). This lack of context
dependence in trait effects may seem surprising, but reinforces the idea that competition for light is important in most forests, and this may
explain why we find consistency across such diverse forest types (further details in Supplementary Discussion).

Our global study supports the hypothesis that trait values
favouring high tolerance of competition or high competitive effects also
render species slow growing in the absence of competition across all
forested biomes (Fig. \ref{res3}). This trait-based trade-off is a key
ingredient in the classical model of successional
coexistence in forests, where fast-growing species are more abundant
in early successional stages where competitors are absent or rare, and are
later replaced by slow-growing species in late successional stages where
competitors become more abundant\citep{Rees-2001}. Human or
natural disturbances are conspicuous in all the forests analysed, hence successional
dynamics are likely to be present in all these sites (see Supplementary Information). This trade-off was strongest for wood
density, with high wood density associated with slow potential
growth rate but high tolerance to competition and strong competitive effect
(Fig. \ref{res3}). A similar pattern was present, though less clear, for SLA. High SLA was
correlated with low competitive effect but fast maximum
growth (confidence intervals not spanning zero in three
biomes, Fig. \ref{res1} and \ref{res3}). Given that long-term
outcomes of competition at the population level may be more influenced by
tolerance of competition than by competitive effect\citep{Goldberg-1996}, SLA
might be less influential in succession.

Coordination between trait values conferring strong competitive effect and
trait values conferring high tolerance of competition has
been widely expected\citep{Goldberg-1996, Kunstler-2012}, but rarely
documented\citep{Goldberg-1996, Wang-2010}.
Only wood density showed such coordination, as it was correlated with both competitive effect and tolerance of competition in the same direction (Fig. \ref{res1}).

The globally consistent links that we report here between traits and
competition have considerable promise for predicting species
interactions governing forest communities across different forest
biomes and continents of the globe. Our analysis demonstrates that trait dissimilarity is not the major determinant of
local-scale competitive impacts on tree growth, at least for these three
traits. In contrast, the trait-based trade-off in performance with \textit{vs.} without
competition, reported here, could promote
coexistence of species with diverse traits, provided disturbances
create a mosaic of successional stages. A challenge for the
future is to move beyond growth to analyse all key demographic rates
and life history stages, and analyse how traits influence
competitive outcomes and stable coexistence at the population
level.

\textbf{Supplementary Information} is available in the online version of
the paper.

\textbf{Acknowledgements} We are especially grateful to the
researchers whose long-term commitment to establish and maintain
forest plots and their associated databases made this study possible,
and to those who granted us data access: forest inventories and
permanent plots of New Zealand, Spain (MAGRAMA), France, Switzerland,
Sweden, US, Canada (for the provinces of Quebec, Ontario,
Saskatchewan, Manitoba, New Brunswick, Newfoundland and Labrador),
CTFS (BCI, Fushan and Luquillo), Cirad (Paracou), Cirad, MEFCP, and
ICRA (M’Baïki) and Japan. We thank the three anonymous reviewers whose
comments and suggestions helped improve and clarify this manuscript. GK was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Program (Demo-Traits project, no. 299340). The working group that initiated this synthesis was supported by Macquarie University and by Australian Research Council through a fellowship to MW.

\textbf{Author contributions} GK and MW conceived the study and with
DF led a
workshop with the participation of DAC, FH,
RMK, DCL, LP, MV, GV, and SJW. GK wrote the manuscript with key inputs from all workshop participants and help from all authors. GK, DF and FH wrote the computer code and processed the data. GK devised the main analytical approach and performed analyses with assistance from DF for the figures.
GK, DAC, DF, FH, RMK, DCL, MV, GV, SJW, MA, CB, JC, JHCC, SGF, MH, BH,
JK, HK, YO, JP, HP, MU, SR, PRB, IFS, GS, NS, JT, BW, CW, MAZ, HZ, JZ,
NEZ collected and processed the raw data.

\textbf{Author information}
The authors declare no competing financial interests.

