diff --git a/R/analysis/lmer.output-fun.R b/R/analysis/lmer.output-fun.R
index 83a7552dcd0441fe2198807eac6935682ab78404..b774826f2784c19010ff0fba46f09f4f165ef5c5 100644
--- a/R/analysis/lmer.output-fun.R
+++ b/R/analysis/lmer.output-fun.R
@@ -305,6 +305,8 @@ fun.generate.pred.param.kikj.dat <-  function(list.sd, Tf.low,
     mean.sumBn <- 1#max(seq.sumBn)
     print(mean.sumBn)
     seq.Tf <-  seq(from = Tf.low, to = Tf.high, length.out = N.pred)
+
+    
     if(!intra.TF){
     df <- data.frame('logG' =  rep(0 , N.pred),
                   'logD' = rep(D.mean, N.pred),
@@ -341,6 +343,7 @@ fun.generate.pred.param.rho.dat <-  function(list.sd, Tf.low,
                                              intra.TF = FALSE){
     Tf.mean <- 0
     D.mean <-  0
+    print(list.sd)
     sd_sumBn.intra <- list.sd$sd.sumBn.intra
     sd_sumBn.inter <- list.sd$sd.sumBn.inter
     sd_sumBn <- list.sd$sd.sumBn
@@ -354,22 +357,22 @@ fun.generate.pred.param.rho.dat <-  function(list.sd, Tf.low,
     df <- data.frame('logG' =  rep(0 , N.pred),
                   'logD' = rep(D.mean, N.pred),
                   'Tf' =seq.Tf,
-                  'sumBn' = rep(mean.sumBn, N.pred)/sd_sumBn,
-                  'sumTfBn' = seq.Tf*mean.sumBn/sd_sumTfBn,
-                  'sumTnBn' = seq.Tf*mean.sumBn/sd_sumTnBn,
+                  'sumBn' = rep(mean.sumBn, N.pred),
+                  'sumTfBn' = (seq.Tf-Tf.low)*mean.sumBn,
+                  'sumTnBn' = rep(Tf.low, N.pred)*mean.sumBn,
                   'sumTnTfBn.abs' = abs(seq.Tf-Tf.low)*
-                                    mean.sumBn/sd_sumTnTfBn.abs)
+                                    mean.sumBn)
     }
     if(intra.TF){
     df <- data.frame('logG' =  rep(0 , N.pred),
                   'logD' = rep(D.mean, N.pred),
                   'Tf' =seq.Tf,
-                  'sumBn.intra' = -rep(mean.sumBn, N.pred)/sd_sumBn.intra,
-                  'sumBn.inter' = rep(mean.sumBn, N.pred)/sd_sumBn.inter,
-                  'sumTfBn' = seq.Tf*mean.sumBn/sd_sumTfBn,
-                  'sumTnBn' = seq.Tf*mean.sumBn/sd_sumTnBn,
+                  'sumBn.intra' = -rep(mean.sumBn, N.pred),
+                  'sumBn.inter' = rep(mean.sumBn, N.pred),
+                  'sumTfBn' = (seq.Tf-Tf.low)*mean.sumBn,
+                  'sumTnBn' = rep(Tf.low, N.pred)*mean.sumBn,
                   'sumTnTfBn.abs' = abs(seq.Tf-Tf.low)*
-                                    mean.sumBn/sd_sumTnTfBn.abs)
+                                    mean.sumBn)
     }
     if(MAT.MAP.TF){
     df$MAT <- rep(1,nrow(df))
@@ -525,6 +528,9 @@ easyPredCI.param <- function(list.res, type, newdata, alpha=0.05,alpha_0 = 'sumB
                        alphal = c(alpha_0, "sumTnTfBn.abs"),
                        alpha0 = alpha_0)
     X[, !colnames(X) %in% sel.keep] <-  0
+    if (type == 'alpha0'){
+    X[, colnames(X) == alpha_0] <-  1
+    }    
     pred <- X %*% beta
     pred.se <- sqrt(diag(X %*% V %*% t(X))) ## std errors of predictions
     ## inverse-link (logistic) function: could also use plogis()
@@ -563,10 +569,12 @@ easyPredCI.stabl <- function(list.res, type, newdata, alpha=0.05) {
                    newdata)
     sel.keep <- switch(type ,
                        kikj = c('Tf', 'sumTfBn'),
-                       GiGj.intra = c('Tf', 'sumTfBn', 'sumBn.intra','sumBn.inter','sumTnTfBn.abs'),
+                       GiGj.intra = c('Tf', 'sumTfBn', 'sumBn.intra',
+                           'sumBn.inter','sumTnTfBn.abs'),
                        GiGj = c('Tf', 'sumTfBn', 'sumTnTfBn.abs'),
                        rho = c('sumBn','sumTnTfBn.abs'),
-                       rho.intra = c('sumBn.intra','sumBn.inter','sumTnTfBn.abs'))
+                       rho.intra = c('sumBn.intra','sumBn.inter',
+                           'sumTnTfBn.abs'))
     X[, !colnames(X) %in% sel.keep] <-  0
     pred <- X %*% beta
     pred.se <- sqrt(diag(X %*% V %*% t(X))) ## std errors of predictions
@@ -694,9 +702,9 @@ pred.res.rho$Tf <-  seq(from = list.var[[1]][['ql.o']],
                        to = list.var[[1]][['qh.o']],
                        length.out = 100) - list.var[[1]][['ql.o']]
 pred.res.rho$param.type <- 'rho'
-pred.res.rho$pred <- 1- exp(-pred.res.rho$pred)
-pred.res.rho$lwr <- 1 - exp(-pred.res.rho$lwr)
-pred.res.rho$upr <- 1 - exp(-pred.res.rho$upr)
+pred.res.rho$pred <- (-pred.res.rho$pred)
+pred.res.rho$lwr <- (-pred.res.rho$lwr)
+pred.res.rho$upr <- (-pred.res.rho$upr)
 
 new.data.GiGj <- fun.generate.pred.param.kikj.dat( list.sd = list.res$list.sd,
                                   Tf.low = list.var[[1]][['ql']],
@@ -710,9 +718,9 @@ pred.res.GiGj$Tf <-  seq(from = list.var[[1]][['ql.o']],
                        to = list.var[[1]][['qh.o']],
                        length.out = 100) - list.var[[1]][['ql.o']]
 pred.res.GiGj$param.type <- 'GiGj'
-pred.res.GiGj$pred <- exp(pred.res.GiGj$pred)
-pred.res.GiGj$lwr <- exp(pred.res.GiGj$lwr)
-pred.res.GiGj$upr <- exp(pred.res.GiGj$upr)
+pred.res.GiGj$pred <- (pred.res.GiGj$pred)
+pred.res.GiGj$lwr <- (pred.res.GiGj$lwr)
+pred.res.GiGj$upr <- (pred.res.GiGj$upr)
 
 }
 
@@ -728,9 +736,9 @@ pred.res.rho$Tf <-  seq(from = list.var[[1]][['ql.o']],
                        to = list.var[[1]][['qh.o']],
                        length.out = 100) - list.var[[1]][['ql.o']]
 pred.res.rho$param.type <- 'rho'
-pred.res.rho$pred <- 1 - exp(-pred.res.rho$pred)
-pred.res.rho$lwr <- 1 - exp(-pred.res.rho$lwr)
-pred.res.rho$upr <- 1 - exp(-pred.res.rho$upr)
+pred.res.rho$pred <- (-pred.res.rho$pred)
+pred.res.rho$lwr <- (-pred.res.rho$lwr)
+pred.res.rho$upr <- (-pred.res.rho$upr)
 
 
 new.data.GiGj <- fun.generate.pred.param.kikj.dat( list.sd = list.res$list.sd,
@@ -744,9 +752,9 @@ pred.res.GiGj$Tf <-  seq(from = list.var[[1]][['ql.o']],
                        to = list.var[[1]][['qh.o']],
                        length.out = 100) - list.var[[1]][['ql.o']]
 pred.res.GiGj$param.type <- 'GiGj'
-pred.res.GiGj$pred <- exp(pred.res.GiGj$pred)
-pred.res.GiGj$lwr <- exp(pred.res.GiGj$lwr)
-pred.res.GiGj$upr <- exp(pred.res.GiGj$upr)
+pred.res.GiGj$pred <- (pred.res.GiGj$pred)
+pred.res.GiGj$lwr <- (pred.res.GiGj$lwr)
+pred.res.GiGj$upr <- (pred.res.GiGj$upr)
 }
 
 new.data.kikj <- fun.generate.pred.param.kikj.dat( list.sd = list.res$list.sd,
@@ -761,9 +769,9 @@ pred.res.kikj$Tf <-  seq(from = list.var[[1]][['ql.o']],
                        to = list.var[[1]][['qh.o']],
                        length.out = 100) - list.var[[1]][['ql.o']]
 pred.res.kikj$param.type <- 'kikj'
-pred.res.kikj$pred <- exp(pred.res.kikj$pred)
-pred.res.kikj$lwr <- exp(pred.res.kikj$lwr)
-pred.res.kikj$upr <- exp(pred.res.kikj$upr)
+pred.res.kikj$pred <- (pred.res.kikj$pred)
+pred.res.kikj$lwr <- (pred.res.kikj$lwr)
+pred.res.kikj$upr <- (pred.res.kikj$upr)
 
 return(rbind(pred.res.rho, pred.res.kikj, pred.res.GiGj))
 }
@@ -1288,8 +1296,8 @@ fun.param.descrip <-  function(seq.jitter,  n.param, x.line = -0.73, intra.TF =
             y.at.2 <- 3
             y.at.2.la <- 2
             y.at.2.lb <- 4
-         }            
-        
+         }
+
         mtext("Trait independent", side=2,
               at = y.at.1,
               cex =1.6,
@@ -1371,6 +1379,8 @@ Var <- "Trait indep"
 intra <-  "intra"
 fun.layout()
 b <- border.size()
+traits_letters <- c('a', 'b', 'c')
+names(traits_letters) <- c('Wood.density', 'SLA', 'Max.height')
 ##################################
  ## model fixed biomes
  for (i in traits){
@@ -1533,8 +1543,8 @@ fun.plot.all.param <-  function(list.res,
                                 intra.TF = FALSE,
                                 ylim.list = list(maxG = c(-0.75, 0.75), alphae = c(-0.02, 0.009),
                                     alphar = c(-0.013, 0.013), alphal = c(-0.017, 0.007),
-                                    alpha0 = c(0.003, 0.016), alpha0.intra =  c(0.003, 0.028),
-                                    alpha0.inter = c(0.003, 0.028))
+                                    alpha0 = c(0.003, 0.016), alpha0.intra =  c(0.025, 0.32),
+                                    alpha0.inter = c(0.025, 0.32))
                                   ){
 traits <- c('Wood.density', 'SLA', 'Max.height')
 
@@ -1587,6 +1597,13 @@ names.param <- c("Tf","sumTnBn",
 names(names.param) <- c('maxG', 'alphae', 'alphar', 'alphal', 'alpha0.inter', 'alpha0.intra')
 first.p <- 'alpha0.intra'
 }
+
+traits_letters <- matrix(letters[1:(3*(length(names(expr.p.vec))-1))],
+                         nrow = length(names(expr.p.vec)) - 1, ncol = 3)
+traits_letters <- rbind(traits_letters[1,], traits_letters)
+colnames(traits_letters) <- c('Wood density', 'Specific leaf area', 'Maximum height')
+rownames(traits_letters) <- names(expr.p.vec)
+
  for (t in c('Wood density', 'Specific leaf area', 'Maximum height')){
  for (p in names(expr.p.vec)){
 df.t <- data.param[data.param$traits == t, ]
@@ -1595,7 +1612,8 @@ par(mai = fun.mai.plot.param(t, p, big.m, small.m, first.p = first.p, last.p = '
 if(t == 'Wood density'){
 if(p == 'maxG'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = traits.exp[[t]],
                   labels.x = TRUE, labels.y = TRUE,
                   col.vec = col.vec,
@@ -1604,14 +1622,16 @@ if(p == 'maxG'){
  }else{
      if(p == 'alpha0.inter'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = NA,
                   labels.x = FALSE, labels.y = FALSE,
                   col.vec = col.vec,
                   expr.param = NA, cex.lab = 1.1, cex.axis =0.85, cex = 1, add = TRUE,  add.ylab.TF = FALSE)
       }else{
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = NA,
                   labels.x = FALSE, labels.y = TRUE,
                   col.vec = col.vec,
@@ -1624,7 +1644,8 @@ if(p == 'maxG'){
  if(t %in% c('Specific leaf area', 'Maximum height')){
   if(p == 'maxG'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = traits.exp[[t]],
                   labels.x = TRUE, labels.y = FALSE,
                   col.vec = col.vec,
@@ -1634,7 +1655,8 @@ if(p == 'maxG'){
    }else{
      if(p == 'alpha0.inter'){
      fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = NA,
                   labels.x = FALSE, labels.y = FALSE,
                   col.vec = col.vec,
@@ -1642,7 +1664,8 @@ if(p == 'maxG'){
                   cex = 1, add =TRUE)
      }else{
      fun.plot.param.tf(df = df.t,
-                  p = p,names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   xlab = NA,
                   labels.x = FALSE, labels.y = FALSE,
                   col.vec = col.vec,
@@ -1725,6 +1748,10 @@ names.param <- c("Tf","sumTnBn",
 names(names.param) <- c('maxG', 'alphae', 'alphar', 'alphal', 'alpha0.inter', 'alpha0.intra')
 first.p <- 'maxG'
 }
+
+traits_letters <- matrix(letters[1:6], nrow = 3, ncol = 2)
+colnames(traits_letters) <- c('Wood density', 'Specific leaf area')
+rownames(traits_letters) <- c('maxG', 'alphar', 'alphae')
  for (t in c('Wood density', 'Specific leaf area')){
  for (p in c( 'maxG', 'alphar', 'alphae')){
 df.t <- data.param[data.param$traits == t, ]
@@ -1733,7 +1760,8 @@ par(mai = fun.mai.plot.param(t, p, big.m, small.m, first.p = first.p, last.p = '
 if(t == 'Wood density'){
 if(p == 'alphae'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,
                   xlab = traits.exp[[t]],
                   labels.x = TRUE, labels.y = TRUE,
                   col.vec = col.vec,
@@ -1741,7 +1769,8 @@ if(p == 'alphae'){
                   cex.axis =0.85, cex = 1, ylim = ylim.list[[p]])
  }else{
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,
                   xlab = NA,
                   labels.x = FALSE, labels.y = TRUE,
                   col.vec = col.vec,
@@ -1750,10 +1779,11 @@ if(p == 'alphae'){
   }
  }
 
