- $\gamma_f$ determines the rate at which growth changes with size for species $f$, modelled with a normally distributed random effect of species $\epsilon_{\gamma, f}$ (as $\gamma_f = \gamma_0 + \epsilon_{\gamma, f}$)

- $N_p$ is the number of competitor species on plot $p$ ,

- $\alpha_{c,f}$ is the per unit basal area effect of individuals from species $c$ on growth of an individual in species $f$, and

- $B_{c,p,s}= 0.25\, \pi \, w_i \sum_i D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on plot size.

- $B_{c,p,s}= 0.25\, \pi \, \sum_i w_i \, D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on subplot size where tree $i$ was measured.

Values of $\alpha_{c,f}< 0$ indicate competition, whereas $\alpha_{c,f}$ > 0 indicates facilitation. Log-transformation of eq. \ref{G1} leads to a linearised model of form

...

...

@@ -38,10 +38,10 @@ To include traits effects on competition presented in Fig. 1, competitive intera

\end{equation}

where:

- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{0, s}$),

- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$,

- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$, and

- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$.

- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{\alpha_0, s}$),

- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_r,s}$),

- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_i,s}$), and

- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_s,s}$).

[^GK1]: With basal area of species $c$ this equation can be simplified as a function of total basal area, the weighted mean of the traits of the competitors and the weighted mean of the traits similarity.

...

...

@@ -49,7 +49,7 @@ Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of growth,

To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically closest biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.

To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically similar biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.

**\color{red}TO BE DONE** Because traits similarity may be more strongly related to multi-traits distance than a single trait distance we also explored a model with all three traits and a traits distance based on the euclidean distance of the three traits (standardized). This model expand the equation 1 with a parameter $m_1$, $\alpha_i$ and $\alpha_r$ per trait and an effect of multi-traits similarity (with the parameter $\alpha_s$).

...

...

@@ -70,7 +70,7 @@ For each individual tree, we estimated the local abundance of competitor species

For the NFI data, the coordinates of individual trees in the plot were generally not available, thus the neighbourhood was defined based on plot size. Mostly, the size of the sampled plots varied between 10-25m in radius. 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 10-25m radius, with most plots between 10-15m radius.

We extracted mean annual temperature (MAT) and mean annual sum of precipitation (MAP) from the [worldclim](http://www.worldclim.org/) data base [@hijmans_very_2005], using the plot latitude and longitude. MAT and MAP data were then used to classify plots into biomes, using the diagram provided by @ricklefs_economy_2001 (after Whittaker). In addition we used ecoregion classification[@olson_terrestrial_2001] to group data in similar abiotic conditions to have a fine definition within each data set.

We extracted mean annual temperature (MAT) and mean annual sum of precipitation (MAP) from the [worldclim](http://www.worldclim.org/) data base [@hijmans_very_2005], using the plot latitude and longitude. MAT and MAP data were then used to classify plots into biomes, using the diagram provided by @ricklefs_economy_2001 (after Whittaker).

## Traits

...

...

@@ -135,7 +135,7 @@ rownames(dat.2) <- NULL

dat.2 <- dat.2[, 1:11]

pandoc.table(dat.2[, 1:6], caption = "Table M1. Data description",

- $\gamma_f$ determines the rate at which growth changes with size for species $f$, modelled with a normally distributed random effect of species $\epsilon_{\gamma, f}$ (as $\gamma_f = \gamma_0 + \epsilon_{\gamma, f}$)

- $N_p$ is the number of competitor species on plot $p$ ,

- $\alpha_{c,f}$ is the per unit basal area effect of individuals from species $c$ on growth of an individual in species $f$, and

- $B_{c,p,s}= 0.25\,\pi \,w_i \sum_i D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on plot size.

- $B_{c,p,s}= 0.25\,\pi \,\sum_i w_i \,D_{i,c,p,s}^2$ is the basal area of the species $c$ within the plot $p$ and dataset $s$, where $w_i$ is a constant based on subplot size where tree $i$ was measured.

Values of $\alpha_{c,f}<0$indicatecompetition,whereas$\alpha_{c,f}$> 0 indicates facilitation. Log-transformation of eq. \ref{G1} leads to a linearised model of form

...

...

@@ -38,10 +38,10 @@ To include traits effects on competition presented in Fig. 1, competitive intera

\end{equation}

where:

- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{0, s}$),

- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$,

- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$, and

- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$.

- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{\alpha_0, s}$),

- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_r,s}$),

- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_i,s}$), and

- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_s,s}$).

[^GK1]:With basal area of species $c$ this equation can be simplified as a function of total basal area, the weighted mean of the traits of the competitors and the weighted mean of the traits similarity.

...

...

@@ -49,7 +49,7 @@ Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of growth,

To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically closest biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.

To estimate standardised coefficients (one type of standardised effect size)[@schielzeth_simple_2010], response and explanatory variables were standardized prior to analyse (divided by standard deviation). Moreover, trait and diameter were also centred to facilitate convergence. The model were fitted using $lmer$ in [lme4](http://cran.r-project.org/web/packages/lme4/index.html). We fitted two versions of this model. In the first version parameters $m_{0}, m_1, \alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across all biomes, we repeated the same analysis but including different fixed estimates of these parameters fort each biome. This enabled us to explore variation between biomes. Because some biomes had very few observation we merged several biomes with climatically similar biome: tundra was merged with taiga, tropical rainforest and tropical seasonal forest were merged in tropical forest, and desert were not include in this final analysis as to few data was available.

**\color{red}TO BE DONE** Because traits similarity may be more strongly related to multi-traits distance than a single trait distance we also explored a model with all three traits and a traits distance based on the euclidean distance of the three traits (standardized). This model expand the equation 1 with a parameter $m_1$, $\alpha_i$ and $\alpha_r$ per trait and an effect of multi-traits similarity (with the parameter $\alpha_s$).

...

...

@@ -70,7 +70,7 @@ For each individual tree, we estimated the local abundance of competitor species

For the NFI data, the coordinates of individual trees in the plot were generally not available, thus the neighbourhood was defined based on plot size. Mostly, the size of the sampled plots varied between 10-25m in radius. 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 10-25m radius, with most plots between 10-15m radius.

We extracted mean annual temperature (MAT) and mean annual sum of precipitation (MAP) from the [worldclim](http://www.worldclim.org/) data base [@hijmans_very_2005], using the plot latitude and longitude. MAT and MAP data were then used to classify plots into biomes, using the diagram provided by @ricklefs_economy_2001 (after Whittaker). In addition we used ecoregion classification[@olson_terrestrial_2001] to group data in similar abiotic conditions to have a fine definition within each data set.

We extracted mean annual temperature (MAT) and mean annual sum of precipitation (MAP) from the [worldclim](http://www.worldclim.org/) data base [@hijmans_very_2005], using the plot latitude and longitude. MAT and MAP data were then used to classify plots into biomes, using the diagram provided by @ricklefs_economy_2001 (after Whittaker).

@@ -14,16 +14,16 @@ Competition is a very important type of ecological interaction, especially in te

# Main text

**(MAX 1500 words till the end of Methods = 1494)**

**(MAX 1500 words till the end of Methods = 1482)**

Competition is a fundamental type of interaction in ecological communities. Each individual modify their neighbouring environment and thus influences the performance of neighbouring individuals [@keddy_competition_2001]. Competition influences species composition and its changes over time. Maybe competition is especially important for vegetation on land because most vegetation types have high enough cover that shading and water and nutrient depletion are conspicuous. There have thus been a very large number of studies on competition among plants [@goldberg_patterns_1992], but firm generalizations have yet to be established about its outcomes.

When competition is described as interactions between pairs of species (as it traditionally has been), the number of different interactions to be measured grows explosively with the number of species ($N^2$), and becomes quickly intractable. Also this species-pair approach does not lead naturally to generalization across forests on different continents with different composition. Here we quantify competition between trees (in the sense of influence of neighbours on growth of a focal tree) within a framework, which is novel in two important ways: (i) competition is modelled as a function of traits rather than of species and (ii) we partition how traits drive the outcome of competition in four different key processes (Fig. \ref{ilustr}). Competition can select trait values that are the most competitive. This competitive advantage of trait values can arise because (1) there are correlated with higher potential growth (in absence of competition) [@wright_functional_2010], (2) they are correlated with a higher tolerance to competition [@goldberg_competitive_1996], or (3) they are correlated with higher competitive impact [@gaudet_comparative_1988]. In contrast, competition can promotes the coexistence of a mixture of traits values, if (4) competition decrease with increasing dissimilarity of the traits of the competitors and the focal tree [@macarthur_limiting_1967]. These four processes are likely to be connected to the key traits used to describe plant strategies[@hillerislambers_rethinking_2012; @lasky_trait-mediated_2014], however there is no agreement on their relative contributions to each of these processes and whether the magnitude and direction of these effects are conserved across large scale.