\newpage
\clearpage

\section{METHODS}\label{methods}

\subsection{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}
to model the growth of a focal tree of species \(f\) as a product of its
maximum growth (determined by its traits and size) together with
reductions due to competition from individuals growing in the local
neighbourhood (see definition below). Specifically, we assumed a relationship of the form

\begin{equation} \label{G1}
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_{f,c} B_{i,c,p,s}}\right),
\end{equation}
where:
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
  \(G_{i,f,p,s,t}\) and \(D_{i,f,p,s,t}\) are the annual basal area
  growth and diameter at breast height of individual \(i\) from species
  \(f\), plot or quadrat (see below) \(p\), data set \(s\), and census $t$,
\item
  \(G_{\textrm{max} \, f,p,s}\) is the maximum basal area growth for species \(f\) on plot or quadrat \(p\) in data set \(s\), i.e.~in
  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
  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 $\sigma_{\gamma}${]},
\item
  \(\alpha_{f,c}\) is the per unit basal area effect of individuals from
  species \(c\) on growth of an individual in species \(f\),
\item
  \(B_{i,c,p,s}= 0.25 \, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s,t}^2\) 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
  \(i\), and
\item
  \(N_i\) is the number of competitor species in the local
  neighbourhood of focal tree $i$.
\end{itemize}

Values of \(\alpha_{f,c}> 0\) indicate competition, whereas
\(\alpha_{f,c}\) \textless{} 0 indicates facilitation.

Log-transformation of equ. \ref{G1} leads to a linearised model of the
form

\begin{equation} \label{logG1}
\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_{f,c} B_{i,c,p,s}} \,
.
\end{equation}

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 traits, one trait at a time.
The effect of a focal species' trait value, \(t_f\), on its
maximum growth was included as:

\begin{equation} \label{Gmax}
\log{G_{\textrm{max} \, f,p,s}} = m_{0} + m_1 \, t_f + m_2 \, \textrm{MAT} +
m_3 \, \textrm{MAP} + \varepsilon_{G_{\textrm{max}}, f} +
\varepsilon_{G_{\textrm{max}}, p} + \varepsilon_{G_{\textrm{max}}, s}
\, .
\end{equation}

Here \(m_0\) is the average maximum growth, \(m_1\) gives the effect of
the focal species trait, $m_2$ and $m_3$ the effects of mean annual temperature
$\textrm{MAT}$ and sum of annual precipitation $\textrm{MAP}$ respectively, and \(\varepsilon_{G_{\textrm{max}}, f}\),
\(\varepsilon_{G_{\textrm{max}}, p}\), \(\varepsilon_{G_{\textrm{max}}, s}\)
are normally distributed random effects for species \(f\), plot or
quadrat \(p\) (see below), and data set \(s\) {[}where
\(\varepsilon_{G_{\textrm{max}, f}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, f}})\);
\(\varepsilon_{G_{\textrm{max}, p}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, p}})\)
and
\(\varepsilon_{G_{\textrm{max}, s}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, s}})\){]}.

Previous studies have proposed various decompositions of the competition parameter into key trait-based processes\footnote{Different approaches have been proposed to model $\alpha$ from traits. In one of the first studies Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha =
\alpha_0 + \alpha_d \vert t_f-t_c \vert$. Then Kunstler et al.\citep{Kunstler-2012} used two different models: $\alpha = \alpha_0 + \alpha_d \vert t_f-t_c \vert$ or $\alpha =
\alpha_0 + \alpha_h ( t_f-t_c )$. Finally, Lasky et
al.\citep{Lasky-2014} developed a single model including multiple processes as $\alpha =
\alpha_0 + \alpha_t t_f +\alpha_h ( t_f-t_c ) + \alpha_d \vert t_f-t_c
\vert$. In our study, we extended this last model. We considered that it was clearer to split
$\alpha_h (t_f - t_c)$ into $\alpha_t t_f + \alpha_e t_c$, which is
equivalent to the hierarchical distance if $\alpha_t = - \alpha_e$
(thus avoiding replication of $t_f$ effect through both $\alpha_h$ and
$\alpha_t$). We also included two $\alpha_0$, one for intra and one for
interspecific
competition.}, and here we extended the approach of the most recent study\citep{Lasky-2014}. As presented in Fig. 1, competitive
interactions were modelled using an equation of the form\footnote{For
  fitting the model, the equation of \(\alpha_{f,c}\) was developed with
  species basal area in term of community weighted means of (i) trait values of competitors and (ii) absolute trait distance between focal species and its competitors.}:

\begin{equation} \label{alpha}
\alpha_{f,c}= \alpha_{0 \, \mathrm{intra}, f} \, C + \alpha_{0,\, \mathrm{inter},f} \, (1-C) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
\end{equation}

where:

\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
  $\alpha_{0 \, \mathrm{intra}, f}$ and $\alpha_{0 \, \mathrm{inter}, f}$ are respectively
  \textbf{intraspecific and average interspecific trait independent competition} for the focal
  species \(f\), modelled each with a normally distributed random effect of
  species \(f\) and normally distributed random effect of data set
  \(s\) {[}such as
  \(\alpha_{0 \, \mathrm{intra}, f} = \alpha_{0 \, \mathrm{intra}} +
  \varepsilon_{\alpha_{0 \, \mathrm{intra}}, f}+ \varepsilon_{\alpha_{0 \, \mathrm{intra}}, s}\),
  where \(\varepsilon_{\alpha_{0 \, \mathrm{intra}}, f} \sim \mathcal{N} (0,\sigma_{\alpha_{0 \, \mathrm{intra}}, f})\) and
  \(\varepsilon_{\alpha_{0 \, \mathrm{intra}}, s} \sim \mathcal{N}
  (0,\sigma_{\alpha_{0 \, \mathrm{intra}}, s})\) and replacing intra
  by inter gives the expressions for
  $\alpha_{0 \, \mathrm{inter}, f}${]}. $C$ is a binary variable taking the value one for $f=c$ (conspecific) and zero for $f \neq c$ (heterospecific),
\item
  \(\alpha_t\) is the \textbf{tolerance of competition} by the focal
  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
  {[}\(\varepsilon_{\alpha_t,s} \sim \mathcal{N} (0,\sigma_{\alpha_t})\){]},
\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
  {[}\(\varepsilon_{\alpha_i,s} \sim \mathcal{N} (0,\sigma_{\alpha_i})\){]}, and
\item
  \(\alpha_d\) is the effect of \textbf{trait dissimilarity}, 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
  {[}$\varepsilon_{\alpha_d,s} \sim \mathcal{N} (0,\sigma_{\alpha_d})${]}.
\end{itemize}

Estimating separate $\alpha_0$ for intra and interspecific competition allowed us to account for trait-independent differences in interactions with conspecifics and heterospecifics. We also explored a simpler version of the model where trait-independent competitive effects were pooled (i.e. there was a single value for $\alpha_0$), as previous studies have generally not made this distinction, using the following equation:

\begin{equation} \label{alpha2}
\alpha_{f,c}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c +
\alpha_d \, \vert t_c-t_f \vert \, .
\end{equation}

In this alternative model any differences between intra and interspecific competition do enter into trait dissimilarity effects, with a trait dissimilarity of zero attached to them. This may lead to an overestimation of the trait dissimilarity effect. Results for this model
are presented in Fig. 4 in Extended Data.

Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of
growth based on change in diameter between census $t$
and $t+1$ (respectively at year $y_t$ and $y_{t+1}$), given by

\begin{equation} \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).
\end{equation}

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 the \(lmer\) routine in
the lme4 package \citep{Bates-2014}
in the R statistical environment\citep{RTeam-2014}. We fitted two
versions of each model. In the first
version parameters \(m_{0}, m_1, \alpha_0,\alpha_t,\alpha_i,\alpha_d\)
were estimated as constant across all biomes. In the second version, we
allowed
different fixed estimates of these parameters for each biome. This
enabled us to explore variation among biomes. Because some biomes had
few observations, we merged those with biomes with similar climates. Tundra was
merged with taiga, tropical rainforest and tropical seasonal forest were
merged into tropical forest, and deserts were not included in this final
analysis as too few plots were available. To evaluate whether our results
were robust to the random effect structure we also explored a model
with a random effect
attached to parameters both for the data set and for a local ecoregion using
the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see
Supplementary Results).