- if(t %in% c('Specific leaf area', 'Maximum height')){
+ if(t %in% c('Specific leaf area')){
   if(p == 'alphae'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,
                   xlab = traits.exp[[t]],
                   labels.x = TRUE, labels.y = FALSE,
                   col.vec = col.vec,
@@ -1762,7 +1792,8 @@ if(p == 'alphae'){
                   ylim = ylim.list[[p]])
    }else{
      fun.plot.param.tf(df = df.t,
-                  p = p,names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,
                   xlab = NA,
                   labels.x = FALSE, labels.y = FALSE,
                   col.vec = col.vec,
@@ -1789,8 +1820,8 @@ add.alpha <- function(col, alpha=0.5){
                        rgb(x[1], x[2], x[3], alpha=alpha))
 }
 
-fun.plot.param.tf <-  function(df, p, xlab, labels.x, labels.y,
-                               col.vec, expr.param,names.param,
+fun.plot.param.tf <-  function(df, p, t, xlab, labels.x, labels.y,
+                               col.vec, expr.param,names.param, traits_letters,
                                add.ylab.TF = TRUE,
                                cex.lab = 1.3, cex.axis = 1,
                                cex = 1.3, add = FALSE, ...){
@@ -1802,6 +1833,9 @@ if(!add){
          xlab = xlab, ylab = NA,
          lwd = 3, cex.lab = cex.lab, cex.axis = cex.axis,
          col =  col.vec[names.param[p]], type = 'l',...)
+    y.max <-  par("usr")[4] - (par("usr")[4] - par("usr")[3])*0.05
+    x.min <- par("usr")[1] + (par("usr")[2] - par("usr")[1])*0.05
+    text(x.min, y.max , traits_letters[p, t], cex = 1.5, font = 2)
     axis(1, labels = labels.x)
     axis(2, labels = labels.y)
     polygon(c(df.t[, 'Tf'],
@@ -2106,7 +2140,7 @@ require(dplyr)
 layout(m, heights=hei, widths= wid )
 
 
- expr.p.vec <- c(expression(1-rho),
+ expr.p.vec <- c(expression(inter~italic(vs.)~intra),
                  expression(kappa[i]/kappa[j]),
                  expression(G[i]/G[j]))
 names(expr.p.vec) <- c('rho', 'kikj', 'GiGj')
@@ -2114,6 +2148,13 @@ names.param <- c("rho","kikj", 'GiGj')
 names(names.param) <- c('rho', 'kikj', 'GiGj')
 col.vec <- c('#018571', '#a6611a', '#dfc27d')
 names(col.vec) <-  c("rho","kikj", 'GiGj')
+
+traits_letters <- matrix(letters[1:3],
+                         nrow = 1, ncol = 3)
+colnames(traits_letters) <- c('Wood density', 'Specific leaf area', 'Maximum height')
+rownames(traits_letters) <- 'rho'
+
+ 
 for (t in c('Wood density', 'Specific leaf area', 'Maximum height')){
  for (p in c('rho')){
 df.t <- data.param[data.param$traits == t, ]
@@ -2135,7 +2176,8 @@ if(t == 'Maximum height'){
 
 if(t == 'Wood density'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   ylim = range(filter(df.t,
                                param.type == p)%>% select(upr,lwr)),
                   labels.x = TRUE, labels.y = TRUE,
@@ -2146,7 +2188,8 @@ if(t == 'Wood density'){
 
 if(t == 'Specific leaf area'){
     fun.plot.param.tf(df = df.t,
-                  p= p, names.param = names.param,
+                  p= p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   ylim = range(filter(df.t,
                                param.type == p)%>% select(upr,lwr)),
                   xlab = expression(paste(Delta, ' Specific leaf area (m', m^2, ' m', g^-1, ')')),
@@ -2157,7 +2200,8 @@ if(t == 'Specific leaf area'){
 
 if(t == 'Maximum height'){
     fun.plot.param.tf(df = df.t,
-                  p = p, names.param = names.param,
+                  p = p, t = t, names.param = names.param,
+                  traits_letters = traits_letters,    
                   ylim = range(filter(df.t,
                                param.type == p)%>% select(upr,lwr)),
                   labels.x = TRUE, labels.y = TRUE,
diff --git a/R/utils/maps.R b/R/utils/maps.R
index 98c9c45783ce41b236d4697cc6bfe9ff36cd2a06..9cf8b9c2d73dd199e01c5ac474e2cc4f84c8d688 100644
--- a/R/utils/maps.R
+++ b/R/utils/maps.R
@@ -19,15 +19,16 @@ world.map.all.sites <- function(data,add.legend=FALSE,
                                 cols =  fun.col.pch.set()$col.vec){
 
 sets <- unique(data$set)
-
+type.d <- c(rep('nfi', 8), rep('lpp', 6))
+names(type.d) <- sets
 # new map
 world.map(NA, NA)
 
 for(set in sets){
 	i <- data$set ==set
-	cex = 0.4
-	if(sum(i) <100)
-		cex=1.5
+	cex = 0.3
+	if(type.d[set] == 'lpp')
+		cex=1.1
     world.map(data[i, "Lon"], data[i, "Lat"], col = cols[[set]],
               add=TRUE, cex=cex)
   }
diff --git a/data/metadata/sites/sites_description.csv b/data/metadata/sites/sites_description.csv
index 8f6edea07e00244ea186f6eb0ef0669285b83bd4..5ca1a704e85c0f787fcc167fc2ac7bc1d4dca2fc 100644
--- a/data/metadata/sites/sites_description.csv
+++ b/data/metadata/sites/sites_description.csv
@@ -1 +1 @@
-Data set name,Country,Data type,Plot size,Diameter at breast height threshold,Number of plots,Traits,Source trait data,Evidence of disturbances and succession dynamics,References,Contact of person in charge of data formatting,Comments
Panama,Panama,LPP,1 to 50 ha,1 cm,42,"Wood density, SLA, and Maximum height",local,Gap disturbances are common in the large 50ha BCI plot [see @Young-1991; @Hubbell-1999; @Lobo-2014]. Hubbell et al.[@Hubbell-1999] estimated that less than 30% of the plot experienced no disturbance over a 13-year period.,"3,4,25","Plot data: R. Condit (conditr@gmail.com),  Trait data: J. Wright (wrightj@si.edu)",The data used include both the 50 ha plot of BCI and the network of 1 ha plots from Condit et al. (2013). The two first censuses of BCI plot were excluded.
Japan,Japan,LPP,0.35 to 1.05 ha,2.39 cm,16,"Wood density, SLA, and Maximum height",local,"The network of plot comprise 50% of old growth forest, 17% of old secondary forest and 33% of young secondary forest.",5,"Plot data: M. I. Ishihara (moni1000f_networkcenter@fsc.hokudai.ac.jp),  Trait data: Y Onoda (yusuke.onoda@gmail.com)",
Luquillo,Puerto Rico,LPP,16 ha,1 cm,1,"Wood density, SLA, and Maximum height",local,"The plot has been struck by hurricanes in 1989 and in 1998[@Uriarte-2009]. In addition, two-third of the plot is a secondary forest on land previously used for agriculture and logging[@Uriarte-2009].","6, 23","Plot data: J. Thompson (jiom@ceh.ac.uk) and J. Zimmerman (esskz@ites.upr.edu),  Trait data: N. Swenson (swensonn@msu.edu )",
M'Baiki,Central African Republic,LPP,4 ha,10 cm,10,Wood density and SLA,local,The plot network was established with three levels of harvesting and unharvested control [@Gourlet-Fleury-2013].,"7,8",G. Vieilledent (ghislain.vieilledent@cirad.fr),
Fushan,Taiwan,LPP,25 ha,1 cm,1,Wood density and SLA,local,"Fushan experienced several Typhoon disturbances in 1994 with tree fall events, the main effect was trees defoliation[@Lin-2011].",9,I-F. Sun (ifsun@mail.ndhu.edu.tw),
Paracou,French Guiana,LPP,6.25 ha,10 cm,15,Wood density and SLA,local,The plot network was established with three levels of harvesting and unharvested control (Herault et al. 2010).,"10,11,24","Plot data: B. Herault (bruno.herault@cirad.fr),  Trait data: C. Baraloto (Chris.Baraloto@ecofog.gf)",
France,France,NFI,0.017 to 0.07 ha,7.5 cm,41503,"Wood density, SLA, and Maximum height",TRY,"French forests monitored by the French National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).","12,13",G. Kunstler (georges.kunstler@gmail.com),"The French NFI is based on temporary plots, but 5 years tree radial growth is estimated with a short core. All trees with dbh > 7.5 cm, > 22.5 cm and > 37.5 cm were measured within a radius of 6 m, 9 m and 15 m, respectively. Plots are distributed over forest ecosystems on a 1x1-km grid"
Spain,Spain,NFI,0.0078 to 0.19 ha,7.5 cm,49855,"Wood density, SLA, and Maximum height",TRY,"Spanish forests monitored by the Spanish National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. No data are available on the age structure of the plots.","14,15,16",M. Zavala (madezavala@gmail.com),"Each SFI plot included four concentric circular sub-plots of 5, 10, 15 and 25-m radius. In these sub-plots, adult trees were sampled when diameter at breast height (d.b.h.) was 7.5-12.4 cm, 12.5-22.4 cm, 22.5-42.5 cm and >= 42.5 cm, respectively."
Swiss,Switzerland,NFI,0.02 to 0.05 ha,12 cm,2665,"Wood density, SLA, and Maximum height",TRY,"Swiss forests monitored by the Swiss National Forest Inventory experience several types of natural disturbances (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).","17,26",M. Hanewinkel & N. E. Zimmermann (niklaus.zimmermann@wsl.ch),"All trees with dbh > 12 cm and > 36 cm were measured within a radius of 7.98 m and 12.62 m, respectively."
Sweden,Sweden,NFI,0.0019 to 0.0314 ha,5 cm,22904,"Wood density, SLA, and Maximum height",TRY,"Swedish forests monitored by the Swedish National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).",18,G. Stahl (Goran.Stahl@slu.se),All trees with dbh > 10 cm were measured on circular plots of 10 m radius.
US,USA,NFI,0.0014 to 0.017 ha,2.54 cm,97434,"Wood density, SLA, and Maximum height",TRY,"US forests monitored by the FIA experience several types of natural disturbances (such as wind, forest fire, fungi and insects attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represents a significant percentage of the forested area (see age distribution below).",19,M. Vanderwel (Mark.Vanderwel@uregina.ca),FIA data are made up of clusters of 4 subplots of size 0.017 ha for tree dbh > 1.72 cm and nested within each subplot sampling plots of 0.0014 ha for trees dbh > 2.54 cm. The data for the four subplots were pooled
Canada,Canada,NFI,0.02 to 0.18 ha,2 cm,15019,"Wood density, SLA, and Maximum height",TRY,"Canadian forests monitored by the regional forest monitoring programs experience several types of natural disturbances (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represent a significant percentage of the forested area (see age distribution below).",,J. Caspersen (john.caspersen@utoronto.ca),The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plots are 10 m in radius in this Province.
NZ,New Zealand,NFI,0.04 ha,3 cm,1415,"Wood density, SLA, and Maximum height",local,"New Zealand forests are experiencing disturbance by earthquake, landslide, storm, volcanic eruptions other types. According to Holdaway et al.[@Holdaway-2014] having been disturbed during their measurement interval.","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, and Maximum height",local,The plot network was initially established in the 60s with different levels of selection harvesting[@Kariuki-2006].,"1,2",R. M. Kooyman (robert@ecodingo.com.au) for plot and trait data,Permanents plots established by the NSW Department of State Forests or by RMK
\ No newline at end of file
+Data set name,Country,Data type,Plot size,Diameter at breast height threshold,Number of plots,Traits,Source trait data,Evidence of disturbances and succession dynamics,References,Contact of person in charge of data formatting,Comments
Panama,Panama,LPP,1 to 50 ha,1 cm,42,"Wood density, SLA, and Maximum height",local,Gap disturbances are common in the large 50ha BCI plot [see @Young-1991; @Hubbell-1999; @Lobo-2014]. Hubbell et al.[@Hubbell-1999] estimated that less than 30% of the plot experienced no disturbance over a 13-year period.,"3,4,25","Plot data: R. Condit (conditr@gmail.com),  Trait data: J. Wright (wrightj@si.edu)",The data used include both the 50 ha plot of BCI and the network of 1 ha plots from Condit et al. (2013). The two first censuses of BCI plot were excluded.
Japan,Japan,LPP,0.35 to 1.05 ha,2.39 cm,16,"Wood density, SLA, and Maximum height",local,"The network of plot comprise 50% of old growth forests, 17% of old secondary forests and 33% of young secondary forests.",5,"Plot data: M. I. Ishihara (moni1000f_networkcenter@ fsc.hokudai.ac.jp),  Trait data: Y Onoda (yusuke.onoda@gmail.com)",
Luquillo,Puerto Rico,LPP,16 ha,1 cm,1,"Wood density, SLA, and Maximum height",local,"The plot has been struck by hurricanes in 1989 and in 1998[@Uriarte-2009]. In addition, two-third of the plot is a secondary forest on land previously used for agriculture and logging[@Uriarte-2009].","6, 23","Plot data: J. Thompson (jiom@ceh.ac.uk) and J. Zimmerman (esskz@ites.upr.edu),  Trait data: N. Swenson (swensonn@msu.edu )",
M'Baiki,Central African Republic,LPP,4 ha,10 cm,10,Wood density and SLA,local,The plot network was established with three levels of harvesting and an unharvested control [@Gourlet-Fleury-2013].,"7,8",G. Vieilledent (ghislain.vieilledent@cirad.fr),
Fushan,Taiwan,LPP,25 ha,1 cm,1,Wood density and SLA,local,Fushan experienced several Typhoon disturbances in 1994 with tree fall events. The main disturbance effect was trees defoliation[@Lin-2011].,9,I-F. Sun (ifsun@mail.ndhu.edu.tw),
Paracou,French Guiana,LPP,6.25 ha,10 cm,15,Wood density and SLA,local,The plot network was established with three levels of harvesting and unharvested control[@Herault-2011].,"10,11,24","Plot data: B. Herault (bruno.herault@cirad.fr),  Trait data: C. Baraloto (Chris.Baraloto@ecofog.gf)",
France,France,NFI,0.017 to 0.07 ha,7.5 cm,41503,"Wood density, SLA, and Maximum height",TRY,"French forests monitored by the French National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).","12,13",G. Kunstler (georges.kunstler@gmail.com),"The French NFI is based on temporary plots, but 5 years tree radial growth is estimated with a short core. All trees with dbh > 7.5 cm, > 22.5 cm and > 37.5 cm were measured within a radius of 6 m, 9 m and 15 m, respectively. Plots are distributed over forest ecosystems on a 1x1-km grid"
Spain,Spain,NFI,0.0078 to 0.19 ha,7.5 cm,49855,"Wood density, SLA, and Maximum height",TRY,"Spanish forests monitored by the Spanish National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. No data are available on the age structure of the plots.","14,15,16",M. Zavala (madezavala@gmail.com),"Each SFI plot included four concentric circular sub-plots of 5, 10, 15 and 25-m radius. In these sub-plots, adult trees were sampled when diameter at breast height (d.b.h.) was 7.5-12.4 cm, 12.5-22.4 cm, 22.5-42.5 cm and >= 42.5 cm, respectively."
Swiss,Switzerland,NFI,0.02 to 0.05 ha,12 cm,2665,"Wood density, SLA, and Maximum height",TRY,"Swiss forests monitored by the Swiss National Forest Inventory experienced several types of natural disturbance (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).","17,26",M. Hanewinkel & N. E. Zimmermann (niklaus.zimmermann@wsl.ch),"All trees with dbh > 12 cm and > 36 cm were measured within a radius of 7.98 m and 12.62 m, respectively."
Sweden,Sweden,NFI,0.0019 to 0.0314 ha,5 cm,22904,"Wood density, SLA, and Maximum height",TRY,"Swedish forests monitored by the Swedish National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).",18,G. Stahl (Goran.Stahl@slu.se),All trees with dbh > 10 cm were measured on circular plots of 10 m radius.
US,USA,NFI,0.0014 to 0.017 ha,2.54 cm,97434,"Wood density, SLA, and Maximum height",TRY,"US forests monitored by the FIA experienced several types of natural disturbance (such as wind, forest fire, fungi and insects attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represents a significant percentage of the forested area (see age distribution below).",19,M. Vanderwel (Mark.Vanderwel@uregina.ca),FIA data are made up of clusters of 4 subplots of size 0.017 ha for tree dbh > 1.72 cm and nested within each subplot sampling plots of 0.0014 ha for trees dbh > 2.54 cm. The data for the four subplots were pooled
Canada,Canada,NFI,0.02 to 0.18 ha,2 cm,15019,"Wood density, SLA, and Maximum height",TRY,"Canadian forests monitored by the regional forest monitoring programs experienced several types of natural disturbance (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represent a significant percentage of the forested area (see age distribution below).",,J. Caspersen (john.caspersen@utoronto.ca),"Provinces included are Manitoba,  New Brunswick, Newfoundland and Labrador, Nova Scotia, Ontario, Quebec and Saskatchewan. The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plots are 10 m in radius in this Province."
NZ,New Zealand,NFI,0.04 ha,3 cm,1415,"Wood density, SLA, and Maximum height",local,"New Zealand forests are experiencing disturbance by earthquake, landslide, storm, volcanic eruptions, and other types. According to Holdaway et al.[@Holdaway-2014] the disturbance return interval on the plots is 63 years.","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, and Maximum height",local,The plot network was initially established in the 1960s with different levels of selection harvesting[@Kariuki-2006].,"1,2",R. M. Kooyman (robert@ecodingo.com.au) for plot and trait data,Permanents plots established by the NSW Department of State Forests or by RMK
\ No newline at end of file
diff --git a/docs/paper/Makefile b/docs/paper/Makefile
index e949f77ddcab7933c7ba5f00b183a0d6f6f870fa..1fb116fbf9e991e8c34c49c3bb6061fce8c96543 100644
--- a/docs/paper/Makefile
+++ b/docs/paper/Makefile
@@ -24,11 +24,21 @@ extended_method.docx: extended_method.tex include.tex references.bib
 	pandoc -s -S $< --csl=nature.csl --filter pandoc-citeproc --bibliography=references.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o $@
 
