Commit 7674b82c authored by kunstler's avatar kunstler
Browse files

fixe launch

parent 15110b8a
......@@ -163,7 +163,7 @@ load.data.for.lmer <- function(trait, data.type,
df <- readRDS(file.path(base.dir,paste('data', 'Multi', data.type, 'rds',
sep = '.')))
}else{
df <- readRDS( file.path(base.dir,paste('data', trait, data.type, 'rds',
df <- readRDS( file.path(base.dir,paste('data', trait, 'simple', 'rds',
sep = '.')))
}
df <- mutate(df,sp.name = ifelse(is.na(sp.name), 'missing.sp',
......
Data set name,Country,Data type,Plot size,Dbh threshold,Number of plots,Traits,Source trait data,References,Contact of person in charge of data formatting,Comments
NSW,"New South Wales, Australia",LPP,0.075 to 0.36 ha,10 cm,30,"Wood density, Maximum height, and Seed mass",local,"1,2",R. M. Kooyman (robert@ecodingo.com.au),Permanents plots established by the NSW Department of State Forests or by RMK
Panama,Panama,LPP,1 to 50 ha,1 cm,42,"Wood density, SLA, Maximum height, and Seed mass",local,"3,4,25",R. Condit (conditr@gmail.com),The data used include both the 50 ha lot of BCI and the network of 1 ha plots from Condit et al. (2013). The two first census of BCI plot were excluded.
Japan,Japan,LPP,0.35 to 1.05 ha,2.39 cm,16,"Wood density, SLA, Maximum height, and Seed mass",local,5,M. I. Ishihara (moni1000f_networkcenter@fsc.hokudai.ac.jp),
Luquillo,Puerto Rico,LPP,16 ha,1 cm,1,"Wood density, SLA, Maximum height, and Seed mass",local,"6, 23",J. Zimmerman (esskz@ites.upr.edu),
......@@ -13,3 +12,4 @@ Sweden,Sweden,NFI,0.0019 to 0.0314 ha,5 cm,22904,"Wood density, SLA, Maximum hei
US,USA,NFI,0.0014 to 0.017 ha,2.54 cm,97434,"Wood density, SLA, Maximum height, and Seed mass",TRY,19,M. Vanderwel (Mark.Vanderwel@uregina.ca),FIA data are made up of cluster of 4 subplots of size 0.017 ha for tree dbh > 1.72 cm and nested in each subplot sapling plots of 0.0014 ha for trees dbh > 2.54 cm. The data of the four subplot were lumped together.
Canada,Canada,NFI,0.02 to 0.18 ha,2 cm,15019,"Wood density, SLA, Maximum height, and Seed mass",TRY,,J. Caspersen (john.caspersen@utoronto.ca),The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plot are 10 m in radius in this Province.
NZ,New Zealand,NFI,0.04 ha,3 cm,1415,"Wood density, SLA, Maximum height, and Seed mass",local,"20,21",D. Laughlin (d.laughlin@waikato.ac.nz),Plots are 20 x 20 m.
NSW,Australia,NFI,0.075 to 0.36 ha,10 cm,30,"Wood density, Maximum height, and Seed mass",local,"1,2",R. M. Kooyman (robert@ecodingo.com.au),Permanents plots established by the NSW Department of State Forests or by RMK
......@@ -40,6 +40,7 @@ dat <- read.csv('../../data/metadata/sites/sites_description.csv', check.names=F
# reorder so references column is last
i <- match("References", names(dat))
dat <- dat[,c(seq_len(ncol(dat))[-c(i)], i)]
dat <- dat[,c(2,1,3:ncol(dat))]
refs <- read.csv('../../data/metadata/sites/references.csv', check.names=FALSE,
stringsAsFactors=FALSE)
......@@ -56,13 +57,13 @@ replace_refs <- function(x){
dat$References <- sapply(dat$References, replace_refs)
paste_name_data <- function(df){
sprintf("## %s\n\n%s\n\n", df[["Data set name"]],
sprintf("## %s\n\n%s\n\n", df[["Country"]],
paste0(
llply(names(df)[-c(1)], function(x) sprintf("- %s: %s", x, df[[x]])), collapse="\n")
)
}
list.t <- dlply(dat, 1, paste_name_data)
writeLines(unlist(list.t[dat[["Data set name"]]]))
writeLines(unlist(list.t[dat[["Country"]]]))
```
# Supplementary discussion
......