\subsubsection{Estimating the effect of traits on the average differences between intra and interspecific competition}\label{intrainter}

Differences between inter and intraspecific competition have long been
considered key to community assembly and species
coexistence\citep{Connell-1983, Chesson-2000, Chesson-2012,
  Kraft-2015, Godoy-2014}. Our estimated growth model allowed us to
estimate the average inter and intraspecific competition from
trait-independent and trait-dependent processes. For any combination
of two trait values $t_i$ and $t_j$, we can predict the interspecific
($\alpha_{t_i,t_j}$ and $\alpha_{t_j,t_i}$) and
intraspecific ($\alpha_{t_i,t_i}$ and $\alpha_{t_j,t_j}$) competition parameters for a typical species by leaving out the random species effects in eqn. \ref{alpha}. We can then estimate the average differences between interspecific and intraspecific competition over all trait values combinations using the following expression:

\begin{equation} \label{rhoequ}
\frac{(\alpha_{t_i,t_j} - \alpha_{t_i,t_i}) + (\alpha_{t_j,t_i} -
  \alpha_{t_j,t_j})}{2} .
\end{equation}

Substituting in from eqn. \ref{alpha} (leaving out the species random
effect) this simplifies as:
\begin{equation} \label{rhoequ2}
\alpha_{0 \, \mathrm{inter}} - \alpha_{0 \, \mathrm{intra}} + \alpha_d
\vert t_j - t_i \vert .
\end{equation}

Thus, the average differences between inter and intraspecific
competition are affected only by the difference between $\alpha_{0 \,
  \rm intra}$ and $\alpha_{0 \, \rm inter}$ and by trait dissimilarity via $\alpha_d$ (see Fig. 3 in Extended Data for the results).


\subsection{Data}\label{data}

\subsubsection{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
growth of individual trees and the local abundance of competitors
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 for 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 for LPP data used\citep{Condit-2013, Condit-1993, Lasky-2013, Ishihara-2011, Thompson-2002, Ouedraogo-2013, Herault-2010, Herault-2011} ). 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 plantations, or that overlapped a forest edge.
Finally, we randomly selected only two consecutive census dates per
plot or quadrat to
avoid having to account for repeated measurements (less than a third
of the data had repeated measurements). Because human and natural disturbances are present in all these forests (see Supplementary Information), they probably all experience successional dynamics (as indicated by the forest age distribution available in some of these sites in Supplementary Information). See Supplementary Information and
Extended Data Table 1 for more details on individual data sets.

Basal area growth was estimated from diameter measurements recorded
between the two censuses. For the French NFI, these data were
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
growth measurements, following criteria developed at the BCI site
\citep{Condit-1993} (see the R package
\href{http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/}{CTFS R}),
(ii) that were palms or tree ferns, or (iii) that were
measured at different heights 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
divided plots into regularly spaced 20x20m quadrats and included a
random quadrat effect in the model (see above).

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
10-25 m radius, with most plots 10-15 m radius. We included variation in
neighbourhood size in the constant $w_j$ to compute competitor basal
area in $m^2/ha$.

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 (see Extended Data Fig. 1 for plot locations on a world map\citep{South-2011}). MAT and MAP data were then used to classify plots into
biomes, using the diagram provided by Ricklefs\citep{Ricklefs-2001}
(after Whittaker).

\subsubsection{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 and 3 for trait coverage and their correlations). Where available we used
data collected locally (references for the local trait 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 Information). Several of the NFI data
sets also provided tree height measurements, from which we computed a
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 height measurements from the TRY database. We were
not able to account for trait variability within species.

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 contributed by trees with no species level trait data was
less than 10\%, and (ii) the
percentage of basal area of trees with neither species nor genus level trait data was
less than 5\%.