 
-extended_data.pdf: extended_data.R include.tex references.bib
+extended_data.md: extended_data.R include.tex references.bib
 	Rscript  -e "library(sowsear); sowsear('extended_data.R', 'Rmd')"
 	Rscript  -e "library(knitr);  knit('extended_data.Rmd', output = 'extended_data.md')"
+
+extended_data.tex: extended_data.md include.tex references.bib
 	pandoc extended_data.md  --csl=nature.csl --filter pandoc-citeproc --bibliography=references.bib --standalone --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
 
+extended_data.pdf: extended_data.tex include.tex references.bib
+	xelatex $<
+	bibtex extended_data
+	xelatex extended_data.tex
+	xelatex extended_data.tex
+	rm extended_data.log extended_data.out extended_data.aux extended_data.bbl extended_data.blg
+
+
 SupplMat.pdf: Suppl_Mat.Rmd include.tex references.bib
 	Rscript  -e "library(knitr);  knit('Suppl_Mat.Rmd', output = 'SupplMat.md')"
 	pandoc SupplMat.md  --csl=nature.csl --filter pandoc-citeproc --bibliography=references.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
diff --git a/docs/paper/SupplMat.md b/docs/paper/SupplMat.md
index eedf04881b3ed1c91fd85d9b456a44a05a581e0f..44ee8d99f7dbbb9595050a865b266b74a976d437 100644
--- a/docs/paper/SupplMat.md
+++ b/docs/paper/SupplMat.md
@@ -1,47 +1,5 @@
 % Supplementary Information
 
-# Supplementary Methods
-We developed the equation of $\alpha_{c,f} = \alpha_{0,f,intra} \, CON + \alpha_{0,f,inter} \ (1-CON) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert$ along with the basal area of each competing species in the competition index to show the parameters are directly related to community weighted means of the different trait variables as:
-\begin{equation} \label{alphaBA}
-\sum_{c=1}^{N_i} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f,intra} \, B_{i,f} + \alpha_{0,f,inter} \, B_{i,het}- \alpha_t \, t_f \, B_{i,tot} + \alpha_e \, B_{i,t_c} + \alpha_d \, B_{i,\vert t_c - t_f \vert}
-\end{equation}
-
-Where:
-
-$B_{i,het} = \sum_{c \neq f} {B_{i,c}}$,
-
-$B_{i,t_c} = \sum_{c=1}^{N_i} {t_c \times B_{i,c}}$,
-
-$B_{i,\vert t_c - t_f \vert} = \sum_{c=1}^{N_i} {\vert t_c - t_f \vert \times B_{i,c}}$,
-
-and $N_i$ is the number of species in the local neighbourhood of the tree $i$. Note that the indices $p$ and $s$ respectively for plot and data set are not shown here for sake of simplicity.
-
-## Derivation of $\rho$ for a Lotka-Volterra model based on Godoy \& Levine[@Godoy-2014]
-
-Chesson[@Chesson-2012] proposed to estimate the stabilising niche difference based on the per capita growth rate of a rare invader into a population of a resident species. Godoy \& Levine[@Godoy-2014] used this method on an annual plant population model. This approach can be explained using the Lotka-Volterra model:
-
-\begin{equation}
-\frac{dN_i}{dt} =  N_i \times r_i \times (1 - \alpha'_{ii} N_i -
-\alpha'_{ij} N_j)
-\end{equation}
-
-The criterion for invasion of species $i$ into a resident community of species $j$ (at equilibrium population $\overline{N_j} = \frac{1}{\alpha'_{jj}}$) is:
-
-\begin{equation}
-(1 - \frac{\alpha_{ij}}{\alpha'_{jj}})
-\end{equation}
-
-Thus if $\frac{\alpha_{ij}}{\alpha'_{jj}} <1$ invasion of $i$ into $j$ is possible (and similar approach for $j$ into $i$).
-
-Stable coexistence between species $i$ and species $j$ thus requires
-$\frac{\alpha'_{ij}}{\alpha'_{jj}}$ and $\frac{\alpha'_{ji}}{\alpha'_{ii}}$ to be smaller than 1. Chesson[@Chesson-2012] then defined the average
-stabilising niche
-overlap between species $i$ and $j$ as:
-
-\begin{equation}
-\rho = \sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}}
-\end{equation}
-
 
 ## Details on data sets used
 
@@ -74,8 +32,8 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 16
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: The network of plot comprise 50% of old growth forest, 17% of old secondary forest and 33% of young secondary forest.
-- Contact of person in charge of data formatting: Plot data: M. I. Ishihara (moni1000f_networkcenter@fsc.hokudai.ac.jp),  Trait data: Y Onoda (yusuke.onoda@gmail.com)
+- Evidence of disturbances and succession dynamics: The network of plot comprise 50% of old growth forests, 17% of old secondary forests and 33% of young secondary forests.
+- Contact of person in charge of data formatting: Plot data: M. I. Ishihara (moni1000f_networkcenter@ fsc.hokudai.ac.jp),  Trait data: Y Onoda (yusuke.onoda@gmail.com)
 - Comments: 
 - References: 
 	- Yakushima Forest Environment Conservation Center, Ishihara, M.I., Suzuki, S.N., Nakamura, M., Enoki, T., Fujiwara, A., Hiura, T., Homma, K., Hoshino, D., Hoshizaki, K., Ida, H., Ishida, K., Itoh, A., Kaneko, T., Kubota, K., Kuraji, K., Kuramoto, S., Makita, A., Masaki, T., Namikawa, K., Niiyama, K., Noguchi, M., Nomiya, H., Ohkubo, T., Saito, S., Sakai, T., Sakimoto, M., Sakio, H., Shibano, H., Sugita, H., Suzuki, M., Takashima, A., Tanaka, N., Tashiro, N., Tokuchi, N., Yoshida, T., Yoshida, Y., (2011). Forest stand structure, composition, and dynamics in 34 sites over Japan. Ecological Research 26: 1007-1008. 
@@ -107,7 +65,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 10
 - Traits: Wood density and SLA
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: The plot network was established with three levels of harvesting and unharvested control [@Gourlet-Fleury-2013].
+- Evidence of disturbances and succession dynamics: The plot network was established with three levels of harvesting and an unharvested control [@Gourlet-Fleury-2013].
 - Contact of person in charge of data formatting: G. Vieilledent (ghislain.vieilledent@cirad.fr)
 - Comments: 
 - References: 
@@ -124,7 +82,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 1
 - Traits: Wood density and SLA
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: Fushan experienced several Typhoon disturbances in 1994 with tree fall events, the main effect was trees defoliation[@Lin-2011].
+- Evidence of disturbances and succession dynamics: Fushan experienced several Typhoon disturbances in 1994 with tree fall events. The main disturbance effect was trees defoliation[@Lin-2011].
 - Contact of person in charge of data formatting: I-F. Sun (ifsun@mail.ndhu.edu.tw)
 - Comments: 
 - References: 
@@ -140,7 +98,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 15
 - Traits: Wood density and SLA
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: The plot network was established with three levels of harvesting and unharvested control (Herault et al. 2010).
+- Evidence of disturbances and succession dynamics: The plot network was established with three levels of harvesting and unharvested control[@Herault-2011].
 - Contact of person in charge of data formatting: Plot data: B. Herault (bruno.herault@cirad.fr),  Trait data: C. Baraloto (Chris.Baraloto@ecofog.gf)
 - Comments: 
 - References: 
@@ -158,7 +116,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 41503
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: French forests monitored by the French National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
+- Evidence of disturbances and succession dynamics: French forests monitored by the French National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
 - Contact of person in charge of data formatting: G. Kunstler (georges.kunstler@gmail.com)
 - Comments: The French NFI is based on temporary plots, but 5 years tree radial growth is estimated with a short core. All trees with dbh > 7.5 cm, > 22.5 cm and > 37.5 cm were measured within a radius of 6 m, 9 m and 15 m, respectively. Plots are distributed over forest ecosystems on a 1x1-km grid
 - References: 
@@ -175,7 +133,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 49855
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: Spanish forests monitored by the Spanish National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. No data are available on the age structure of the plots.
+- Evidence of disturbances and succession dynamics: Spanish forests monitored by the Spanish National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. No data are available on the age structure of the plots.
 - Contact of person in charge of data formatting: M. Zavala (madezavala@gmail.com)
 - Comments: Each SFI plot included four concentric circular sub-plots of 5, 10, 15 and 25-m radius. In these sub-plots, adult trees were sampled when diameter at breast height (d.b.h.) was 7.5-12.4 cm, 12.5-22.4 cm, 22.5-42.5 cm and >= 42.5 cm, respectively.
 - References: 
@@ -193,7 +151,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 2665
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: Swiss forests monitored by the Swiss National Forest Inventory experience several types of natural disturbances (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
+- Evidence of disturbances and succession dynamics: Swiss forests monitored by the Swiss National Forest Inventory experienced several types of natural disturbance (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
 - Contact of person in charge of data formatting: M. Hanewinkel & N. E. Zimmermann (niklaus.zimmermann@wsl.ch)
 - Comments: All trees with dbh > 12 cm and > 36 cm were measured within a radius of 7.98 m and 12.62 m, respectively.
 - References: 
@@ -210,7 +168,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 22904
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: Swedish forests monitored by the Swedish National Forest Inventory experience several types of natural disturbances[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
+- Evidence of disturbances and succession dynamics: Swedish forests monitored by the Swedish National Forest Inventory experienced several types of natural disturbance[@Seidl-2014] (such as wind, forest fire, and insect attacks) and harvesting. The age structure reconstructed by Vilen et al.[@Vilen-2012] shows that young forests represent a significant percentage of the forested area (see age distribution below).
 - Contact of person in charge of data formatting: G. Stahl (Goran.Stahl@slu.se)
 - Comments: All trees with dbh > 10 cm were measured on circular plots of 10 m radius.
 - References: 
@@ -226,7 +184,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 97434
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: US forests monitored by the FIA experience several types of natural disturbances (such as wind, forest fire, fungi and insects attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represents a significant percentage of the forested area (see age distribution below).
+- Evidence of disturbances and succession dynamics: US forests monitored by the FIA experienced several types of natural disturbance (such as wind, forest fire, fungi and insects attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represents a significant percentage of the forested area (see age distribution below).
 - Contact of person in charge of data formatting: M. Vanderwel (Mark.Vanderwel@uregina.ca)
 - Comments: FIA data are made up of clusters of 4 subplots of size 0.017 ha for tree dbh > 1.72 cm and nested within each subplot sampling plots of 0.0014 ha for trees dbh > 2.54 cm. The data for the four subplots were pooled
 - References: 
@@ -242,9 +200,9 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 15019
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: TRY
-- Evidence of disturbances and succession dynamics: Canadian forests monitored by the regional forest monitoring programs experience several types of natural disturbances (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represent a significant percentage of the forested area (see age distribution below).
+- Evidence of disturbances and succession dynamics: Canadian forests monitored by the regional forest monitoring programs experienced several types of natural disturbance (such as wind, forest fire, fungi and insect attacks) and harvesting. The age structure reconstructed by Pan et al.[@Pan-2011] shows that young forests represent a significant percentage of the forested area (see age distribution below).
 - Contact of person in charge of data formatting: J. Caspersen (john.caspersen@utoronto.ca)
-- Comments: The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plots are 10 m in radius in this Province.
+- Comments: Provinces included are Manitoba,  New Brunswick, Newfoundland and Labrador, Nova Scotia, Ontario, Quebec and Saskatchewan. The protocol is variable between Provinces. A large proportion of data is from the Quebec province and the plots are 10 m in radius in this Province.
 - References: 
 
