@@ -297,9 +297,7 @@ Two main data type were used: national forest inventories data -- NFI, large per

...

@@ -297,9 +297,7 @@ Two main data type were used: national forest inventories data -- NFI, large per

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with no differences in $\alpha_0$ for intra- and interspecific competition.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits ($\alpha_{0}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres12_TP.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with no differences in $\alpha_0$ for intra- and interspecific competition.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits ($\alpha_{0}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres12_TP.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with random structure in the parameter including the data set and the Koppen-Geiger ecoregion.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits of conspecific ($\alpha_{0 \, intra}$) and heterospecific ($\alpha_{0 \, inter}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres12_ecocode_TP.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with random structure in the parameter including the data set and the Koppen-Geiger ecoregion.** see the figure 2 in the main text for parameters description and see Fig 1a. in the main text for biomes definitions.](../../figs/figres12_ecocode_TP_intra.pdf)

THIS NEED TO BE UPDATED WITH INTRA INTER

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@@ -315,7 +313,7 @@ SLA was positively correlated with maximum basal area growth only in three biome

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@@ -315,7 +313,7 @@ SLA was positively correlated with maximum basal area growth only in three biome

Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@Poorter-2006a; @Poorter-2008; @Wright-2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might select for slower growth in long-lived plants[@Poorter-2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was however a tendency for species with tall maximum height to have stronger competitive effects (though with wider confidence intervals intercepting zero). This might be explained by greater light interception from taller trees. These small effect of maximum height are probably explained by the fact that our analysis focus on short-term effect on tree growth. Size-structure population models[@Adams-2007] have in contrast shown that maximum height is a key drivers of the long-term competitive success in term of population growth rate.

Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@Poorter-2006a; @Poorter-2008; @Wright-2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might select for slower growth in long-lived plants[@Poorter-2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was however a tendency for species with tall maximum height to have stronger competitive effects (though with wider confidence intervals intercepting zero). This might be explained by greater light interception from taller trees. These small effect of maximum height are probably explained by the fact that our analysis focus on short-term effect on tree growth. Size-structure population models[@Adams-2007] have in contrast shown that maximum height is a key drivers of the long-term competitive success in term of population growth rate.

Our results raise the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intra-specific competition, species with strong competitive effects should have evolved a high tolerance to competition. We found clear evidence for such coordination for wood density, and only weak evidence for SLA. High wood density conferred better competitive tolerance and also stronger competitive effects. High SLA conferred stronger competitive effects and higher tolerance of competition, but with wide confidence intervals intercepting zero for the latter. For maximum height, as explained above, there was a tendency for short maximum height to lead to high tolerance of competition but to low competitive effects. This is interesting because a trade-off between competitive tolerance and maximum height has been proposed as a fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@Kohyama-2009]. The mixed results on the coordination between tolerance and effects are important because they mean that competitive interactions are not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_t$ as in @Kunstler-2012; @Kraft-2014; @Lasky-2014). Traits of competitors alone or of focal plants alone may convey more information than the trait hierarchy. These processes of traits linked to either competitive effects or competitive tolerance, nevertheless, still lead to some trait values having an advantage in competitive interactions.

Our results raise the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intra-specific competition, species with strong competitive effects should have evolved a high tolerance to competition. We found clear evidence for such coordination for wood density, but not for the other traits. High wood density conferred better competitive tolerance and also stronger competitive effects. High SLA conferred stronger competitive effects but not effect on tolerance of competition. For maximum height, as explained above, there was a tendency for short maximum height to lead to high tolerance of competition (see also the Figure 4 in Supplementary Results), but no link with competitive effect. The mixed results on the coordination between tolerance and effects are important because they mean that competitive interactions are not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_t$ as in @Kunstler-2012; @Kraft-2014; @Lasky-2014). Traits of competitors alone or of focal plants alone may convey more information than the trait hierarchy. These processes of traits linked to either competitive effects or competitive tolerance, nevertheless, still lead to some trait values having an advantage in competitive interactions. It is also important to not that an analysis that do not account for the trait independent differences between intraspecific *vs.* interspecific led to an overestimation of the trait similarity effect (Figure 3 in Supplementary results).

Given that the effect sizes we report for effects of traits on competitive interactions are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the light compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that traits measured at the individual level rather than as species averages might strengthen the predictive power of our analysis[@Kraft-2014].

Given that the effect sizes we report for effects of traits on competitive interactions are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the light compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that traits measured at the individual level rather than as species averages might strengthen the predictive power of our analysis[@Kraft-2014].