\newpage
\clearpage


\bibliographystyle{naturemag}

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\newpage
\clearpage

\newpage

\section{MAIN FIGURES}\label{figures}

\begin{figure}[htbp]
\centering
\includegraphics{FigDef/Fig1.pdf}
\caption{\textbf{Assessing competitive interactions at global scale.}
\textbf{a}, Precipitation-temperature space occupied by each data set
(NFI -- national forest inventories data, LPP -- large permanent
plots data). For data with multiple plots, the range of climatic condition is
represented by an ellipse covering 98\% of the plots. Biomes are: 1 -
tundra; 2 - taiga; 3 - mediterranean; 4 - temperate forest; 5 - temperate
rainforest; 6 - desert; 7 - tropical seasonal forest; 8 - tropical
rainforest (see methods for details). \textbf{b},
Sampled patches vary in the abundance of competitors from species $c$
around individuals of focal species $f$. \textbf{c}, We modelled how
trait values of the focal tree ($t_f$), and the abundance (measured as
the sum of their basal areas) and traits values of competitor species ($t_c$)
influenced basal area growth of the focal tree. Species maximum growth (red) was
influenced by trait of the focal tree ($m_0 + m_1 \, t_f$, with $m_0$
maximum growth independent of the trait). Reduction
in growth per unit basal area of competitors ($-\alpha_{f,c}$, black) was
modelled as the sum of growth reduction independent of the trait (blue) by conspecific
($\alpha_{0 \, \rm intra}$) and heterospecific ($\alpha_{0 \, \rm inter}$) competitors, the effect of competitor traits ($t_c$) on their
competitive effect ($\alpha_e$), the effect of the focal tree's traits
($t_f$) on its tolerance of competition ($\alpha_t$), and the effect
of trait dissimilarity between the focal tree and its competitors
($\vert t_c-t_f \vert$) on competition ($\alpha_d$). The parameters
$m_0, m_1, \alpha_{0 \, \mathrm{intra}}, \alpha_{0 \, \mathrm{inter}}, \alpha_e, \alpha_t$ and
$\alpha_d$ are fitted from data using a maximum likelihood method.
\label{ilustr}}
\end{figure}

\newpage 

\begin{figure}[htbp]
\centering
\includegraphics{FigDef/Fig2.pdf}
\caption{\textbf{Trait-dependent and trait-independent effects on
maximum growth and competition across the globe and their variation among biomes.}
Standardized regression coefficients for growth models, fitted
separately for wood density (\textbf{a}), specific
leaf area (\textbf{b}) and maximum height (\textbf{c}) (points: mean estimates and lines: 95\%
confidence intervals). Black points and lines represent global estimates
and coloured points and lines represent the biome level estimates. The
parameter estimates represent: effect of focal tree's trait value on maximum
growth \(m_1\), the effect of competitor trait values on their competitive
effect \(\alpha_e\) (positive values indicate that higher trait values
lead to a stronger reduction in growth of the focal tree), the
effect of the focal tree's trait value on its tolerance of competition
\(\alpha_t\) (positive values indicate that greater trait values result
in greater tolerance of competition), the effect on competition of
trait dissimilarity between the focal tree and its competitors \(\alpha_d\)
(negative values indicate that higher trait dissimilarity leads to a
lower reduction of the growth of the focal tree), and the
trait-independent competitive effect of conspecific
$\alpha_{0 \, \rm intra}$ and heterospecific $\alpha_{0 \, \rm inter}$. Tropical rainforest
and tropical seasonal forest were merged together as tropical forest,
tundra was merged with taiga, and desert was not included as too few
plots were available (see Fig 1a. for biomes definitions).
\label{res1}}
\end{figure}

\newpage

\begin{figure}[htbp]
\centering
\includegraphics{FigDef/Fig3.pdf}
\caption{\textbf{Variation of maximum growth, competitive
effects and competitive tolerance with wood density (\textbf{a}, \textbf{b} and \textbf{c}) and specific
leaf area (\textbf{d}, \textbf{e} and \textbf{f}) predicted by global traits models.} Variation of maximum growth
(\(m_1 \, t_f\)), tolerance of competition (\(\alpha_t \, t_f\)) and
competitive effect ($\alpha_e \, t_c$)
parameters with wood density (first column) and specific leaf area
(second column). The shaded
area represents the 95\% confidence interval of the prediction
(including uncertainty associated with \(\alpha_0\) or \(m_0\)).
\label{res3}}
\end{figure}