......@@ -31,7 +31,14 @@ path.root <- git.root()
library(pander)
data.set <-read.csv(file.path(path.root, 'output', 'data.set.csv'), stringsAsFactors = FALSE)
dat.2 <- data.set[, -(2)]
dat.2[dat.2$set == 'NVS',1] <- 'NZ'
dat.2[dat.2$set == 'NVS',1] <- 'New Zealand'
dat.2[dat.2$set == 'NSW',1] <- 'Australia'
dat.2[dat.2$set == 'Swiss',1] <- 'Switzerland'
dat.2[dat.2$set == 'BCI',1] <- 'Panama'
dat.2[dat.2$set == 'Fushan',1] <- 'Taiwan'
dat.2[dat.2$set == 'Luquillo',1] <- 'Puerto Rico'
dat.2[dat.2$set == 'Mbaiki',1] <- 'Central African Republic'
var.names <- colnames(dat.2)
var.names[2] <- '# of trees'
var.names[3] <- '# of species'
......@@ -48,7 +55,7 @@ dat.2 <- as.data.frame(dat.2)
rownames(dat.2) <- NULL
dat.2 <- dat.2[, 1:11]
pandoc.table(dat.2[, 1:6], caption = "Data description, with number of individual tree, species and plot in NFI data and quadrat in LPP data, and percentage of angiosperm and evergreen species.",
digits = 2, split.tables = 200, split.cells = 15)
digits = 3, split.tables = 200, split.cells = 15)
pandoc.table(dat.2[, c(1,9:11)], caption = "Traits coverage in each sites. Percentage of species with species level trait data.",
digits = 2, split.tables = 200, split.cells = 15)
......
......@@ -33,7 +33,14 @@ path.root <- git.root()
library(pander)
data.set <-read.csv(file.path(path.root, 'output', 'data.set.csv'), stringsAsFactors = FALSE)
dat.2 <- data.set[, -(2)]
dat.2[dat.2$set == 'NVS',1] <- 'NZ'
dat.2[dat.2$set == 'NVS',1] <- 'New Zealand'
dat.2[dat.2$set == 'NSW',1] <- 'Australia'
dat.2[dat.2$set == 'Swiss',1] <- 'Switzerland'
dat.2[dat.2$set == 'BCI',1] <- 'Panama'
dat.2[dat.2$set == 'Fushan',1] <- 'Taiwan'
dat.2[dat.2$set == 'Luquillo',1] <- 'Puerto Rico'
dat.2[dat.2$set == 'Mbaiki',1] <- 'Central African Republic'
var.names <- colnames(dat.2)
var.names[2] <- '# of trees'
var.names[3] <- '# of species'
......@@ -50,7 +57,7 @@ dat.2 <- as.data.frame(dat.2)
rownames(dat.2) <- NULL
dat.2 <- dat.2[, 1:11]
pandoc.table(dat.2[, 1:6], caption = "Data description, with number of individual tree, species and plot in NFI data and quadrat in LPP data, and percentage of angiosperm and evergreen species.",
digits = 2, split.tables = 200, split.cells = 15)
digits = 3, split.tables = 200, split.cells = 15)
pandoc.table(dat.2[, c(1,9:11)], caption = "Traits coverage in each sites. Percentage of species with species level trait data.",
digits = 2, split.tables = 200, split.cells = 15)
```
......@@ -91,7 +98,7 @@ row.names(mat.param) <- c('$\\gamma$', '$m_1$', '$alpha_0$',
```
``` {r Table2_Effectsize, echo = FALSE, results='asis', message=FALSE}
pandoc.table(mat.param, caption = "Standaridized parameters estimates and standard error (in bracket) presentedestimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters")
pandoc.table(mat.param, caption = "Standaridized parameters estimates and standard error (in bracket) estimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters")
```
\* We report the conditional $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133142 (2013).