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with no differences in $\alpha_0$ for intra- and interspecific competition.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits ($\alpha_{0}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres12_TP.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with no differences in $\alpha_0$ for intra- and interspecific competition.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits ($\alpha_{0}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres12_TP.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with random structure in the parameter including the data set and the Koppen-Geiger ecoregion.** Standardized regression coefficients for growth models, fitted separately for each trait (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 competitive effect independent of traits of conspecific ($\alpha_{0 \, intra}$) and heterospecific ($\alpha_{0 \, inter}$), 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), and the effect on competition of trait similarity between the focal tree and its competitors ($\alpha_s$) (negative values indicate that higher trait similarity leads to a stronger reduction of the growth of the focal tree). 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).](../../figs/figres1_ecocode_TP_intra.pdf)

![**Global trait effects and trait-independent effects on maximum growth and competition and their variation among biomes for a model with random structure in the parameter including the data set and the Koppen-Geiger ecoregion.** see the figure 2 in the main text for parameters description and see Fig 1a. in the main text for biomes definitions.](../../figs/figres12_ecocode_TP_intra.pdf)

THIS NEED TO BE UPDATED WITH BIOMES ESTIMATES

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...

@@ -114,7 +112,7 @@ SLA was positively correlated with maximum basal area growth only in three biome

...

@@ -114,7 +112,7 @@ SLA was positively correlated with maximum basal area growth only in three biome

Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@Poorter-2006a; @Poorter-2008; @Wright-2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might select for slower growth in long-lived plants[@Poorter-2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was however a tendency for species with tall maximum height to have stronger competitive effects (though with wider confidence intervals intercepting zero). This might be explained by greater light interception from taller trees. These small effect of maximum height are probably explained by the fact that our analysis focus on short-term effect on tree growth. Size-structure population models[@Adams-2007] have in contrast shown that maximum height is a key drivers of the long-term competitive success in term of population growth rate.

Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@Poorter-2006a; @Poorter-2008; @Wright-2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might select for slower growth in long-lived plants[@Poorter-2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was however a tendency for species with tall maximum height to have stronger competitive effects (though with wider confidence intervals intercepting zero). This might be explained by greater light interception from taller trees. These small effect of maximum height are probably explained by the fact that our analysis focus on short-term effect on tree growth. Size-structure population models[@Adams-2007] have in contrast shown that maximum height is a key drivers of the long-term competitive success in term of population growth rate.

Our results raise the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intra-specific competition, species with strong competitive effects should have evolved a high tolerance to competition. We found clear evidence for such coordination for wood density, and only weak evidence for SLA. High wood density conferred better competitive tolerance and also stronger competitive effects. High SLA conferred stronger competitive effects and higher tolerance of competition, but with wide confidence intervals intercepting zero for the latter. For maximum height, as explained above, there was a tendency for short maximum height to lead to high tolerance of competition but to low competitive effects. This is interesting because a trade-off between competitive tolerance and maximum height has been proposed as a fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@Kohyama-2009]. The mixed results on the coordination between tolerance and effects are important because they mean that competitive interactions are not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_t$ as in @Kunstler-2012; @Kraft-2014; @Lasky-2014). Traits of competitors alone or of focal plants alone may convey more information than the trait hierarchy. These processes of traits linked to either competitive effects or competitive tolerance, nevertheless, still lead to some trait values having an advantage in competitive interactions.

Our results raise the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intra-specific competition, species with strong competitive effects should have evolved a high tolerance to competition. We found clear evidence for such coordination for wood density, but not for the other traits. High wood density conferred better competitive tolerance and also stronger competitive effects. High SLA conferred stronger competitive effects but not effect on tolerance of competition. For maximum height, as explained above, there was a tendency for short maximum height to lead to high tolerance of competition (see also the Figure 4 in Supplementary Results), but no link with competitive effect. The mixed results on the coordination between tolerance and effects are important because they mean that competitive interactions are not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_t$ as in @Kunstler-2012; @Kraft-2014; @Lasky-2014). Traits of competitors alone or of focal plants alone may convey more information than the trait hierarchy. These processes of traits linked to either competitive effects or competitive tolerance, nevertheless, still lead to some trait values having an advantage in competitive interactions. It is also important to not that an analysis that do not account for the trait independent differences between intraspecific *vs.* interspecific led to an overestimation of the trait similarity effect (Figure 3 in Supplementary results).

Given that the effect sizes we report for effects of traits on competitive interactions are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the light compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that traits measured at the individual level rather than as species averages might strengthen the predictive power of our analysis[@Kraft-2014].

Given that the effect sizes we report for effects of traits on competitive interactions are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the light compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that traits measured at the individual level rather than as species averages might strengthen the predictive power of our analysis[@Kraft-2014].