\newpage
\newpage
\clearpage

\section{EXTENDED DATA}\label{extend-data}
\renewcommand{\figurename}{Extended Data Figure}
\renewcommand{\tablename}{Extended Data Table}
\setcounter{figure}{0}
\newpage
\clearpage

\begin{figure}
\centering
\includegraphics{FigDef/ED_Fig1.pdf}
\caption{\textbf{Map of the plot locations of all data sets analysed.}
LPP plots are represented with a large points and NFI plots with small
points (The data set of Panama comprises both a 50ha plot and a network
of 1ha plots). The world map is from the R package
\textit{rworldmap} using Natural Earth data.}
\end{figure}

\newpage
\clearpage

\begin{longtable}[c]{@{}lrrrrr@{}}
\caption{\textbf{Trees data description.} For each site is given the
number of individual trees, species and plots in NFI data and quadrats
in LPP data, and the percentage of angiosperm and evergreen
species.}\tabularnewline
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
set
\strut\end{minipage} &
\begin{minipage}[b]{0.10\columnwidth}\raggedleft\strut
\# of trees
\strut\end{minipage} &
\begin{minipage}[b]{0.11\columnwidth}\raggedleft\strut
\# of species
\strut\end{minipage} &
\begin{minipage}[b]{0.17\columnwidth}\raggedleft\strut
\# of plots/quadrats
\strut\end{minipage} &
\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
\% of angiosperm
\strut\end{minipage} &
\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
\% of evergreen
\strut\end{minipage}\tabularnewline
\midrule
\endfirsthead
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
set
\strut\end{minipage} &
\begin{minipage}[b]{0.10\columnwidth}\raggedleft\strut
\# of trees
\strut\end{minipage} &
\begin{minipage}[b]{0.11\columnwidth}\raggedleft\strut
\# of species
\strut\end{minipage} &
\begin{minipage}[b]{0.17\columnwidth}\raggedleft\strut
\# of plots/quadrats
\strut\end{minipage} &
\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
\% of angiosperm
\strut\end{minipage} &
\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
\% of evergreen
\strut\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Sweden
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
202480
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
26
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
22552
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
27.0
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
73.0
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
New Zealand
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
53775
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
117
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
1415
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
94.0
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
99.1
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
US
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
1370541
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
492
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
59840
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
63.3
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
37.2
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Canada
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
495008
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
75
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
14983
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
34.4
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
64.9
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Australia
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
906
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
101
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
63
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
99.9
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
92.4
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
France
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
184316
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
127
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
17611
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
74.1
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
28.5
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Switzerland
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
28286
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
60
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
2597
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
36.4
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
55.2
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Spain
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
418805
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
122
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
36462
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
34.7
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
81.6
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Panama
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
27089
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
237
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
2033
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
99.8
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
77.7
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
French Guiana
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
46360
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
712
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
2157
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
100.0
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
83.5
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Japan
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
4658
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
139
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
318
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
72.8
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
70.0
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Taiwan
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
14701
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
72
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
623
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
92.0
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
75.3
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Puerto Rico
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
14011
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
82
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
399
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
100.0
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
99.0
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Central African Republic
\strut\end{minipage} &
\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
17638
\strut\end{minipage} &
\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
204
\strut\end{minipage} &
\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
989
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
99.5
\strut\end{minipage} &
\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
72.4
\strut\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\newpage
\clearpage