 
@@ -257,7 +215,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 1415
 - Traits: Wood density, SLA, and Maximum height
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: New Zealand forests are experiencing disturbance by earthquake, landslide, storm, volcanic eruptions other types. According to Holdaway et al.[@Holdaway-2014] having been disturbed during their measurement interval.
+- Evidence of disturbances and succession dynamics: New Zealand forests are experiencing disturbance by earthquake, landslide, storm, volcanic eruptions, and other types. According to Holdaway et al.[@Holdaway-2014] the disturbance return interval on the plots is 63 years.
 - Contact of person in charge of data formatting: D. Laughlin (d.laughlin@waikato.ac.nz)
 - Comments: Plots are 20 x 20 m.
 - References: 
@@ -274,7 +232,7 @@ Two main data types were used: national forest inventories -- NFI, large permane
 - Number of plots: 30
 - Traits: Wood density, and Maximum height
 - Source trait data: local
-- Evidence of disturbances and succession dynamics: The plot network was initially established in the 60s with different levels of selection harvesting[@Kariuki-2006].
+- Evidence of disturbances and succession dynamics: The plot network was initially established in the 1960s with different levels of selection harvesting[@Kariuki-2006].
 - Contact of person in charge of data formatting: R. M. Kooyman (robert@ecodingo.com.au) for plot and trait data
 - Comments: Permanents plots established by the NSW Department of State Forests or by RMK
 - References: 
@@ -283,23 +241,20 @@ Two main data types were used: national forest inventories -- NFI, large permane
 
 \newpage
 
-## Age distribution for Europe and North America.
+## Forests age distribution for Europe and North America.
 
 
-![Age distribution of forest area in 20-year age class for France, Switzerland and Sweden, estimated by Vilen et al.[@Vilen-2012]. The last class plotted at 150 years is for age > 140 years (except for Sweden where the last class 110 is age > 100 years).](../../figs/age_europe.pdf)
+![**Age distribution of forest area in 20-year age class for France, Switzerland and Sweden, estimated by Vilen et al.[@Vilen-2012].** The last class plotted at 150 years is for age > 140 years (except for Sweden where the last class 110 is age > 100 years).](../../figs/age_europe.pdf)
 
-![Age distribution of forest area in 20-year age class for North America (USA and Canada), estimated by Pan et al.[@Pan-2011]. The last class plotted at 150 years is for age > 140 years.](../../figs/age_na.pdf)
+![**Age distribution of forest area in 20-year age class for North America (USA and Canada), estimated by Pan et al.[@Pan-2011].** The last class plotted at 150 years is for age > 140 years.](../../figs/age_na.pdf)
 
 \newpage
 
 # Supplementary Results
 
 ![**Trait-dependent and trait-independent effects on
-maximum growth and competition across the globe and their variation among biomes for a model without separation of $\alpha_0$ between intra and interspecific competition.** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_TP.pdf)
-
-
-![**Trait-dependent and trait-independent effects on
-maximum growth and competition across the globe and their variation among biomes for a model with random structure in the parameters including the data set and the Koppen-Geiger ecoregion.** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_ecocode_TP_intra.pdf)
+maximum growth and competition across the globe and their variation among biomes for models with random effect in the parameters for data set and the Koppen-Geiger ecoregion for wood density (a), specific
+leaf area (b) and maximum height (c).** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_ecocode_TP_intra.pdf)
 
 \newpage
 
@@ -307,15 +262,17 @@ maximum growth and competition across the globe and their variation among biomes
 
 ## Trait effects and potential mechanisms
 
-The most important driver of individual growth was individual tree size with a positive effect on basal area growth (see Extended Data Table 3). This is unsurprising as tree size is known to be a key driver of tree growth[@Stephenson-2014; @Enquist-1999]. Then there was a consistent negative effect of the total basal area of conspecific and heterospecific neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height >= 10cm) agrees well with the idea that facilitation processes are generally limited to the regeneration phase rather than to the adult stage [@Callaway-1997]. Differences in $\alpha_{0 \, intra} \, \& \, \alpha_{0 \, inter}$ between biomes are not great with large overlap of their confidence intervals.
+The most important driver of individual growth was individual tree size with a positive effect on basal area growth (see Extended Data Table 3). This is unsurprising as tree size is known to be a key driver of tree growth[@Stephenson-2014; @Enquist-1999]. Then there was a consistent negative effect of the total basal area of conspecific and heterospecific neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height >= 10cm) agrees well with the idea that facilitation processes are generally limited to the regeneration phase rather than to the adult stage [@Callaway-1997]. Differences in $\alpha_{0 \, intra} \, \& \, \alpha_{0 \, inter}$ between biomes are not great with large overlap of their confidence intervals. Because the data coverage with different among traits, the data used to fit the models is not identical for all traits. This may explain variation between biomes for trait-independent parameters?
+
+In terms of trait effects, wood density (WD) was strongly negatively associated with maximum growth, which is in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (full light conditions) than shade tolerant species[@Nock-2009; @Wright-2010]. One advantage of low wood density is clearly that it is cheaper to build light than dense wood, thus for the same biomass growth low wood density species will have higher basal area increments than species with high wood density[@Enquist-1999]. Other advantages of low wood density may include higher xylem conductivity[@Chave-2009], though for angiosperms this is a correlated trait rather than a direct consequence. A countervailing advantage for high wood density species was their better tolerance of competition (less growth reduction per unit of basal area of competitors), which is in line with the idea that these species are more shade tolerant[@Chave-2009; @Nock-2009; @Wright-2010]. This has most often been related to the higher survival associated with high wood density[@Kraft-2010] via resistance to mechanical damage, herbivores and pathogens[@Chave-2009; @Kraft-2010]. Survival was not analysed here. The growth-response differences that were analysed might be related to lower maintenance respiration[@Larjavaara-2010], that may lead to a direct advantage in deep shade. This relationship might also arise through correlated selection for high survival and high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effects. This might possibly have been mediated by larger crowns (both in depth and radius)[@Poorter-2006a; @Aiba-2009], casting a deeper shade.
 
-In terms of trait effects, wood density (WD) was strongly negatively associated with maximum growth, which is in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (full light conditions) than shade tolerant species[@Nock-2009; @Wright-2010]. One advantage of low wood density is clearly that it is cheaper to build light than dense wood, thus for the same biomass growth low wood density species will have higher basal area increments than species with high wood density[@Enquist-1999]. Other advantages of low wood density may include higher xylem conductivity[@Chave-2009], though for angiosperms this is a correlated trait rather than a direct consequence. A countervailing advantage for high wood density species was their better tolerance of competition (less growth reduction per unit of basal area of competitors), which is in line with the idea that these species are more shade tolerant[@Chave-2009; @Nock-2009; @Wright-2010]. This has most often been related to the higher survival associated with high wood density[@Kraft-2010] via resistance to mechanical damage, herbivores and pathogens[@Chave-2009; @Kraft-2010]. Survival was not analysed here. The growth-response differences that were analysed might be related to lower maintenance respiration[@Larjavaara-2010].  be related to lower respiration may lead to a direct advantage in deep shade, but this relationship might also arise through correlated selection for high survival and high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effects. This might possibly have been mediated by larger crowns (both in depth and radius)[@Poorter-2006a; @Aiba-2009], casting a deeper shade.
+SLA appeared positively correlated with maximum basal area growth, though only significantly in three of five biomes and with weak effects. Previous studies have reported strong positive correlations among SLA, gas exchange (the 'leaf economic spectrum'[@Wright-2004]) and young seedling relative growth rate[@Shipley-2006; @Wright-2001]. Studies[@Poorter-2008; @Wright-2010] on adult trees have however generally reported weak and marginal correlation between SLA and maximum growth. In short, our results are in line with previous reports. Low SLA was also correlated with a stronger competitive effect. This may be related to a longer leaf life span characteristic of low SLA species because leaf longevity leads to a higher accumulation of leaf in the canopy and thus a higher light interception[@Niinemets-2010].
 
-SLA appeared positively correlated with maximum basal area growth, though only significantly in three of five biomes and with weak effects. Previous studies have reported strong positive correlation between SLA and gas exchange (the 'leaf economic spectrum'[@Wright-2004]) and young seedling relative growth rate[@Shipley-2006; @Wright-2001]. Studies[@Poorter-2008; @Wright-2010] on adult trees have however generally reported weak and marginal correlation between SLA and maximum growth. This is also in agreement with the fact that SLA is the only trait for which the null model (no traits effect) has better AIC than the trait model (see Table 3 in Extended Data). In short, our results are in line with previous reports. Low SLA was also correlated with a stronger competitive effect. This may be related to a longer leaf life span characteristic of low SLA species because leaf longevity leads to a higher accumulation of leaf in the canopy and thus a higher light interception[@Niinemets-2010].
+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] have 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 weakly negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest, tropical forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was very little correlation between maximum height and competitive effects, despite the fact that taller trees are generally considered to have a greater light interception ability. It is however important to note that we are analysing the species maximum height and not the actual tree height of the individual. These weak effects of maximum height are probably explained by the fact that our analysis deals with short-term competition effects on tree growth. Size-structured population models[@Adams-2007] have in contrast shown that maximum height can be a key driver of long-term competitive success in terms 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] have 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 weakly 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 effects of maximum height are probably explained by the fact that our analysis deals with short-term effects on tree growth. Size-structured population models[@Adams-2007] have in contrast shown that maximum height can be a key driver of long-term competitive success in terms 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 two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intraspecific 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 better 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. These mixed results on 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. One key question regarding competitive effect and competitive response is their relative importance in terms of long-term effects on population level outcomes of competition. In some simple population models[@Tilman-1977; @Goldberg-1996] the population outcome of competition was not affected by the competitive effect. On this basis competitive tolerance would be more important than competitive effect. However more complex resource competition models[@Tilman-1990], or size-structured forest models of competition for light[@Adams-2007], do show that the competitive effect may influence the long-term population outcome of competition.
 
-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 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 better 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. These mixed results on 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 note that trait dissimilarity effects appeared stronger when trait independent differences between intra \textit{vs.} interspecies competition were not separated  (Figure 3 in Supplementary Results). In other words, competitive effects were distinctly stronger when traits were identical compared to when they were a little different.
+It is also important to note that trait dissimilarity effects appeared stronger when trait independent differences between intra and interspecies competition were not separated  (Figure 3 in Supplementary Results). In other words, competitive effects were distinctly stronger when traits were identical compared to when they were a little different.
 
 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 may be more powerful. For instance the leaf area index of the competitors or the light compensation point at leaf or whole-plant level might have superior predictive power in relation to competition for light. It is possible also that traits measured at the individual level rather than as species averages might have strengthened the predictive power of our analysis[@Kraft-2014].
 
diff --git a/docs/paper/Suppl_Mat.Rmd b/docs/paper/Suppl_Mat.Rmd
index 06163465bfa1b6474048e9efbe82eb1cc04e97dc..105d9a8af653a63764e10009f0042dd5d8b03fec 100644
--- a/docs/paper/Suppl_Mat.Rmd
+++ b/docs/paper/Suppl_Mat.Rmd
@@ -1,47 +1,5 @@
 % Supplementary Information
 
-# Supplementary Methods
-We developed the equation of $\alpha_{c,f} = \alpha_{0,f,intra} \, CON + \alpha_{0,f,inter} \ (1-CON) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert$ along with the basal area of each competing species in the competition index to show the parameters are directly related to community weighted means of the different trait variables as:
-\begin{equation} \label{alphaBA}
-\sum_{c=1}^{N_i} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f,intra} \, B_{i,f} + \alpha_{0,f,inter} \, B_{i,het}- \alpha_t \, t_f \, B_{i,tot} + \alpha_e \, B_{i,t_c} + \alpha_d \, B_{i,\vert t_c - t_f \vert}
-\end{equation}
-
-Where:
-
-$B_{i,het} = \sum_{c \neq f} {B_{i,c}}$,
-
-$B_{i,t_c} = \sum_{c=1}^{N_i} {t_c \times B_{i,c}}$,
-
-$B_{i,\vert t_c - t_f \vert} = \sum_{c=1}^{N_i} {\vert t_c - t_f \vert \times B_{i,c}}$,
-
-and $N_i$ is the number of species in the local neighbourhood of the tree $i$. Note that the indices $p$ and $s$ respectively for plot and data set are not shown here for sake of simplicity.
-
-## Derivation of $\rho$ for a Lotka-Volterra model based on Godoy \& Levine[@Godoy-2014]
-
-Chesson[@Chesson-2012] proposed to estimate the stabilising niche difference based on the per capita growth rate of a rare invader into a population of a resident species. Godoy \& Levine[@Godoy-2014] used this method on an annual plant population model. This approach can be explained using the Lotka-Volterra model:
-
-\begin{equation}
-\frac{dN_i}{dt} =  N_i \times r_i \times (1 - \alpha'_{ii} N_i -
-\alpha'_{ij} N_j)
-\end{equation}
-
-The criterion for invasion of species $i$ into a resident community of species $j$ (at equilibrium population $\overline{N_j} = \frac{1}{\alpha'_{jj}}$) is:
-
-\begin{equation}
-(1 - \frac{\alpha_{ij}}{\alpha'_{jj}})
-\end{equation}
-
-Thus if $\frac{\alpha_{ij}}{\alpha'_{jj}} <1$ invasion of $i$ into $j$ is possible (and similar approach for $j$ into $i$).
-
-Stable coexistence between species $i$ and species $j$ thus requires
-$\frac{\alpha'_{ij}}{\alpha'_{jj}}$ and $\frac{\alpha'_{ji}}{\alpha'_{ii}}$ to be smaller than 1. Chesson[@Chesson-2012] then defined the average
-stabilising niche
-overlap between species $i$ and $j$ as:
-
-\begin{equation}
-\rho = \sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}}
-\end{equation}
-
 
 ## Details on data sets used
 
@@ -82,23 +40,20 @@ writeLines(unlist(list.t[dat[["Country"]]]))
 
 \newpage
 
-## Age distribution for Europe and North America.
+## Forests age distribution for Europe and North America.
 