When competition is described as interactions between pairs of species (as it traditionally has been), the number of different interactions to be measured grows explosively with the number of species ($N^2$), and becomes quickly intractable. Also this species-pair approach does not lead naturally to generalization across forests on different continents with different composition. Here we quantify competition between trees (in the sense of influence of neighbours on growth of a focal tree) within a framework, which is novel in two important ways: (i) competition is modelled as a function of traits rather than of species and (ii) we partition how traits drive the outcome of competition in four different key processes (Fig. \ref{ilustr}). Competition can select trait values that are the most competitive. This competitive advantage of trait values can arise because (1) there are correlated with higher maximum growth (in absence of competition) [@wright_functional_2010], (2) they are correlated with a higher tolerance to competition [@goldberg_competitive_1996], or (3) they are correlated with higher competitive impact [@gaudet_comparative_1988]. In contrast, competition can promotes the coexistence of a mixture of traits values, if (4) competition decrease with increasing dissimilarity of the traits of the competitors and the focal tree [@macarthur_limiting_1967]. These four processes are likely to be connected to the key traits used to describe plant strategies[@hillerislambers_rethinking_2012; @lasky_trait-mediated_2014], however there is no agreement on their relative contributions to each of these processes and whether the magnitude and direction of these effects are conserved across large scale.

Here we dissect how three key traits[@westoby_plant_2002; @chave_towards_2009] (maximum height, wood density and specific leaf area - *SLA*) affect these four processes involved in competition between trees using neighbouring modeling approach[@uriarte_neighborhood_2004]. We compiled data of growth along side local abundance of their competitor for more than 7 million trees representing more than 2500 species covering all the major biomes of the earth (Fig. \ref{res2}b). We analysed how the potential growth of each individual tree was reduced by the local abundance of its competitors. Our analysis accounts for the trait of both the focal tree and its competitors estimating the trait effect for each of the processes presented in Fig. \ref{ilustr}.

Here we dissect how three key traits[@westoby_plant_2002; @chave_towards_2009] (maximum height, wood density and specific leaf area - *SLA*) affect competition between trees using neighbouring modeling approach[@uriarte_neighborhood_2004]. We compiled data of growth along side local abundance of their competitor for more than 3 million trees representing more than 2500 species covering all the major biomes of the earth (Fig. \ref{res2}b). We analysed how the potential growth of each individual tree was reduced by the local abundance of its competitors. Our analysis accounts for the trait of both the focal tree and its competitors estimating the trait effect for each of the processes presented in Fig. \ref{ilustr}.

Across all biomes we found that strongest drivers of individual growth

were tree size and the local abundance of competitors. Then amomg the trait effect, the direct influence of the focal plant’s traits on its growth was the most important effect

were tree size and the local abundance of competitors. Then among the trait effect, the direct influence of the focal plant’s traits on its growth was the most important effect

(Fig. \ref{res1} Extended data Table D1). We detected only negative

effect of the abundance of competitors showing that competition was

predominant. Among the three traits wood density had the strongest

...

...

@@ -31,17 +31,15 @@ direct effect, followed by SLA whereas confidence interval for maximum height in

influence of neighbour traits on their competitive impact, and of

focal species traits on tolerance of competition

(Fig. \ref{res1}). Taken together these two effects are in the range

of half or quarter as big as the direct trait effect (Extend data

Table D1), down to zero influence depending on the trait (Fig

of the direct trait effect (Extend data

Table D1; Fig

\ref{res1}). Finally, there is a small but consistent effect whereby

the wider is the absolute trait separation between focal and neighbour

species, the weaker is competitive suppression of growth

(Fig. \ref{res1}). This may arise because of negative density

dependence arising for species with similar trait because, for

instance, a higher load of herbivores or pathogens

[@bagchi_pathogens_2014] or less efficient use of resources (such a

less efficient light use[@sapijanskas_tropical_2014] or less efficient

litter recylcing[@sapijanskas_beyond_2013])[^todo]. Analyses allowing for different effect between biomes did no show strong evidence for any particular biome behaving consistently differently from the others (Fig. \ref{res3}). For Wood density only taiga which has relatively small sample size and few species showed a different competitive response parameter (Fig. \ref{res2}). The results were more variable for SLA (Fig. \ref{res2}), which may be related to different relationship between shade-tolerance and SLA between deciduous and evergreeen species[@lusk_why_2008].