\begin{longtable}[c]{@{}lrrr@{}}
\caption{\textbf{Traits data description.} The coverage in each site is
given with the percentage of species with species level trait
data.}\tabularnewline
\toprule
\begin{minipage}[b]{0.27\columnwidth}\raggedright\strut
set
\strut\end{minipage} &
\begin{minipage}[b]{0.15\columnwidth}\raggedleft\strut
\% cover SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.25\columnwidth}\raggedleft\strut
\% cover Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.22\columnwidth}\raggedleft\strut
\% cover Max height
\strut\end{minipage}\tabularnewline
\midrule
\endfirsthead
\toprule
\begin{minipage}[b]{0.27\columnwidth}\raggedright\strut
set
\strut\end{minipage} &
\begin{minipage}[b]{0.15\columnwidth}\raggedleft\strut
\% cover SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.25\columnwidth}\raggedleft\strut
\% cover Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.22\columnwidth}\raggedleft\strut
\% cover Max height
\strut\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Sweden
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
98
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
New Zealand
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
US
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
91
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
94
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Canada
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Australia
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
0
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
France
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Switzerland
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
97
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
95
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Spain
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
97
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Panama
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
93
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
93
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
95
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
French Guiana
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
73
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
74
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
64
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Japan
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
100
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Taiwan
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
100
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
96
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Puerto Rico
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
99
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
99
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
Central African Republic
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
40
\strut\end{minipage} &
\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
47
\strut\end{minipage} &
\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
0
\strut\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\newpage
\clearpage

\begin{longtable}[c]{@{}cccc@{}}
\caption{\textbf{Species traits pairwise correlations}. Pearson's r
correlations for the three traits.}\tabularnewline
\toprule
\begin{minipage}[b]{0.23\columnwidth}\centering\strut
~
\strut\end{minipage} &
\begin{minipage}[b]{0.18\columnwidth}\centering\strut
Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.07\columnwidth}\centering\strut
SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.15\columnwidth}\centering\strut
Max height
\strut\end{minipage}\tabularnewline
\midrule
\endfirsthead
\toprule
\begin{minipage}[b]{0.23\columnwidth}\centering\strut
~
\strut\end{minipage} &
\begin{minipage}[b]{0.18\columnwidth}\centering\strut
Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.07\columnwidth}\centering\strut
SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.15\columnwidth}\centering\strut
Max height
\strut\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.23\columnwidth}\centering\strut
\textbf{Wood density}
\strut\end{minipage} &
\begin{minipage}[t]{0.18\columnwidth}\centering\strut
1
\strut\end{minipage} &
\begin{minipage}[t]{0.07\columnwidth}\centering\strut
0.18
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\centering\strut
-0.035
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.23\columnwidth}\centering\strut
\textbf{SLA}
\strut\end{minipage} &
\begin{minipage}[t]{0.18\columnwidth}\centering\strut
\strut\end{minipage} &
\begin{minipage}[t]{0.07\columnwidth}\centering\strut
1
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\centering\strut
0.241
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.23\columnwidth}\centering\strut
\textbf{Max height}
\strut\end{minipage} &
\begin{minipage}[t]{0.18\columnwidth}\centering\strut
\strut\end{minipage} &
\begin{minipage}[t]{0.07\columnwidth}\centering\strut
\strut\end{minipage} &
\begin{minipage}[t]{0.15\columnwidth}\centering\strut
1
\strut\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\newpage

\begin{figure}[htbp]
\centering
\includegraphics{FigDef/ED_Fig2.pdf}
\caption{\textbf{Variation of trait-independent inter and intraspecific
competition, trait dissimilarity (\(|t_f - t_c| \, \alpha_d\)),
competitive effect (\(t_c \, \alpha_e\)), tolerance to competition
(\(t_f \, \alpha_t\)) and maximum growth (\(t_f \, m_1\)) with wood
density (respectively \textbf{a, b, c, d} and \textbf{e}), specific leaf area
(respectively \textbf{f, g, h, i} and \textbf{j}) and maximum height (respectively \textbf{k, l,
m, n} and \textbf{o}).} Trait varied from their quantile at 5\% to their quantile
at 95\%. The shaded area represents the 95\% confidence interval of the
prediction (including uncertainty associated with \(\alpha_0\) or
\(m_0\)). \(\alpha_{0 \, \rm intra}\) and \(\alpha_{0 \, \rm inter}\), which do
not vary with traits are represented with their associated confidence
intervals.}
\end{figure}

\newpage
\clearpage


\begin{figure}[htbp]
\centering
\includegraphics{FigDef/ED_Fig3.pdf}
\caption{\textbf{Average difference between interspecific and
intraspecific competition predicted with estimates of trait-independent
and trait-dependent processes influencing competition for models fitted
with wood density (\textbf{a}), specific leaf area (\textbf{b}) or maximum height (\textbf{c}).} The
average differences between interspecific and intraspecific competition
are influenced by \(\alpha_{0 \, \rm intra}\), \(\alpha_{0 \, \rm inter}\) and
\(\alpha_d\) coefficients (see Extended Methods for details). Negative
values indicate that intraspecific competition is stronger than
interspecific competition.}
\end{figure}