......@@ -16,74 +16,76 @@
----------------------------------------------------------------------------------------
set # of trees # of species # of % of angiosperm % of evergreen
plots/quadrats
-------- ------------ -------------- ---------------- ----------------- ----------------
Sweden 2e+05 26 22552 0.27 0.73
-----------------------------------------------------------------------------------------------
set # of trees # of species # of % of angiosperm % of evergreen
plots/quadrats
--------------- ------------ -------------- ---------------- ----------------- ----------------
Sweden 202469 26 22552 0.27 0.729
NZ 53775 117 1415 0.94 0.99
New Zealand 53775 117 1415 0.94 0.991
US 1369815 493 59840 0.63 0.37
US 1369815 493 59840 0.633 0.372
Canada 5e+05 75 14983 0.34 0.65
Canada 495008 75 14983 0.344 0.649
NSW 906 101 63 1 0.92
Australia 906 101 63 0.999 0.924
France 184316 127 17611 0.74 0.28
France 184316 127 17611 0.741 0.285
Swiss 28207 65 2597 0.36 0.56
Switzerland 28207 65 2597 0.361 0.555
Spain 418805 122 36462 0.35 0.82
Spain 418805 122 36462 0.347 0.816
BCI 26994 238 2033 1 0.78
Panama 26994 238 2033 0.998 0.777
Paracou 46382 714 2157 1 0.83
Paracou 46382 714 2157 1 0.835
Japan 4637 138 318 0.72 0.71
Japan 4637 138 318 0.722 0.708
Fushan 14701 72 623 0.92 0.75
Taiwan 14701 72 623 0.92 0.753
Luquillo 14011 82 399 1 0.99
Puerto Rico 14011 82 399 1 0.99
Mbaiki 17602 203 989 0.99 0.72
----------------------------------------------------------------------------------------
Central African 17602 203 989 0.995 0.725
Republic
-----------------------------------------------------------------------------------------------
Table: Data description, with number of individual tree, species and plot in NFI data and quadrat in LPP data, and percentage of angiosperm and evergreen species.
---------------------------------------------------
set % cover SLA % cover Wood % cover Max
density height
-------- ------------- -------------- -------------
Sweden 1 1 0.98
----------------------------------------------------------
set % cover SLA % cover Wood % cover Max
density height
--------------- ------------- -------------- -------------
Sweden 1 1 0.98
NZ 1 1 1
New Zealand 1 1 1
US 0.91 0.94 1
US 0.91 0.94 1
Canada 0.99 0.99 1
Canada 0.99 0.99 1
NSW 0 0.99 1
Australia 0 0.99 1
France 0.99 0.99 1
France 0.99 0.99 1
Swiss 0.97 0.95 1
Switzerland 0.97 0.95 1
Spain 0.97 0.99 1
Spain 0.97 0.99 1
BCI 0.93 0.93 0.95
Panama 0.93 0.93 0.95
Paracou 0.73 0.73 0.63
Paracou 0.73 0.73 0.63
Japan 1 1 1
Japan 1 1 1
Fushan 1 0.99 0.96
Taiwan 1 0.99 0.96
Luquillo 0.99 0.99 0.99
Puerto Rico 0.99 0.99 0.99
Mbaiki 0.4 0.47 0
---------------------------------------------------
Central African 0.4 0.47 0
Republic
----------------------------------------------------------
Table: Traits coverage in each sites. Percentage of species with species level trait data.
......@@ -113,6 +115,6 @@ Table: Traits coverage in each sites. Percentage of species with species level t
**$R^2$*** 0.7072 0.7514 0.7156
------------------------------------------------------------------
Table: Standaridized parameters estimates and standard error (in bracket) presentedestimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters
Table: Standaridized parameters estimates and standard error (in bracket) estimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters
\* We report the conditional $R^2$ of the models using the methods of 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).
% Extended Methods
# Model and analysis
We use a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its maximum growth rate (determined by its traits and size) and reductions due to competition with individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
\begin{equation} \label{G1}
G_{i,f,p,s} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}\right),
\end{equation}
where:
- $G_{i,f,p,s}$ and $D_{i,f,p,s}$ are the the annual basal area growth and diameter of individual $i$ from species $f$, plot $p$ and dataset $s$,
- $G_{\textrm{max} \, f,p,s}$ is the potential growth rate in basal area growth for species $f$ on plot $p$ in data set $s$, i.e. in absence of competition,
- $\gamma_f$ 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
- $B_{c,p,s}= 0.25\, \pi \, \sum_i w_i \, D_{i,c,p,s}^2$ 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
\begin{equation} \label{logG1}
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}.