(Fig. \ref{res1}). Several processes may explain this, for instance species with similar trait could have, a higher load of herbivores or pathogens

[@bagchi_pathogens_2014] or a less efficient use of resources (such a

less efficient light use[@sapijanskas_tropical_2014] or a less efficient

litter recylcing[@sapijanskas_beyond_2013])[^todo]. Analyses allowing for different effect between biomes did no show strong evidence for any particular biome behaving consistently differently from the others (Fig. \ref{res3}). For Wood density only taiga, which has relatively small sample size and few species, showed a different competitive response parameter (Fig. \ref{res2}). The results were more variable for SLA (Fig. \ref{res2}), which may be related to different responses between deciduous and evergreeen[@lusk_why_2008].

[^todo]:**I'M PLANNING TO ADD An analysis using a multiple-traits distance rather than a single trait distance didn't show different pattern (extended data Figure **\color{red}?**). \color{red}BUT Still running.**

...

...

@@ -50,10 +48,10 @@ litter recylcing[@sapijanskas_beyond_2013])[^todo]. Analyses allowing for differ

literature. High wood density was lined with

slow potential growth rate but high tolerance to competition, in

agreement with shade-tolerant

species having high wood density[@wright_functional_2010]. High wood density also resulted in a

higher competitive impact, that may be related to deeper crown

[@poorter_architecture_2006; @aiba_architectural_2009]. The small direct effect of *SLA* on maximum growth agree well with the weak correlation previously reported for adult

trees [@wright_functional_2010]. Increasing SLA was also related to decreased competitive impact, in agrement with the postive relationship between leaf life span and light interception [@niinemets_review_2010]. No effect of SLA on competitive tolerance were found. Finally, maximum height was

species having high wood density[@wright_functional_2010]. High wood density was also weakly correlated with

higher competitive impact, this may be related to deeper crown

[@poorter_architecture_2006; @aiba_architectural_2009]. The small positive effect of *SLA* on maximum growth agree well with the weak correlation previously reported for adult

trees [@wright_functional_2010]. Increasing SLA was also related to decreased competitive impact, in agrement with the postive relationship between leaf life span and light interception [@niinemets_review_2010]. Finally, maximum height was

positively related to maximum growth in most biomes (but with large confidence interval in tropical forest) as previously

reported[@wright_functional_2010]. Species with small maximum height

were also much more tolerant to competition than taller species, in

...

...

@@ -132,25 +130,22 @@ G.K. conceived the study with feedback from M.W and D.F. G. K., M. W, D. F. and

# FIGURES & TABLES

![**Assessing competitive interactions at global scale.** **a,** Precipitation-temperature space occupied by the natural forest communities studied (NFI data : national forest Inventories, LPP data : large permanent plots) . Biomes follow the definition of Whittaker [@ricklefs_economy_2001]: 1, tundra; 2, taiga; 3, woodland/shrubland; 4, temperate forest; 5, temperate rainforest; 6, desert; 7, tropical seasonal forest; 8, tropical rainforest. **b,** Sampled patches vary in the density of competitors from species $c$ around individuals from a focal species $f$. For each tree we record the stem diameter $D_i$ across multiple censuses, and link this with records for the traits of the focal and competitor species, $t_f$ and $t_c$ respectively. **c,** We use a neighbourhood modelling framework to model the effects of the traits and size of the focal tree, and the total basal area ($B_c$) and traits of competitor species on growth of the focal tree. These effects can be broken down into those influencing maximum growth rate (red) and those influencing reduction in growth per unit basal area of competitor (blue), $\alpha_{c,f}$. Trait value of focal tree ($t_f$) can influences the tree growth without competition (maximum growth, $m_1$). The trait value of the focal tree can influences its tolerance to competition ($t_f \, \alpha_r$) and the trait values of the competitors can influence their competitive impact ($t_c \, \alpha_i$). Finally, the trait similarity between the focal tree and its competitors can influences competitive interactions ($\alpha_s \, \vert t_c-t_f \vert$) (see extended methods). The parameters $m_1, \gamma, \alpha_0, \alpha_i, \alpha_r$ and $\alpha_s$ are fitted from data. \label{ilustr}](image/fig1e.pdf)