 
-![Age distribution of forest area in 20-year age class for France, Switzerland and Sweden, estimated by Vilen et al.[@Vilen-2012]. The last class plotted at 150 years is for age > 140 years (except for Sweden where the last class 110 is age > 100 years).](../../figs/age_europe.pdf)
+![**Age distribution of forest area in 20-year age class for France, Switzerland and Sweden, estimated by Vilen et al.[@Vilen-2012].** The last class plotted at 150 years is for age > 140 years (except for Sweden where the last class 110 is age > 100 years).](../../figs/age_europe.pdf)
 
-![Age distribution of forest area in 20-year age class for North America (USA and Canada), estimated by Pan et al.[@Pan-2011]. The last class plotted at 150 years is for age > 140 years.](../../figs/age_na.pdf)
+![**Age distribution of forest area in 20-year age class for North America (USA and Canada), estimated by Pan et al.[@Pan-2011].** The last class plotted at 150 years is for age > 140 years.](../../figs/age_na.pdf)
 
 \newpage
 
 # Supplementary Results
 
 ![**Trait-dependent and trait-independent effects on
-maximum growth and competition across the globe and their variation among biomes for a model without separation of $\alpha_0$ between intra and interspecific competition.** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_TP.pdf)
-
-
-![**Trait-dependent and trait-independent effects on
-maximum growth and competition across the globe and their variation among biomes for a model with random structure in the parameters including the data set and the Koppen-Geiger ecoregion.** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_ecocode_TP_intra.pdf)
+maximum growth and competition across the globe and their variation among biomes for models with random effect in the parameters for data set and the Koppen-Geiger ecoregion for wood density (a), specific
+leaf area (b) and maximum height (c).** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_ecocode_TP_intra.pdf)
 
 \newpage
 
@@ -106,15 +61,17 @@ maximum growth and competition across the globe and their variation among biomes
 
 ## Trait effects and potential mechanisms
 
-The most important driver of individual growth was individual tree size with a positive effect on basal area growth (see Extended Data Table 3). This is unsurprising as tree size is known to be a key driver of tree growth[@Stephenson-2014; @Enquist-1999]. Then there was a consistent negative effect of the total basal area of conspecific and heterospecific neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height >= 10cm) agrees well with the idea that facilitation processes are generally limited to the regeneration phase rather than to the adult stage [@Callaway-1997]. Differences in $\alpha_{0 \, intra} \, \& \, \alpha_{0 \, inter}$ between biomes are not great with large overlap of their confidence intervals.
+The most important driver of individual growth was individual tree size with a positive effect on basal area growth (see Extended Data Table 3). This is unsurprising as tree size is known to be a key driver of tree growth[@Stephenson-2014; @Enquist-1999]. Then there was a consistent negative effect of the total basal area of conspecific and heterospecific neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height >= 10cm) agrees well with the idea that facilitation processes are generally limited to the regeneration phase rather than to the adult stage [@Callaway-1997]. Differences in $\alpha_{0 \, intra} \, \& \, \alpha_{0 \, inter}$ between biomes are not great with large overlap of their confidence intervals. Because the data coverage with different among traits, the data used to fit the models is not identical for all traits. This may explain variation between biomes for trait-independent parameters?
+
+In terms of trait effects, wood density (WD) was strongly negatively associated with maximum growth, which is in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (full light conditions) than shade tolerant species[@Nock-2009; @Wright-2010]. One advantage of low wood density is clearly that it is cheaper to build light than dense wood, thus for the same biomass growth low wood density species will have higher basal area increments than species with high wood density[@Enquist-1999]. Other advantages of low wood density may include higher xylem conductivity[@Chave-2009], though for angiosperms this is a correlated trait rather than a direct consequence. A countervailing advantage for high wood density species was their better tolerance of competition (less growth reduction per unit of basal area of competitors), which is in line with the idea that these species are more shade tolerant[@Chave-2009; @Nock-2009; @Wright-2010]. This has most often been related to the higher survival associated with high wood density[@Kraft-2010] via resistance to mechanical damage, herbivores and pathogens[@Chave-2009; @Kraft-2010]. Survival was not analysed here. The growth-response differences that were analysed might be related to lower maintenance respiration[@Larjavaara-2010], that may lead to a direct advantage in deep shade. This relationship might also arise through correlated selection for high survival and high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effects. This might possibly have been mediated by larger crowns (both in depth and radius)[@Poorter-2006a; @Aiba-2009], casting a deeper shade.
 
-In terms of trait effects, wood density (WD) was strongly negatively associated with maximum growth, which is in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (full light conditions) than shade tolerant species[@Nock-2009; @Wright-2010]. One advantage of low wood density is clearly that it is cheaper to build light than dense wood, thus for the same biomass growth low wood density species will have higher basal area increments than species with high wood density[@Enquist-1999]. Other advantages of low wood density may include higher xylem conductivity[@Chave-2009], though for angiosperms this is a correlated trait rather than a direct consequence. A countervailing advantage for high wood density species was their better tolerance of competition (less growth reduction per unit of basal area of competitors), which is in line with the idea that these species are more shade tolerant[@Chave-2009; @Nock-2009; @Wright-2010]. This has most often been related to the higher survival associated with high wood density[@Kraft-2010] via resistance to mechanical damage, herbivores and pathogens[@Chave-2009; @Kraft-2010]. Survival was not analysed here. The growth-response differences that were analysed might be related to lower maintenance respiration[@Larjavaara-2010].  be related to lower respiration may lead to a direct advantage in deep shade, but this relationship might also arise through correlated selection for high survival and high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effects. This might possibly have been mediated by larger crowns (both in depth and radius)[@Poorter-2006a; @Aiba-2009], casting a deeper shade.
+SLA appeared positively correlated with maximum basal area growth, though only significantly in three of five biomes and with weak effects. Previous studies have reported strong positive correlations among SLA, gas exchange (the 'leaf economic spectrum'[@Wright-2004]) and young seedling relative growth rate[@Shipley-2006; @Wright-2001]. Studies[@Poorter-2008; @Wright-2010] on adult trees have however generally reported weak and marginal correlation between SLA and maximum growth. In short, our results are in line with previous reports. Low SLA was also correlated with a stronger competitive effect. This may be related to a longer leaf life span characteristic of low SLA species because leaf longevity leads to a higher accumulation of leaf in the canopy and thus a higher light interception[@Niinemets-2010].
 
-SLA appeared positively correlated with maximum basal area growth, though only significantly in three of five biomes and with weak effects. Previous studies have reported strong positive correlation between SLA and gas exchange (the 'leaf economic spectrum'[@Wright-2004]) and young seedling relative growth rate[@Shipley-2006; @Wright-2001]. Studies[@Poorter-2008; @Wright-2010] on adult trees have however generally reported weak and marginal correlation between SLA and maximum growth. This is also in agreement with the fact that SLA is the only trait for which the null model (no traits effect) has better AIC than the trait model (see Table 3 in Extended Data). In short, our results are in line with previous reports. Low SLA was also correlated with a stronger competitive effect. This may be related to a longer leaf life span characteristic of low SLA species because leaf longevity leads to a higher accumulation of leaf in the canopy and thus a higher light interception[@Niinemets-2010].
+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] have 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 weakly negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest, tropical forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was very little correlation between maximum height and competitive effects, despite the fact that taller trees are generally considered to have a greater light interception ability. It is however important to note that we are analysing the species maximum height and not the actual tree height of the individual. These weak effects of maximum height are probably explained by the fact that our analysis deals with short-term competition effects on tree growth. Size-structured population models[@Adams-2007] have in contrast shown that maximum height can be a key driver of long-term competitive success in terms 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] have 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 weakly 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 effects of maximum height are probably explained by the fact that our analysis deals with short-term effects on tree growth. Size-structured population models[@Adams-2007] have in contrast shown that maximum height can be a key driver of long-term competitive success in terms 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 two central elements of a species' competitive ability[@Goldberg-1991]. One may expect that because of intraspecific 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 better 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. These mixed results on 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. One key question regarding competitive effect and competitive response is their relative importance in terms of long-term effects on population level outcomes of competition. In some simple population models[@Tilman-1977; @Goldberg-1996] the population outcome of competition was not affected by the competitive effect. On this basis competitive tolerance would be more important than competitive effect. However more complex resource competition models[@Tilman-1990], or size-structured forest models of competition for light[@Adams-2007], do show that the competitive effect may influence the long-term population outcome of competition.
 
-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 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 better 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. These mixed results on 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 note that trait dissimilarity effects appeared stronger when trait independent differences between intra \textit{vs.} interspecies competition were not separated  (Figure 3 in Supplementary Results). In other words, competitive effects were distinctly stronger when traits were identical compared to when they were a little different.
+It is also important to note that trait dissimilarity effects appeared stronger when trait independent differences between intra and interspecies competition were not separated  (Figure 3 in Supplementary Results). In other words, competitive effects were distinctly stronger when traits were identical compared to when they were a little different.
 
 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 may be more powerful. For instance the leaf area index of the competitors or the light compensation point at leaf or whole-plant level might have superior predictive power in relation to competition for light. It is possible also that traits measured at the individual level rather than as species averages might have strengthened the predictive power of our analysis[@Kraft-2014].
 
diff --git a/docs/paper/extended_data.R b/docs/paper/extended_data.R
index 3f81a0ce0a8022d3aa6c31aec8ce200864b6fa0c..39c603ff0ac3c3f7a1566756d97c9e6df1faeadf 100644
--- a/docs/paper/extended_data.R
+++ b/docs/paper/extended_data.R
@@ -5,8 +5,9 @@
 ## ```
 
 
-## ![Map of the plot locations of all data sets analysed. LPP plots are represented with a large points and NFI plots with small points (The data set of Panama comprises both a 50ha plot and a network of 1ha plots).](../../figs/world_map.pdf) 
+## ![**Map of the plot locations of all data sets analysed.** LPP plots are represented with a large points and NFI plots with small points (The data set of Panama comprises both a 50ha plot and a network of 1ha plots). World map is from the R package *rworldmap*[^South].](../../figs/world_map.pdf)
 
+## [^South]: South, A. Rworldmap: A new r package for mapping global data. The R Journal 3, 35–43 (2011).
 
 
 ## \newpage
@@ -60,12 +61,12 @@ dat.2 <- dat.2[, 1:11]
 dat.2[,5:11] <- dat.2[,5:11]*100
 
 pandoc.table(dat.2[, 1:6],
-             caption = "Data description, with number of individual trees, species and plots in NFI data and quadrats in LPP data, and percentage of angiosperm and evergreen species.",
+             caption = "**Trees data description.** For each site is given the number of individual trees, species and plots in NFI data and quadrats in LPP data, and the percentage of angiosperm and evergreen species.",
              digits = c(3,3,3,0,0), split.tables = 200, split.cells = 35,
              justify = c('left', rep('right', 5)), keep.trailing.zeros = TRUE)
 
 pandoc.table(dat.2[, c(1,9:11)],
-             caption = "Traits coverage in each site. Percentage of species with species level trait data.",
+             caption = "**Traits data description.** The coverage in each site is given with the percentage of species with species level trait data.",
              digits = 1, split.tables = 200, split.cells = 25,
              justify = c('left', rep('right', 3)),
              keep.trailing.zeros = TRUE)
@@ -90,17 +91,22 @@ colnames(cor.mat)  <- row.names(cor.mat) <-  c("Wood density", "SLA",
                                                "Max height")
 ##+ Table1_cor, echo = FALSE, results='asis', message=FALSE
 pandoc.table(cor.mat,
-             caption = "Pairwise functional trait correlations (Pearson's r)",
+             caption = "**Pairwise functional trait correlations**. Pearson's r correlations for the three traits.",
              digits = 3)
 
 ## \newpage
 
 ## # Model results
 
-## ![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 dissimilarity ($|t_f - t_c| \, \alpha_d$ ($t_c$ 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)
+## ![**Variation of trait-independent inter and intraspecific competition, trait dissimilarity ($|t_f - t_c| \, \alpha_d$), competitive effect ($t_c \, \alpha_e$), tolerance to competition ($t_f \, \alpha_t$) and maximum growth ($t_f \, m_1$) with wood density (respectively a, b, c, d and e), specific leaf area (respectively f, g, h, i and j) and maximum height (respectively k, l, m, n and o).** Trait varied from their quantile at 5\% to their quantile at 95\%. The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$). $\alpha_{0 \, intra}$ and $\alpha_{0 \, inter}$, which do not vary with traits are 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 (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)
+## ![**Average difference between interspecific and intraspecific competition predicted with estimates of trait-independent and trait-dependent processes influencing competition for models fitted for wood density (a), specific leaf area (b) or maximum height (c).** The average differences between interspecific and intraspecific competition are influenced by $\alpha_{0 \, intra}$, $\alpha_{0 \, inter}$ and $\alpha_d$ coefficients (see Extended Methods for details). Negative value indicates that intraspecific competition is stronger than interspecific competition.](../../figs/rho_set_TP_intra.pdf)
+
+## ![**Trait-dependent and trait-independent effects on
+## maximum growth and competition across the globe and their variation among biomes for models without separation of $\alpha_0$ between intra and interspecific competition for wood density (a), specific
+## leaf area (b) and maximum height (c).** See Figure 2 in the main text for parameters description and see Fig 1a in the main text for biome definition.](../../figs/figres12_TP.pdf)
+
 