\end{equation}
To include the effect of a focal trees' traits, $t_f$, on its growth, we let:
\begin{equation} \label{Gmax}
\log{G_{\textrm{max} \, f,p,s}} = m_{0} + m_1 \, t_f + \epsilon_{G_{\textrm{max}}, f} + \epsilon_{G_{\textrm{max}}, p} + \epsilon_{G_{\textrm{max}}, s}.
\end{equation}
Here $m_0$ is the average maximum growth, $m_1$ gives the effect of the focal trees trait, and $\epsilon_{G_{\textrm{max}}, f}$, $\epsilon_{G_{\textrm{max}}, p}$, $\epsilon_{G_{\textrm{max}}, s}$ are normally distributed random effect for species $f$, plot or quadrat $p$ (see below), and data set $s$.
To include traits effects on competition presented in Fig. 1, competitive interactions were modelled using an equation of the form (for fitting the model this equation was simplified as community weighted mean of the different trait dimension, see Supplementary methods for more details) :
\begin{equation} \label{alpha}
\alpha_{c,f}= \alpha_{0,f} + \alpha_r \, t_f + \alpha_i \, t_c + \alpha_s \, \vert t_c-t_f \vert
\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 $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{\alpha_0, s}$),
- $\alpha_r$ 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 $s$ ($\epsilon_{\alpha_s,s}$).
Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of growth, given by
\begin{equation} \label{logGobs} G_{i,f,p,s} = 0.25 \pi \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right).
\end{equation}
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 $\alpha_s$). -->
# Data
## Growth data
Our main objective was collate data sets spanning the dominant forest biomes of
the world. Datasets were included if they (i) allowed both growth rate of individual trees and the local abundance of competitors to be estimated, and (ii) had good (>50%) coverage for at least one
of the traits of interest (SLA, wood density, and maximum height).
The datasets collated fell into two broad categories: (1) national forest inventories (NFI), in which trees above a given diameter are sampled in a network of small plots (often on a regular grid) covering the country; (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. These LPP were mostly located in tropical regions. The minimum diameter of recorded trees varied among sites from 1-12cm. To allow comparison between data sets, we restricted our analysis to trees greater than 10cm. Moreover, we excluded from the analysis any plots with harvesting during the growth measurement period, that was identified as a plantation, or overlapping a forest edge. Finally, we selected only two consecutive census for each tree to avoid to have to account for repeated measurements, as only less than a third of teh data had repeated measurements. See the Supplementary methods and Extended data Table 1 for more details on the individual datasets.
Basal area growth was estimated from diameter measurements recorded across successive time points. For the French NFI, these data were obtained from short tree cores. For all other datasest, diameter at breast height ($D$) of each individual was recorded at multiple censuses. We excluded trees with extreme positive or negative diameter growth rates, following criteria developed at the BCI site [@condit_mortality_1993] and implemented in the R package [CTFS R](http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/).
For each individual tree, we estimated the local abundance of competitor species as the sum of basal area for all individuals > 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[@uriarte_neighborhood_2004; @lamanna_functional_2014]. To avoid edge effects, we also excluded trees less than 15m from the edge of a plot. To account for variation of the abiotic conditions within the LPPs we divided the plot in 20x20m quadrats.
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).
## Traits
Data on species functional traits was 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 [@wright_functional_2010; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] (see Extended data Table 2 for traits coverage). Where available we used data collected locally; otherwise we sourced data from the [TRY](http://www.try-db.org/) trait data base [@kattge_try_2011]. Local data were available for most tropical sites and species (see Table M1). Several of the NFI datasets also provided height measurements, from which we computed a species' maximum height as the 99% quantile of observed values (France, US, Spain, Switzerland; for Sweden we used the estimate from the French data and for Canada we used the estimate from the US data). Otherwise, we extracted measurement from the TRY database.