![**Assessing competitive interactions at global scale.** **a,** Precipitation-temperature space occupied by the natural forest communities studied (NFI data : national forest Inventories, LPP data : large permanent plots) . Biomes follow the definition of Whittaker [@ricklefs_economy_2001]: 1, tundra; 2, taiga; 3, woodland/shrubland; 4, temperate forest; 5, temperate rainforest; 6, desert; 7, tropical seasonal forest; 8, tropical rainforest. **b,** Sampled patches vary in the density of competitors from species $c$ around individuals from a focal species $f$. For each tree, basal area growth and stem diameter $D_i$ were recorded, and was linked with records for the traits of the focal and competitor species, $t_f$ and $t_c$ respectively. **c,** We use a neighbourhood modelling framework to model the effects of the traits and size of the focal tree, and the total basal area ($B_c$) and traits of competitor species on growth of the focal tree. These effects can be broken down into those influencing maximum growth rate (red) and those influencing reduction in growth per unit basal area of competitor (blue), $\alpha_{c,f}$. Tree size $D_i$ adn trait value of focal tree ($t_f$) can influences the maximum growth (without competition, $\gamma$ and $m_1$). The trait value of the focal tree can influences its tolerance to competition ($t_f \, \alpha_r$) and the trait values of the competitors can influence their competitive impact ($t_c \, \alpha_i$). Finally, the trait similarity between the focal tree and its competitors can influences competitive interactions ($\alpha_s \, \vert t_c-t_f \vert$) (see extended methods). The parameters $m_1, \gamma, \alpha_0, \alpha_i, \alpha_r$ and $\alpha_s$ are fitted from data. \label{ilustr}](image/fig1e.pdf)

\newpage

![**Traits effects and traits independent effects on maximum growth and competition.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits (Wood density, Specific leaf area, and Maximum height). The parameters estimate represents the effect explained in the Fig 1c.: the size effect effect on maximum growth, the direct trait effect on maximum growth of the focal tree, the competition trait independent, the trait of the competitors effect on their competitive impact, the trait of the focal tree effect on its competitive response, and trait similarity between the focal tree and its competitors effect on competition. The points represent the mean estimate and the line the 95\% confidence interval. \label{res1}](../../figs/figres1.pdf)

![**Traits effects and traits independent effects on maximum growth and competition.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits (Wood density, Specific leaf area, and Maximum height). The parameters estimate represents the effect explained in the Fig 1c.: the size effect effect on maximum growth, the direct trait of focal tree effect on maximum growth, the competition trait independent, the trait of the competitors effect on their competitive impact, the trait of the focal tree effect on its competitive response, and trait similarity between the focal tree and its competitors effect on competition. The points represent the mean estimate and the line the 95\% confidence interval. \label{res1}](../../figs/figres1.pdf)

\newpage

![**Variation of traits effects on maximum growth and competition between biomes.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits as in Fig. 2, but with a different estimates for each biomes (see Fig 1a. for the definitions of the biomes). Note that tropical rainforest and tropical seasonal forest were merged togetherin tropical forest, tundra was merged with taiga, and desert were not included in this analysis as to few data were available. \label{res2}](../../figs/figres2.pdf)

![**Variation of traits effects on maximum growth and competition between biomes.** Standardized regression coefficients of the growth models in function of the trait of the focal tree and its competitors fitted separately for each traits as in Fig. 2, but with a different estimates for each biomes (see Fig 1a. for the definitions of the biomes). Note that tropical rainforest and tropical seasonal forest were merged togetherin tropical forest, tundra was merged with taiga, and desert were not included in this analysis as to few data were available. \label{res2}](../../figs/figres2.pdf)

\newpage

![**Trade off between growth without competition and growth with competition underpinned by Maximum height, Specific leaf area, and wood density**. The growth of a focal tree with low or high trait value (respectively 5 and 95\% quantile) in function of the local basal area of competitors with trait value resulting in a high competitive impact. The shaded area represents the 95% confidence interval of the prediction. \label{res3}](../../figs/figres3.pdf)

![**Trade off between growth without competition and growth with competition underpinned by Maximum height, Specific leaf area, and Wood density**. The growth of a focal tree with low or high trait value (respectively 5 and 95\% quantile) in function of the local basal area of competitors with trait value resulting in a high competitive impact. The shaded area represents the 95% confidence interval of the prediction. \label{res3}](../../figs/figres3.pdf)