 
 
@@ -123,133 +129,6 @@ mat.param[!row.names(mat.param) %in% c("(Intercept)", "logD",
                                             'MAT', 'MAP',
                                              "sumTfBn"),]
 
-fun.plot.rho <- function(i, mat.param, T = seq(0.1, 1, length.out = 50)){
-param <- mat.param[, i]    
-exp((param['sumBn.inter'] - param['sumBn.intra'] +param['sumTnTfBn.abs'] *abs(T -min(T))))
-}
-
-generate.random.param <- function(trait,
-                                  list.res, n = 500,
-                                  model= 'lmer.LOGLIN.ER.AD.Tf.MAT.MAP.intra.r.set.species',
-                                  data.type = 'intra',
-                                  param.name = c('sumBn.inter', 'sumBn.intra',
-                                                 'sumTfBn', 'sumTnBn', 'sumTnTfBn.abs')){
-    
-require(mvtnorm)
-mean.param <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$lmer.summary$fixed.coeff.E
-vcov <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$vcov
-mean.param.s <- mean.param[param.name]
-vcov.s <- as.matrix(vcov[param.name, param.name])
-res <- rmvnorm(n, mean=mean.param.s, sigma=vcov.s, method="chol")
-return(res)
-}
-
-
-ratio.dan <- function(i, T1, T2, mat.param,list.sd){
-param <- mat.param[i, ]
-aer <- param['sumBn.inter']/list.sd[['sd.sumBn.inter']]
-ara <- param['sumBn.intra']/list.sd[['sd.sumBn.intra']]
-at <- param['sumTfBn']/list.sd[['sd.sumTfBn']]
-ae <- param['sumTnBn']/list.sd[['sd.sumTnBn']]
-ad <- param['sumTfTnBn.abs']/list.sd[['sd.sumTfTnBn.abs']]
-
-dan <-(aer at *T1 + ae *T2 + ad *abs(T2 -T1))*
-   (aer +at *T2 + ae *T1 + ad *abs(T2 -T1))/
-((ara +at *T1 + ae *T1) *
- (ara + at *T2 + ae *T2))
-return(dan)
-
-}
-
-fun.plot.dan <- function(i, mat.param, T1 = 0.1,
-                         T2 = seq(0.1, 1, length.out = 50)){
-
-list.sd <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$list.sd
-dan <- outer(T1, T2, ratio.dan, i, mat.param, list.sd)
-return(dan)
-}
-
-fun.dan.ci <- function(trait, list.res, alpha= 0.05, T1 = 1,
-                         T2 = seq(0.1, 1, length.out = 50), n = 500){
-mat.param.r <- generate.random.param(trait, n = n, list.res = list.all.results)
-res.ci <- sapply(1:n, ratio.dan, T1, T2, mat.param.r)
-mean.p <- apply(res.ci, MARGIN = 1, median)
-ci.p <- apply(res.ci, MARGIN = 1, quantile, probs = c(alpha/2, 1-alpha/2))
-return(cbind(mean.p, t(ci.p)))
-}
-
-
-get.predict.var.scaled <- function(trait, dir.root='../..', log.TF = FALSE, N.pred = 100){
-if(log.TF) {file.type <- ''}
-else{file.type <- 'no.log'}
-dir.read <- 'output/processed'
-sd.traits <-
-    readRDS(file.path(dir.root, dir.read,
-                      paste0('data.sd.traits.', file.type, '.rds')))
-quant.data <-
-    readRDS(file.path(dir.root, dir.read,
-                      paste0('data.quant.traits.', file.type, '.rds')))
-trait.quant <-fun.std.quant.trait(trait, dat.q = quant.data
-       , dat.sd = sd.traits)
-seq.BATOT <- seq(from = 0,
-                 to = quant.data[['qh.BATOT']],
-                 length.out = N.pred)
-return(list(trait.quant, seq.BATOT))
-}
-
-
-fun.plot.rho.dan <- function(trait, list.res, fun.tf = max){
-qa <- get.predict.var.scaled(trait)[[1]]
-T2 <- seq(qa[['ql']], qa[['qh']], length.out = 50)
-T1 <-  fun.tf(T2)
-T <- seq(qa[['ql.o']], qa[['qh.o']], length.out = 50) - qa[['ql.o']]
-mat.p <- fun.dan.ci(trait,  list.res, T1=T1, T2=T2)
-plot(T, mat.p[,1],type = 'l', lwd = 2, ylim =range(mat.p), col = '#018571')
-    polygon(c(T,
-          rev(T)),
-        c(mat.p[, 2],
-          rev(mat.p[, 3])),
-       col = add.alpha('#018571', 0.5), border = NA)
-lines(T,mat.p[,2], lty= 2)
-lines(T,mat.p[,3], lty= 2)
-}
-
-add.alpha <- function(col, alpha=0.5){
-  if(missing(col))
-    stop("Please provide a vector of colours.")
-  apply(sapply(col, col2rgb)/255, 2,
-                     function(x)
-                       rgb(x[1], x[2], x[3], alpha=alpha))
-}
-
-x11()
-par(mfcol = c(1,3))
-fun.plot.rho.dan('Wood.density', list.all.results)
-fun.plot.rho.dan('SLA', list.all.results)
-fun.plot.rho.dan('Max.height', list.all.results)
-
-
-
-plot(T,1-fun.plot.dan(1, mat.param))
-plot(T,1-fun.plot.dan2(1, mat.param))
-plot(T,1- fun.plot.rho(2, mat.param))
-plot(T,1-fun.plot.dan(2, mat.param))
-plot(T,1-fun.plot.dan2(2, mat.param))
-plot(T,1- fun.plot.rho(3, mat.param))
-plot(T,1-fun.plot.dan(3, mat.param))
-plot(T,1-fun.plot.dan2(3, mat.param))
-
-
-
-par(mfrow= c(1,3))
-image(fun.plot.dan(1, mat.param, T1 = seq(0.1, 1, length.out = 50)))
-image(fun.plot.dan(2, mat.param, T1 = seq(0.1, 1, length.out = 50)))
-image(fun.plot.dan(3, mat.param, T1 = seq(0.1, 1, length.out = 50)))
-
-
 mat.param.sd <- do.call('cbind',
                 lapply(c('Wood.density', 'SLA', 'Max.height'),
                     extract.param.sd, list.res = list.all.results,
@@ -300,7 +179,7 @@ row.names(mat.param) <-  c('$m_0$', '$\\gamma$', '$m_1$', '$m_2$','$m_3$',
                            '$\\Delta$ AIC', '$\\Delta$ AIC no trait')
 
 ##+ Table2_Effectsize, echo = FALSE, results='asis', message=FALSE
-pandoc.table(mat.param[c(1:14), ], caption = "Standardized parameters estimates and standard error (in bracket) estimated for each trait, $R^2$* of models and $\\Delta$ AIC of the model and of a model with no trait effect. Best model have a $\\Delta$ AIC of zero. See section Method for explanation of parameters",
+pandoc.table(mat.param[c(1:14), ], caption = "**Standardized coefficient estimates from models fitted for each traits.**  Estimates and standard error (in bracket) estimated for each trait, $R^2$* of models and $\\Delta$ AIC of the model and of a model with no trait effect. Best model have a $\\Delta$ AIC of zero. See section Method for explanation of parameters",
              digits = 3,  justify = c('left', rep('right', 3)),
              emphasize.strong.cells = bold.index, split.tables = 200)
 
@@ -310,6 +189,4 @@ pandoc.table(mat.param[c(1:14), ], caption = "Standardized parameters estimates
 ## [^2]: Johnson, P. C. D. Extension of Nakagawa and Schielzeth’s R2GLMM to random slopes models. Methods in Ecology and Evolution 5, 944–946 (2014).
 ## [^3]: Burnham, K. P. & Anderson, D. R. Model selection and multimodel inference: A practical information-theoretic approach. (Springer-Verlag, New-York, 2002).
 
-## THERE IS AN ISSUE WITH THE AIC COMPARISON BECAUSE NOT THE SAME NUMBER OF OBS AS DIFFERENT SAMPLING OF THE CENSUS, I M RERUNNING THAT, HOPING THIS WILL MAKE AIC OF NULL MODEL HIGHER IN ALL CASE (THERE WAS MUCH MORE DATA SAMPLED FOR THE TRAITS DATA IN SLA)
-
 