## ![Variation of the four parameters linking wood density, specific leaf area and maximum height with maximum growth and competition - maximum growth ($t_f \, m_1$), tolerance to competition ($t_f \, \alpha_t$), competitive effect ($t_c \, \alpha_e$) and limiting similarity ($|t_f - t_c| \, \alpha_l$ ($t_c$ was fixed at the lowest value and $t_f$ varying from quantile 5 to 95\%). The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$).](../../figs/figres4b.pdf)

## ![Variation of the four parameters linking wood density, specific leaf area and maximum height with maximum growth and competition - maximum growth ($t_f \, m_1$), tolerance to competition ($t_f \, \alpha_t$), competitive effect ($t_c \, \alpha_e$) and limiting similarity ($|t_f - t_c| \, \alpha_l$ ($t_c$ was fixed at the lowest value and $t_f$ varying from quantile 5 to 95\%). The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$). $\alpha_{0 \, intra}$ and $\alpha_{0 \, inter}$, which do not vary with traits are also represented with their associated confidence intervals.](../../figs/

## figres4b_TP_intra.pdf)

## ![**Stabilising effect of competition between pairs of species in function of their traits distance, predicted according to the basal area growth models fitted for wood density, specific leaf area and maximum height.** $1 -\rho$ measure the relative strengh of intra-specific competition compared to inter-specific competition (where $\rho$ is defined as $\sqrt{\frac{\alpha{ij} \alpha{ji}}{\alpha{jj} \alpha{ii}}}$), where $\rho$ is a measure of niche overlap between a pair of species. If inter-specific competition is equal or greater than inter-specific competition $1- \rho \leqslant 0$, and there is no stabilising processes. If inter-specific competition is smaller than inter-specific competition $1- \rho > 0$, and this indicates the occurence of stabilising processes resulting in stronger intra- than inter-specific competition. As the niche overlap $\rho$ is estimated only with competition effect on individual tree basal area growth, this can not be taken as a direct indication of coexistence as with population growth model.](../../figs/rho_set_TP_intra.pdf)

## ![**Stabilising effect of competition between pairs of species in function of their traits distance, predicted according to the basal area growth models fitted for wood density, specific leaf area and maximum height.** $1 -\rho$ measure the relative strengh of intra-specific competition compared to inter-specific competition (see Methods), where $\rho$ is a measure of niche overlap between a pair of species. If inter-specific competition is equal or greater than intra-specific competition $1- \rho \leqslant 0$, and there is no stabilising processes. If inter-specific competition is smaller than intra-specific competition $1- \rho > 0$, and this indicates the occurence of stabilising processes resulting in stronger intra- than inter-specific competition. As the niche overlap $\rho$ is estimated only with competition effect on individual tree basal area growth and not on population growth, this can not be taken as a direct indication of coexistence.](../../figs/rho_set_TP_intra.pdf)

@@ -188,7 +188,7 @@ Estimating different $\alpha_0$ for intra- and interspecific competition allow t

...

@@ -188,7 +188,7 @@ Estimating different $\alpha_0$ for intra- and interspecific competition allow t

We also explored a simpler version of the model where only one $\alpha_0$ was include in the model of $\alpha_{c,f}$ as most previous studies have generally not make this distinction which may lead into an overestimation of the trait similarity effect. In this alternative model the equation was:

We also explored a simpler version of the model where only one $\alpha_0$ was include in the model of $\alpha_{c,f}$ as most previous studies have generally not make this distinction which may lead into an overestimation of the trait similarity effect. In this alternative model the equation was:

@@ -223,11 +223,11 @@ for the parameters with both the data set and a local ecoregion using

...

@@ -223,11 +223,11 @@ for the parameters with both the data set and a local ecoregion using

the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see

the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see

Supplementary Results).

Supplementary Results).

\subsection{Estimating of strength of stabilising processes}\label{rho}

\subsection{Estimating the effect of traits on the mean ratio of intra- \textit{vs.} inter-specific competition}\label{rho}

To estimate if traits effects on competition have the potential to lead to a stable coexistence of species with diverse traits values, studies\citep{Kraft-2015, Godoy-2014} have recently proposed to use the method developed by Chesson\citep{Chesson-2012} to estimate the stabilising niche difference between species which estimates the strength process favouring the establishment of a species as rare invader in an other species already established (see an example based on the Lotka-Volterra model based on Godoy \& Levine\citep{Kraft-2015, Godoy-2014} in the Supplementary Methods). This approach shows that $\rho$ defined as the ratio of geometric mean of interspecific competition over intraspecific competition ($\rho=\sqrt{\frac{\alpha'_{ij}\alpha'_{ji}}{\alpha'_{jj}\alpha'_{ii}}}$, where $\alpha'_{ij}$ represent the population level competitive effect of species $j$ on species $i$) to quantify stabilising niche overlap. Our model only estimate competition effect on the individual basal area growth, and not on the population growth, it is thus impossible to estimate the fitness of a rare invader. We can, however, compare the relative importance of interspecific to intraspecific competition using the same approach as $\rho$. The competitive effect of species $j$ on species $i$ can be defined by the inverse of the growth reduction per unit of basal area of the species $j$ on species $j$ predicted by tree basal area growth model (see equ. \ref{logG1}). According to this model$\alpha'_{ij}=\frac{1}{e^{-\alpha_{ij}}}$, with $\alpha_{ij}$ defined by equ. \ref{alpha}. $\rho$ can then be simplified based on eqn. \ref{alpha} as:

The ratio of inter- \textit{vs.} intra-specific competition is generally considered as key in controlling species coexistence. For instance, recent studies\citep{Kraft-2015, Godoy-2014} have recently proposed to analyse the link between traits and $\rho$ defined as the geometric mean of the ratio of interspecific competition over intraspecific competition to understand traits effects on coexistence. This is based on a method developed by Chesson\citep{Chesson-2012} which demonstrates that $\rho$ can be used to quantify the stabilising niche difference between pairs of species (this estimates the strength processes favouring the establishment of a species as rare invader in the population of an other species already established, see an example based on the Lotka-Volterra model based on Godoy \& Levine\citep{Godoy-2014} in the Supplementary Methods). In this approach $\rho$ is defined as $\rho=\sqrt{\frac{\alpha'_{ij}\alpha'_{ji}}{\alpha'_{jj}\alpha'_{ii}}}$, where $\alpha'_{ij}$ represent the population level competitive effect of species $j$ on species $i$. Even if our model estimate competition effect only on the individual basal area growth, and not on the population growth, it is interesting to quantify how this ratio of inter- \textit{vs.} intra-specific competition is influenced by traits. The competitive effect of species $j$ on species $i$ can be defined in the tree basal area growth model (see equ. \ref{logG1}) as the reduction of growth of species $i$ by one unit of basal area of competitors of the species $j$ ( thus as $\alpha'_{ij}=\frac{1}{e^{-\alpha_{ij}}}$, with $\alpha_{ij}$ defined by equ. \ref{alpha}). $\rho$ can then be related to the estimated parameters of eqn. \ref{alpha} as:

\title{Plant functional traits have globally consistent effects on competition}

\title{Plant functional traits have globally consistent effects on competition}

\author[1,2,3]{Georges Kunstler}

\author[1,2,3]{Georges Kunstler}

\author[4]{David A. Coomes}

\author[3]{Daniel Falster}

\author[3]{Daniel Falster}

\author[4]{David A. Coomes}

\author[5]{Francis Hui}

\author[5]{Francis Hui}

\author[3,6]{Robert M. Kooyman}

\author[3,6]{Robert M. Kooyman}

\author[7]{Daniel C. Laughlin}

\author[7]{Daniel C. Laughlin}

...

@@ -330,8 +330,7 @@ been expected\citep{Goldberg-1996, Kunstler-2012}, but rarely

...

@@ -330,8 +330,7 @@ been expected\citep{Goldberg-1996, Kunstler-2012}, but rarely

documented\citep{Goldberg-1996, Wang-2010}.

documented\citep{Goldberg-1996, Wang-2010}.

We found evidences for such coordination for wood density with the

We found evidences for such coordination for wood density with the

same direction for its competitive effect and tolerance of competition

same direction for its competitive effect and tolerance of competition

parameters. Similar pattern was present for specific leaf area, however this coordination was weak because confidence interval of its tolerance of competition parameter

parameters (Fig. \ref{res1}).

intercepted zero (Fig. \ref{res1}).

The globally consistent links that we report here between traits and

The globally consistent links that we report here between traits and

competition have considerable promise to predict the complex species

competition have considerable promise to predict the complex species

...

@@ -366,10 +365,9 @@ Framework Program (Demo-traits project, no. 299340). The working group

...

@@ -366,10 +365,9 @@ Framework Program (Demo-traits project, no. 299340). The working group

that initiated this synthesis was supported by Macquarie University and

that initiated this synthesis was supported by Macquarie University and

by Australian Research Council through a fellowship to MW.

by Australian Research Council through a fellowship to MW.

\textbf{Author contributions} GK and MW conceived the study and led a

\textbf{Author contributions} GK and MW conceived the study and led --with help form DF-- a

workshop to develop this analysis with the participation of DAC, DF, FH,

workshop to develop this analysis with the participation of DAC, FH,

RMK, DCL, LP, MV, GV, and SJW. GK wrote the manuscript with input

RMK, DCL, LP, MV, GV, and SJW. GK wrote the manuscript with key inputs form all workshop participants and help form 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.

from all authors. GK processed the data, devised the main analytical approach, wrote the computer code and performed analyses with assistance from DF and FH.