\newpage
\clearpage


\begin{figure}[htbp]
\centering
\includegraphics{FigDef/ED_Fig4.pdf}
\caption{\textbf{Trait-dependent and trait-independent effects on
maximum growth and competition across the globe and their variation
among biomes for models without separation of \(\alpha_0\) between intra
and interspecific competition for wood density (\textbf{a}), specific leaf area
(\textbf{b}) and maximum height (\textbf{c}).} See Fig. 2 in the main text for
parameters description and see Fig. 1a in the main text for biome
definition.}
\end{figure}

\newpage
\clearpage


\begin{longtable}[c]{@{}lrrr@{}}
\caption{\textbf{Standardized coefficient estimates from models fitted
for each traits.} Estimates and standard error (in bracket) estimated
for each trait, \(R^2\)* of models and \(\Delta\) AIC of the model and
of a model with no trait effect. Best model have a \(\Delta\) AIC of
zero. See section Method for explanation of parameters}\tabularnewline
\toprule
\begin{minipage}[b]{0.29\columnwidth}\raggedright\strut
~
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
Maximum height
\strut\end{minipage}\tabularnewline
\midrule
\endfirsthead
\toprule
\begin{minipage}[b]{0.29\columnwidth}\raggedright\strut
~
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
Wood density
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
SLA
\strut\end{minipage} &
\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
Maximum height
\strut\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(m_0\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.016 (0.127)
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
-0.087 (0.132)
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.084 (0.089)
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\gamma\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.418 (0.011)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.401 (0.012)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.42 (0.01)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(m_1\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{-0.149 (0.036)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.119 (0.057)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.063 (0.04)
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(m_2\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.111 (0.003)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.093 (0.003)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.081 (0.002)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(m_3\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.053 (0.002)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.056 (0.003)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.048 (0.002)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\alpha_{0 \, \rm intra}\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.24 (0.037)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.213 (0.052)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.194 (0.046)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\alpha_{0 \, \rm inter}\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.086 (0.022)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.071 (0.025)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.094 (0.024)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\alpha_e\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.034 (0.016)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{-0.083 (0.023)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.017 (0.026)
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\alpha_t\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{0.069 (0.021)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
-0.009 (0.033)
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{-0.071 (0.032)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\alpha_d\)}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0 (0.009)
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
-0.018 (0.015)
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
\textbf{-0.017 (0.008)}
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(R^2_m\)}*
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.1393
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.1637
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.1429
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(R^2_c\)}*
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.7297
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.7593
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0.7166
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\Delta\) AIC}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
0
\strut\end{minipage}\tabularnewline
\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
\textbf{\(\Delta\) AIC no trait}
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
2469
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
1651
\strut\end{minipage} &
\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
2748
\strut\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

* We report the conditional and marginal \(R^2\) of the models using the
methods of reference\footnote{Nakagawa, S. \& Schielzeth, H. A general
  and simple method for obtaining R2 from generalized linear
  mixed-effects models. Methods in Ecology and Evolution 4, 133--142
  (2013).}, modified by reference\footnote{Johnson, P. C. D. Extension
  of Nakagawa and Schielzeth's R2GLMM to random slopes models. Methods
  in Ecology and Evolution 5, 944--946 (2014).}. \(\Delta\) AIC is the
difference in AIC between the model and the best model (lowest AIC). AIC
is the Akaike's Information Criterion (as defined by reference\footnote{Burnham,
  K. P. \& Anderson, D. R. Model selection and multimodel inference: A
  practical information-theoretic approach. (Springer-Verlag, New-York,
  2002).}), and the best-fitting model was identified as the one with a
\(\Delta\) AIC of zero. \(\Delta\) AIC greater than 10 shows strong
support for the best model\textsuperscript{3}.



\end{document}