For each focal tree, our approach requires 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 were 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 were the percentage of basal area of trees with (i) no species level trait data was less than 10%, and (ii) no genus level data was less than 5%.
\newpage
# References
......@@ -33,11 +33,11 @@
showgrid="false"
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inkscape:cy="459.68881"
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......@@ -1574,10 +1574,10 @@
y="-565.29169"
style="font-size:10.3749733px"><tspan
style="font-size:8.64581108px;font-variant:normal;font-weight:normal;writing-mode:lr-tb;fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;-inkscape-font-specification:Helvetica"
x="207.91449 214.15677 219.92352"
y="-565.29169"
sodipodi:role="line"
id="tspan4122">NSW</tspan></text>
id="tspan4122"
x="207.91449"
y="-565.29169">Australia</tspan></text>
<text
transform="scale(1.0398674,-0.96166108)"
id="text4124"
......
......@@ -5,7 +5,7 @@ Competition is a very important type of ecological interaction in terrestrial ve
# Main text
<!-- **(MAX 1500 words till the end of Methods = 1403)** -->
<!-- **(MAX 1500 words till the end of Methods = 1403?)** -->
Competition is a ubiquitous type of interaction in ecological communities. Each individual modifies their immediate environment and thus influences the performance of neighbouring individuals either negatively - competition - or positively - facilitation [@keddy_competition_2001]. These interactions influence species composition and its dynamics over time. Competition is especially important for vegetation on land because most vegetation types have enough foliage cover for shading and both water and nutrient depletion to be conspicuous. There have been many studies on competition among plants [@goldberg_patterns_1992], which traditionally have described competition as interactions between pairs of species. The problem with this approach is that this quickly become intractable as the number of different interactions rises as $N^2$ with the number of species $N$. Also this species-pair approach does not lead naturally to generalization across different vegetation types and different continents because of differences in species composition. Modeling competition as of phenotypic traits rather than of species may allow to overcome this limitation and enable the detection of general relationships at biome to global scale. There is however still too few studies[@uriarte_trait_2010; @kunstler_competitive_2012; @hillerislambers_rethinking_2012; @lasky_trait-mediated_2014; @kraft_plant_2015] to have firm generalizations about the traits effect and the main mechanisms by which traits influences competition.
Here we quantify competition between trees as the influence of neighbours on growth of a focal tree with a framework novel and important in two ways: (i) competition is analysed as a function of traits rather than of species at an unprecedented scale covering all the major biomes on Earth (Fig. \ref{ilustr}a) and (ii) the influence of traits on competition is partitioned among four fundamental processes affecting competition and coexistence (Fig. \ref{ilustr}) as follows. A competitive advantage for some trait values compared to others can arise because (1) trait values are directly correlated with faster maximum growth in absence of competition[@wright_functional_2010], (2) they are correlated with better competitive response[@goldberg_competitive_1996], leading to a higher tolerance to competition (*i.e.* growth being less affected by competition), or (3) they are correlated with higher competitive impact[@gaudet_comparative_1988] (*i.e.* strongly reduce the growth of their neighbours). Finally (4) a higher trait similarity between the competitors and the focal tree can leads to higher competitive interaction[@macarthur_limiting_1967], a process promoting traits diversity at local scale. These four processes are likely to be connected to the key traits used to describe plant strategies[@uriarte_trait_2010; @kunstler_competitive_2012; @hillerislambers_rethinking_2012; @lasky_trait-mediated_2014; @kraft_plant_2015], and here we dissect how three of these traits[@westoby_plant_2002; @chave_towards_2009], wood density, specific leaf area (SLA), and maximum height affect competition between neighbouring trees[@uriarte_neighborhood_2004]. We compiled data for radial growth and for local density of competitors for more than 3 million trees representing more than 2500 species covering all the major biomes on Earth (Fig. \ref{res2}b). We analysed how the maximum growth of each individual tree was reduced by the local density of its competitors, accounting for traits of both the focal tree and its competitors. This analysis allowed to estimate the effects for each of the processes presented in Fig. \ref{ilustr}, but also the effect of tree size on maximum growth and the trait independent competition (*i.e.* the effect of the local density of competitors independent of their traits).
......
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