diff --git a/docs/paper/extended_data.tex b/docs/paper/extended_data.tex
new file mode 100644
index 0000000000000000000000000000000000000000..cecbd7da850a4aa506ac35582a6d1b5583a259c6
--- /dev/null
+++ b/docs/paper/extended_data.tex
@@ -0,0 +1,953 @@
+% THIS FILE TAKEN FROM PANDOC DEMOS PAGE:http://johnmacfarlane.net/pandoc/demos.html,http://johnmacfarlane.net/pandoc/demo/mytemplate.tex
+
+\documentclass[12pt,, a4paper]{article}
+
+\RequirePackage[hmargin=2cm,vmargin=2cm]{geometry}
+
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{longtable}
+\usepackage{booktabs}
+\usepackage{amssymb,amsmath}
+\usepackage{ifxetex,ifluatex}
+\usepackage{fixltx2e} % provides \textsubscript
+
+% \usepackage{setspace}
+% \doublespacing
+% \usepackage{lineno}
+% \modulolinenumbers[5]
+% \linenumbers
+
+% use microtype if available
+\IfFileExists{microtype.sty}{\usepackage{microtype}}{}
+% use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+  \usepackage[utf8]{inputenc}
+
+\else % if luatex or xelatex
+  \usepackage{fontspec}
+  \ifxetex
+    \usepackage{xltxtra,xunicode}
+  \fi
+  \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase}
+  \newcommand{\euro}{€}
+    \setmainfont{Times New Roman}
+    \setsansfont{Arial}
+\fi
+
+% Fancy HEADER
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\pagenumbering{arabic}
+\lhead{\itshape{\nouppercase{\leftmark}}}
+\chead{}
+\rhead{\thepage}
+%\lfoot{v }
+\cfoot{}
+%\rfoot{\thepage}
+
+\usepackage{longtable}
+\usepackage{booktabs}
+\usepackage{graphicx}
+% We will generate all images so they have a width \maxwidth. This means
+% that they will get their normal width if they fit onto the page, but
+% are scaled down if they would overflow the margins.
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
+\else\Gin@nat@width\fi}
+\makeatother
+\let\Oldincludegraphics\includegraphics
+\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=\maxwidth]{#1}}
+\ifxetex
+  \usepackage[setpagesize=false, % page size defined by xetex
+              unicode=false, % unicode breaks when used with xetex
+              xetex]{hyperref}
+\else
+  \usepackage[unicode=true]{hyperref}
+\fi
+\hypersetup{breaklinks=true,
+            bookmarks=true,
+            pdfauthor={},
+            pdftitle={},
+            colorlinks=true,
+            urlcolor=blue,
+            linkcolor=magenta,
+            pdfborder={0 0 0}}
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{6pt plus 2pt minus 1pt}
+\setlength{\emergencystretch}{3em}  % prevent overfull lines
+\setcounter{secnumdepth}{0}
+ 
+%% FROM https://github.com/humburg/reproducible-reports/blob/master/include/report.latex
+%% \author{}
+\date{}
+
+\begin{document}
+
+\section{Extend data}\label{extend-data}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics{../../figs/world_map.pdf}
+\caption{\textbf{Map of the plot locations of all data sets analysed.}
+LPP plots are represented with a large points and NFI plots with small
+points (The data set of Panama comprises both a 50ha plot and a network
+of 1ha plots). World map is from the R package
+rworldmap\protect\footnotemark.}
+\end{figure}
+
+\footnotetext{South, A. Rworldmap: A new r package for mapping global data. The R Journal 3, 35–43 (2011).}
+\newpage
+
+\section{Data description}\label{data-description}
+
+\begin{longtable}[c]{@{}lrrrrr@{}}
+\caption{\textbf{Trees data description.} For each site is given the
+number of individual trees, species and plots in NFI data and quadrats
+in LPP data, and the percentage of angiosperm and evergreen
+species.}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
+set
+\strut\end{minipage} &
+\begin{minipage}[b]{0.10\columnwidth}\raggedleft\strut
+\# of trees
+\strut\end{minipage} &
+\begin{minipage}[b]{0.11\columnwidth}\raggedleft\strut
+\# of species
+\strut\end{minipage} &
+\begin{minipage}[b]{0.17\columnwidth}\raggedleft\strut
+\# of plots/quadrats
+\strut\end{minipage} &
+\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
+\% of angiosperm
+\strut\end{minipage} &
+\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
+\% of evergreen
+\strut\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
+set
+\strut\end{minipage} &
+\begin{minipage}[b]{0.10\columnwidth}\raggedleft\strut
+\# of trees
+\strut\end{minipage} &
+\begin{minipage}[b]{0.11\columnwidth}\raggedleft\strut
+\# of species
+\strut\end{minipage} &
+\begin{minipage}[b]{0.17\columnwidth}\raggedleft\strut
+\# of plots/quadrats
+\strut\end{minipage} &
+\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
+\% of angiosperm
+\strut\end{minipage} &
+\begin{minipage}[b]{0.14\columnwidth}\raggedleft\strut
+\% of evergreen
+\strut\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Sweden
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+202480
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+26
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+22552
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+27.0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+73.0
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+New Zealand
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+53775
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+117
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+1415
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+94.0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+99.1
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+US
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+1370541
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+492
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+59840
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+63.3
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+37.2
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Canada
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+495008
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+75
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+14983
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+34.4
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+64.9
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Australia
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+906
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+101
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+63
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+99.9
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+92.4
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+France
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+184316
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+127
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+17611
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+74.1
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+28.5
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Switzerland
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+28286
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+60
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+2597
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+36.4
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+55.2
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Spain
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+418805
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+122
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+36462
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+34.7
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+81.6
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Panama
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+27089
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+237
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+2033
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+99.8
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+77.7
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+French Guiana
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+46360
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+712
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+2157
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+100.0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+83.5
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Japan
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+4658
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+139
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+318
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+72.8
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+70.0
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Taiwan
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+14701
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+72
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+623
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+92.0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+75.3
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Puerto Rico
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+14011
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+82
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+399
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+100.0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+99.0
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
+Central African Republic
+\strut\end{minipage} &
+\begin{minipage}[t]{0.10\columnwidth}\raggedleft\strut
+17638
+\strut\end{minipage} &
+\begin{minipage}[t]{0.11\columnwidth}\raggedleft\strut
+204
+\strut\end{minipage} &
+\begin{minipage}[t]{0.17\columnwidth}\raggedleft\strut
+989
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+99.5
+\strut\end{minipage} &
+\begin{minipage}[t]{0.14\columnwidth}\raggedleft\strut
+72.4
+\strut\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+\begin{longtable}[c]{@{}lrrr@{}}
+\caption{\textbf{Traits data description.} The coverage in each site is
+given with the percentage of species with species level trait
+data.}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.27\columnwidth}\raggedright\strut
+set
+\strut\end{minipage} &
+\begin{minipage}[b]{0.15\columnwidth}\raggedleft\strut
+\% cover SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.25\columnwidth}\raggedleft\strut
+\% cover Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.22\columnwidth}\raggedleft\strut
+\% cover Max height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.27\columnwidth}\raggedright\strut
+set
+\strut\end{minipage} &
+\begin{minipage}[b]{0.15\columnwidth}\raggedleft\strut
+\% cover SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.25\columnwidth}\raggedleft\strut
+\% cover Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.22\columnwidth}\raggedleft\strut
+\% cover Max height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Sweden
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+98
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+New Zealand
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+US
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+91
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+94
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Canada
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Australia
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+France
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Switzerland
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+97
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+95
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Spain
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+97
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Panama
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+93
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+93
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+95
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+French Guiana
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+73
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+74
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+64
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Japan
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Taiwan
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+100
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+96
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Puerto Rico
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+99
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.27\columnwidth}\raggedright\strut
+Central African Republic
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\raggedleft\strut
+40
+\strut\end{minipage} &
+\begin{minipage}[t]{0.25\columnwidth}\raggedleft\strut
+47
+\strut\end{minipage} &
+\begin{minipage}[t]{0.22\columnwidth}\raggedleft\strut
+0
+\strut\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+\subsection{Species traits
+correlation}\label{species-traits-correlation}
+
+\begin{longtable}[c]{@{}cccc@{}}
+\caption{\textbf{Pairwise functional trait correlations}. Pearson's r
+correlations for the three traits.}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.23\columnwidth}\centering\strut
+~
+\strut\end{minipage} &
+\begin{minipage}[b]{0.18\columnwidth}\centering\strut
+Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.07\columnwidth}\centering\strut
+SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.15\columnwidth}\centering\strut
+Max height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.23\columnwidth}\centering\strut
+~
+\strut\end{minipage} &
+\begin{minipage}[b]{0.18\columnwidth}\centering\strut
+Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.07\columnwidth}\centering\strut
+SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.15\columnwidth}\centering\strut
+Max height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.23\columnwidth}\centering\strut
+\textbf{Wood density}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.18\columnwidth}\centering\strut
+1
+\strut\end{minipage} &
+\begin{minipage}[t]{0.07\columnwidth}\centering\strut
+0.18
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\centering\strut
+-0.035
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.23\columnwidth}\centering\strut
+\textbf{SLA}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.18\columnwidth}\centering\strut
+\strut\end{minipage} &
+\begin{minipage}[t]{0.07\columnwidth}\centering\strut
+1
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\centering\strut
+0.241
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.23\columnwidth}\centering\strut
+\textbf{Max height}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.18\columnwidth}\centering\strut
+\strut\end{minipage} &
+\begin{minipage}[t]{0.07\columnwidth}\centering\strut
+\strut\end{minipage} &
+\begin{minipage}[t]{0.15\columnwidth}\centering\strut
+1
+\strut\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+\newpage
+
+\section{Model results}\label{model-results}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics{../../figs/figres4b_TP_intra.pdf}
+\caption{\textbf{Variation of trait-independent inter and intraspecific
+competition, trait dissimilarity (\(|t_f - t_c| \, \alpha_d\)),
+competitive effect (\(t_c \, \alpha_e\)), tolerance to competition
+(\(t_f \, \alpha_t\)) and maximum growth (\(t_f \, m_1\)) with wood
+density (respectively a, b, c, d and e), specific leaf area
+(respectively f, g, h, i and j) and maximum height (respectively k, l,
+m, n and o).} Trait varied from their quantile at 5\% to their quantile
+at 95\%. The shaded area represents the 95\% confidence interval of the
+prediction (including uncertainty associated with \(\alpha_0\) or
+\(m_0\)). \(\alpha_{0 \, intra}\) and \(\alpha_{0 \, inter}\), which do
+not vary with traits are represented with their associated confidence
+intervals.}
+\end{figure}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics{../../figs/rho_set_TP_intra.pdf}
+\caption{\textbf{Average difference between interspecific and
+intraspecific competition predicted with estimates of trait-independent
+and trait-dependent processes influencing competition for models fitted
+for wood density (a), specific leaf area (b) or maximum height (c).} The
+average differences between interspecific and intraspecific competition
+are influenced by \(\alpha_{0 \, intra}\), \(\alpha_{0 \, inter}\) and
+\(\alpha_d\) coefficients (see Extended Methods for details). Negative
+value indicates that intraspecific competition is stronger than
+interspecific competition.}
+\end{figure}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics{../../figs/figres12_TP.pdf}
+\caption{\textbf{Trait-dependent and trait-independent effects on
+maximum growth and competition across the globe and their variation
+among biomes for models without separation of \(\alpha_0\) between intra
+and interspecific competition for wood density (a), specific leaf area
+(b) and maximum height (c).} See Figure 2 in the main text for
+parameters description and see Fig 1a in the main text for biome
+definition.}
+\end{figure}
+
+\begin{longtable}[c]{@{}lrrr@{}}
+\caption{\textbf{Standardized coefficient estimates from models fitted
+for each traits.} Estimates and standard error (in bracket) estimated
+for each trait, \(R^2\)* of models and \(\Delta\) AIC of the model and
+of a model with no trait effect. Best model have a \(\Delta\) AIC of
+zero. See section Method for explanation of parameters}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.29\columnwidth}\raggedright\strut
+~
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+Maximum height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.29\columnwidth}\raggedright\strut
+~
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+Wood density
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+SLA
+\strut\end{minipage} &
+\begin{minipage}[b]{0.20\columnwidth}\raggedleft\strut
+Maximum height
+\strut\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(m_0\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.016 (0.127)
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+-0.087 (0.132)
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.084 (0.089)
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\gamma\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.418 (0.011)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.401 (0.012)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.42 (0.01)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(m_1\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{-0.149 (0.036)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.119 (0.057)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.063 (0.04)
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(m_2\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.111 (0.003)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.093 (0.003)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.081 (0.002)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(m_3\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.053 (0.002)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.056 (0.003)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.048 (0.002)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\alpha_{0 \, intra}\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.24 (0.037)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.213 (0.052)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.194 (0.046)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\alpha_{0 \, inter}\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.086 (0.022)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.071 (0.025)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.094 (0.024)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\alpha_e\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.034 (0.016)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{-0.083 (0.023)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.017 (0.026)
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\alpha_t\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{0.069 (0.021)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+-0.009 (0.033)
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{-0.071 (0.032)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\alpha_d\)}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0 (0.009)
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+-0.018 (0.015)
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+\textbf{-0.017 (0.008)}
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(R^2_m\)}*
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.1393
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.1637
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.1429
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(R^2_c\)}*
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.7297
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.7593
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0.7166
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\Delta\) AIC}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+0
+\strut\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.29\columnwidth}\raggedright\strut
+\textbf{\(\Delta\) AIC no trait}
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+2469
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+1651
+\strut\end{minipage} &
+\begin{minipage}[t]{0.20\columnwidth}\raggedleft\strut
+2748
+\strut\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+* We report the conditional and marginal \(R^2\) of the models using the
+methods of reference\footnote{Nakagawa, S. \& Schielzeth, H. A general
+  and simple method for obtaining R2 from generalized linear
+  mixed-effects models. Methods in Ecology and Evolution 4, 133--142
+  (2013).}, modified by reference\footnote{Johnson, P. C. D. Extension
+  of Nakagawa and Schielzeth's R2GLMM to random slopes models. Methods
+  in Ecology and Evolution 5, 944--946 (2014).}. \(\Delta\) AIC is the
+difference in AIC between the model and the best model (lowest AIC). AIC
+is the Akaike's Information Criterion (as defined by reference\footnote{Burnham,
+  K. P. \& Anderson, D. R. Model selection and multimodel inference: A
+  practical information-theoretic approach. (Springer-Verlag, New-York,
+  2002).}), and the best-fitting model was identified as the one with a
+\(\Delta\) AIC of zero. \(\Delta\) AIC greater than 10 shows strong
+support for the best model\textsuperscript{3}.
+
+\end{document}
diff --git a/docs/paper/extended_method.tex b/docs/paper/extended_method.tex
index aeb33c3adbdbdc093d3ce0a9f2b25a9708c3d830..8cc2883409718bf4f1ad448020075f6322bda80a 100644
--- a/docs/paper/extended_method.tex
+++ b/docs/paper/extended_method.tex
@@ -68,13 +68,13 @@ reductions due to competition from individuals growing in the local
 neighbourhood (see definition below). Specifically, we assumed a relationship of the form
 
 \begin{equation} \label{G1}
-G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \,  \exp\left(\sum_{c=1}^{N_i} {-\alpha_{c,f} B_{i,c,p,s}}\right),
+G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \,  \exp\left(\sum_{c=1}^{N_i} {-\alpha_{f,c} B_{i,c,p,s}}\right),
 \end{equation}
 where:
 \begin{itemize}
 \itemsep1pt\parskip0pt\parsep0pt
 \item
-  \(G_{i,f,p,s,t}\) and \(D_{i,f,p,s,t}\) are the the annual basal area
+  \(G_{i,f,p,s,t}\) and \(D_{i,f,p,s,t}\) are the annual basal area
   growth and diameter at breast height of individual \(i\) from species
   \(f\), plot or quadrat (see below) \(p\), data set \(s\), and census $t$,
 \item
@@ -88,7 +88,7 @@ where:
   \(\varepsilon_{\gamma, f} \sim \mathcal{N} (0,\sigma_{\gamma})\) -- a
   normal distribution of mean 0 and standard deviation $\sigma_{\gamma}${]}
 \item
-  \(\alpha_{c,f}\) is the per unit basal area effect of individuals from
+  \(\alpha_{f,c}\) is the per unit basal area effect of individuals from
   species \(c\) on growth of an individual in species \(f\),
 \item
   \(B_{i,c,p,s}= 0.25\, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s,t}^2\) is
@@ -106,14 +106,14 @@ where:
   neighbourhood of focal tree $i$.
 \end{itemize}
 
-Values of \(\alpha_{c,f}> 0\) indicate competition, whereas
-\(\alpha_{c,f}\) \textless{} 0 indicates facilitation.
+Values of \(\alpha_{f,c}> 0\) indicate competition, whereas
+\(\alpha_{f,c}\) \textless{} 0 indicates facilitation.
 
-Log-transformation of eq. \ref{G1} leads to a linearised model of the
+Log-transformation of equ. \ref{G1} leads to a linearised model of the
 form
 
 \begin{equation} \label{logG1}
-\log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s,t}} +  \sum_{c=1}^{N_i} {-\alpha_{c,f} B_{i,c,p,s}}.
+\log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s,t}} +  \sum_{c=1}^{N_i} {-\alpha_{f,c} B_{i,c,p,s}}.
 \end{equation}
 
 To include the effects of traits on the parameters of the growth model we build on previous studies that explored the role of traits for tree performances and tree competition\citep{Uriarte-2010, Kunstler-2012, Lasky-2014}. We modelled the effect of traits, one trait at a time.
@@ -136,24 +136,24 @@ quadrat \(p\) (see below), and data set \(s\) {[}where
 and
 \(\varepsilon_{G_{\textrm{max}, s}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, s}})\){]}.
 
-Previous studies have proposed various decompositions of the competition parameter into key trait-based processes\footnote{There have been different approaches to modeling $\alpha$ from traits. In one of the first studies Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha =
+Previous studies have proposed various decompositions of the competition parameter into key trait-based processes\footnote{Different approaches have been proposed to model $\alpha$ from traits. In one of the first studies Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha =
 \alpha_0 + \alpha_d \vert t_f-t_c \vert$. Then Kunstler et al.\citep{Kunstler-2012} used two different models: $\alpha = \alpha_0 + \alpha_d \vert t_f-t_c \vert$ or $\alpha =
 \alpha_0 + \alpha_h ( t_f-t_c )$. Finally, Lasky et
 al.\citep{Lasky-2014} developed a single model including multiple processes as $\alpha =
 \alpha_0 + \alpha_t t_f +\alpha_h ( t_f-t_c ) + \alpha_d \vert t_f-t_c
-\vert$. In this study, we extended this last model. We considered that it was clearer to split
+\vert$. In our study, we extended this last model. We considered that it was clearer to split
 $\alpha_h (t_f - t_c)$ into $\alpha_t t_f + \alpha_e t_c$, which is
 equivalent to the hierarchical distance if $\alpha_t = - \alpha_e$
 (thus avoiding replication of $t_f$ effect through both $\alpha_h$ and
-$\alpha_t$). We also split $\alpha_0$ into intra and interspecific
+$\alpha_t$). We also included two $\alpha_0$, one for intra and one for
+interspecific
 competition.}, and here we extended the approach of the most recent study\citep{Lasky-2014}. As presented in Fig. 1, competitive
 interactions were modelled using an equation of the form\footnote{For
-  fitting the model the equation of \(\alpha_{c,f}\) was developed with
-  species basal area in term of community weighted mean of the trait,
-  see Supplementary Methods for more details.}:
+  fitting the model, the equation of \(\alpha_{f,c}\) was developed with
+  species basal area in term of community weighted means of (i) trait values of competitors and (i) absolute trait distance between focal species and its competitors.}:
 
 \begin{equation} \label{alpha}
-\alpha_{c,f}= \alpha_{0,f,intra} \, C + \alpha_{0,f,inter} \, (1-C) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
+\alpha_{f,c}= \alpha_{0,f,intra} \, C + \alpha_{0,f,inter} \, (1-C) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
 \end{equation}
 
 where:
@@ -161,7 +161,8 @@ where:
 \begin{itemize}
 \itemsep1pt\parskip0pt\parsep0pt
 \item
-  $\alpha_{0,f,intra}$ and $\alpha_{0,f,inter}$ are respectively  \textbf{intra and interspecific trait independent competition} for the focal
+  $\alpha_{0,f,intra}$ and $\alpha_{0,f,inter}$ are respectively
+  \textbf{intraspecific and average interspecific trait independent competition} for the focal
   species \(f\), modelled with a normally distributed random effect of
   species \(f\) and each with normally distributed random effect of data set
   \(s\) {[}as
@@ -187,15 +188,13 @@ where:
   {[}$\varepsilon_{\alpha_d,s} \sim \mathcal{N} (0,\sigma_{\alpha_d})${]}.
 \end{itemize}
 
-Estimating separate $\alpha_0$ for intra and interspecific competition allowed us to account for trait-independent differences in interactions with conspecifics and heterospecifics.
-
-We also explored a simpler version of the model where trait-independent competitive effects were pooled (i.e. there was a single value for $\alpha_0$), as most previous studies have generally not make this distinction which may lead into an overestimation of the trait dissimilarity effect. In this alternative model the equation was:
+Estimating separate $\alpha_0$ for intra and interspecific competition allowed us to account for trait-independent differences in interactions with conspecifics and heterospecifics. We also explored a simpler version of the model where trait-independent competitive effects were pooled (i.e. there was a single value for $\alpha_0$), as most previous studies have generally not made this distinction, using the following equation:
 
 \begin{equation} \label{alpha2}
-\alpha_{c,f}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
+\alpha_{f,c}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
 \end{equation}
 
-In this alternative model any differences between intra and interspecific competition do enter into trait dissimilarity effects, with a trait dissimilarity of zero attached to them. Results for this model
+In this alternative model any differences between intra and interspecific competition do enter into trait dissimilarity effects, with a trait dissimilarity of zero attached to them. This may lead to an overestimation of the trait dissimilarity effect. Results for this model
 are presented in Supplementary Results.
 
 Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of
@@ -210,7 +209,7 @@ To estimate standardised coefficients (one type of standardised effect
 size)\citep{Schielzeth-2010}, response and explanatory variables
 were standardized (divided by their standard deviations) prior to
 analysis. Trait and diameter were also centred to facilitate
-convergence. The models were fitted using the \(lmer\) routine in 
+convergence. The models were fitted using the \(lmer\) routine in
 the lme4 package \citep{Bates-2014}
 in the R statistical environment\citep{RTeam-2014}. We fitted two
 versions of each model. In the first
@@ -229,36 +228,25 @@ attached to parameters both for the data set and for a local ecoregion using
 the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see
 Supplementary Results).
 
-\subsection{Estimating the effect of traits on the mean ratio of intra \textit{vs.} interspecific competition}\label{rho}
-
-The ratio of inter \textit{vs.} intraspecific competition has long been
-considered as key in controlling species coexistence and a key quantity to estimate\citep{widely}. 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, in order to understand trait effects on coexistence. This
-approach 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. Stabilising niche
-differences estimate the strength of processes favouring the
-establishment of a species as a rare invader into an established
-population of a different resident species (see an example based on
-the Lotka-Volterra model based on Godoy \& Levine\citep{Godoy-2014} in
-Supplementary Methods). In this approach $\rho$ is defined as $\rho =
-\sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}}$,
-where $\alpha'_{ij}$ represents the population level competitive
-effect of species $j$ on species $i$. Even though our model estimates
-competition only as its affects on individual basal area growth,
-rather than on rate population growth, it is interesting to quantify how this ratio of inter \textit{vs.} intraspecific 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:
+\subsection{Estimating the effect of traits on the average differences between intra and interspecific competition}\label{intrainter}
+
+Differences between inter and intraspecific competition have long been considered key to community assembly and species coexistence\citep{Connell-1983, Chesson-2000, Chesson-2012, Kraft-2015, Godoy-2014}. Our estimated growth model allowed us to estimate the average inter and intraspecific competition from trait-independent and trait-dependent processes. Using eqn. \ref{alpha}, we can predict for any combination of two values of trait $t_i$ and $t_j$ the interspecific
+($\alpha_{t_i,t_j}$ and $\alpha_{t_j,t_i}$) and
+intraspecific ($\alpha_{t_i,t_i}$ and $\alpha_{t_j,t_j}$)
+competition competition of typical (or mean) species (thus leaving out the random species effects). We can then estimate the average differences between interspecific and intraspecific competition over the two combinations using the following expression:
 
 \begin{equation} \label{rhoequ}
-\rho = \sqrt{\frac{\alpha'_{ij} \alpha'_{ji}}{\alpha'_{jj} \alpha'_{ii}}} = e^{(\alpha_{0,inter} - \alpha_{0,intra} + \alpha_d \vert t_j - t_i \vert)}
+\frac{(\alpha_{t_i,t_j} - \alpha_{t_i,t_i}) + (\alpha_{t_j,t_i} - \alpha_{t_j,t_j})}{2}
 \end{equation}
 
-The stabilising niche difference is then defined as $1-\rho$. In
-summary, $\rho$ is only influenced by the difference between
-$\alpha_{0, intra}$ \textit{vs.} $\alpha_{0, inter}$ and the trait
-effect via $\alpha_d$.
+Substituting in from eqn. \ref{alpha} (leaving out the species random
+effect) this simplifies as:
+\begin{equation} \label{rhoequ2}
+\alpha_{0,inter} - \alpha_{0,intra} + \alpha_d \vert t_j - t_i \vert
+\end{equation}
+
+Thus, the average differences between inter and intraspecific competition are affected only by the difference between $\alpha_{0, intra}$ and $\alpha_{0, inter}$ and by trait dissimilarity via $\alpha_d$ (see Figure 3. in Extended Data for the results). 
+
 
 \section{Data}\label{data}
 
@@ -346,7 +334,7 @@ species' maximum height as the 99\% quantile of observed values (for
 France, US, Spain, Switzerland). For Sweden we used the estimate from
 the French data set and for Canada we used the estimate from the US data
 set. Otherwise, we extracted height measurements from the TRY database. We were
-not able to account for trait variability within species between sites.
+not able to account for trait variability within species.
 
 For each focal tree, our approach required us to also account for the
 traits of all competitors present in the neighbourhood. Most of our
@@ -357,13 +345,13 @@ data was available, we used the mean of the species present in the
 country. However, we restricted our analysis to plots where (i) the
 percentage of basal area contributed by trees with no species level trait data was
 less than 10\%, and (ii) the
-percentage of basal area of trees with no species and genus level trait data was
+percentage of basal area of trees with neither species nor genus level trait data was
 less than 5\%.
 
 \newpage
 \clearpage
 
-\section{References}\label{references}
+% \section{References}\label{references}
 
 \bibliographystyle{naturemag}
 \bibliography{references}
diff --git a/docs/paper/image/fig1f_intra.svg b/docs/paper/image/fig1f_intra.svg
index 67de937e4204f8210da7c180b142fdf2c90821ae..1bc4b5397805f430e19809b409c79177ecc22ab4 100644
--- a/docs/paper/image/fig1f_intra.svg
+++ b/docs/paper/image/fig1f_intra.svg
@@ -18,7 +18,7 @@
    width="992.5"
    height="760"
    xml:space="preserve"
-   sodipodi:docname="fig1f_intra.eps"><sodipodi:namedview
+   sodipodi:docname="fig1f_intra.svg"><sodipodi:namedview
      pagecolor="#ffffff"
      bordercolor="#666666"
      borderopacity="1"
@@ -32,15 +32,15 @@
      id="namedview4"
      showgrid="false"
      inkscape:zoom="1.9865664"
-     inkscape:cx="601.12624"
-     inkscape:cy="136.83341"
+     inkscape:cx="517.56498"
+     inkscape:cy="177.1039"
      inkscape:window-x="65"
      inkscape:window-y="24"
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      inkscape:current-layer="g10" /><metadata
      id="metadata8"><rdf:RDF><cc:Work
          rdf:about=""><dc:format>image/svg+xml</dc:format><dc:type
-           rdf:resource="http://purl.org/dc/dcmitype/StillImage" /><dc:title></dc:title></cc:Work></rdf:RDF></metadata><defs
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" /><dc:title /></cc:Work></rdf:RDF></metadata><defs
      id="defs6"><marker
        inkscape:stockid="Arrow2Mend"
        orient="auto"
@@ -292,42 +292,12 @@
          y="-246.84271"
          x="502.45032"
          id="tspan4111-0-7-0"
-         sodipodi:role="line">Direct trait </tspan></text>
+         sodipodi:role="line">Trait link </tspan></text>
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diff --git a/docs/paper/paper.tex b/docs/paper/paper.tex
index 890a44719815280966d897cc31a41b21e317bbc0..31b704b8fcb0d919d186ee7a3bd1aa0654d63ea7 100644
--- a/docs/paper/paper.tex
+++ b/docs/paper/paper.tex
@@ -1,6 +1,7 @@
 \documentclass[a4paper,11pt]{article}
 \usepackage{lmodern}
  \usepackage{amssymb,amsmath}
+\usepackage{longtable}
 \usepackage{ifxetex,ifluatex}
 \usepackage{fixltx2e} % provides \textsubscript
 \ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
@@ -103,7 +104,7 @@
 \affil[2]{Univ. Grenoble Alpes, F-38402 Grenoble, France}
 \affil[3]{Department of Biological Sciences, Macquarie University NSW 2109, Australia}
 \affil[4]{Forest Ecology and Conservation Group, Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK}
-\affil[5]{Mathematical Sciences Institute, The Australian National University, Canberra, Australia}
+\affil[5]{Mathematical Sciences Institute, Australian National University, Canberra, Australia}
 \affil[6]{National Herbarium of New South Wales, Royal Botanic Gardens and Domain Trust, Sydney, NSW, Australia}
 \affil[7]{Environmental Research Institute, School of Science, University of Waikato, Hamilton, New Zealand}
 \affil[8]{Forest Ecology and Forest Management Group, Wageningen University, Wageningen, The Netherlands}
@@ -143,34 +144,36 @@
 \begin{document}
 \maketitle
 
-\section{Summary paragraph outline (224/max 300 but rather 200)}\label{summary-paragraph-outline}
+\section{Summary paragraph outline}\label{summary-paragraph-outline}
 
+% (235/max 300 but rather 200)
 Phenotypic traits and their associated trade-offs have been shown to have globally consistent
 effects on individual plant physiological
 functions\citep{Westoby-2002, Wright-2004, Chave-2009}, but
 it has remained unclear how these effects scale up to
 influence competition -- a key driver of
 community assembly in terrestrial
-vegetation\citep{Keddy-1989}. Here we use growth data from
+vegetation\citep{Keddy-1989}. Here we use growth data, from
 more than 3 million trees in more than 140000 plots across the world, to show how three key functional traits -- wood density, specific leaf area
 and maximum height -- consistently influence competitive interactions.
-Fast maximum growth of a focal tree was correlated with low wood
-density in all biomes and with high specific leaf area in most biomes. Low wood density
+Fast maximum growth of a species was correlated negatively with its
+wood
+density in all biomes and positively with its specific leaf area in most biomes. Low wood density
 was also correlated with a low ability to tolerate competition and a
-low competitive impact on neighbours (competitive effect), and high
-specific leaf area with a low competitive effect. Thus traits generate trade-offs between performances with \emph{vs.} without
-competition, a fundamental ingredient in the classic hypothesis
+low competitive impact on neighbours (competitive effect), while high
+specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with \emph{vs.} without
+competition, a fundamental ingredient in the classical hypothesis
 that coexistence of plant species is enabled via differentiation in
-successional strategy\citep{Rees-2001}. Competition within species was
-stronger than between species, but the degree of trait dissimilarity
+their successional strategies\citep{Rees-2001}. Competition within species was
+stronger than between species, but an increase in trait dissimilarity
 between species had little influence in weakening competition. No
 benefit of dissimilarity was detected for specific leaf area and wood density and
 only a weak benefit for maximum height. Our trait-based approach to
 modelling competition makes generalisation possible across the forest
 ecosystems of the globe and their highly diverse species composition.
 
-\section{Main text (1528/max 1500)}\label{main-text}
-
+\section{Main text}\label{main-text}
+% (1554/max 1500)
 Phenotypic traits are considered fundamental drivers of community
 assembly and thus species diversity \citep{Westoby-2002, Adler-2013}. The effects of traits on individual
 plant physiologies and functions are increasingly understood, and have been shown to be underpinned
@@ -179,25 +182,25 @@ by well-known and globally consistent trade-offs
 For instance, traits such as wood density and specific leaf area capture
 trade-offs between the construction cost and longevity or strength of
 wood and leaf tissues\citep{Wright-2004, Chave-2009}.
-In contrast, we still have limited understanding of how trait-based trade-offs translate into
+In contrast, we still have limited understanding of how such trait-based trade-offs translate into
 competitive interactions between species,
-particularly for long-lived forest ecosystems. Competition is a key
+particularly for long-lived organisms such as trees. Competition is a key
 filter through which ecological and evolutionary success is
-determined\citep{Keddy-1989}. A long-standing hypothesis is that the intensity of competition decreases as two species diverge 
+determined\citep{Keddy-1989}. A long-standing hypothesis is that the intensity of competition decreases as two species diverge
 in trait values\citep{MacArthur-1967} (trait dissimilarity). The few
 studies\citep{Uriarte-2010, Kunstler-2012, HilleRisLambers-2012, Lasky-2014, Kraft-2015, Mayfield-2010}
 that have explored links between traits and competition have shown
-that they were more complex; however, as particular trait values may also
+that linkages were more complex than this, as particular trait values may also
 confer competitive advantage independently from trait dissimilarity\citep{Mayfield-2010, Kunstler-2012, Kraft-2014}. This
 distinction is fundamental for species coexistence and the
 local mixture of traits. If neighbourhood competition is driven
 mainly by trait dissimilarity, this will favour a wide spread of trait
-values at local scale. In contrast, if neighbourhood interactions are mainly
+values at a local scale. In contrast, if neighbourhood interactions are mainly
 driven by the competitive advantage associated with particular trait
 values, those trait values should be strongly selected at the local
 scale, with coexistence operating at larger spatial or temporal
-scales\citep{Mayfield-2010, Adler-2013}. Yet
-empirical investigations have been limited to a few particular
+scales\citep{Mayfield-2010, Adler-2013}. Empirical investigations have
+been limited so far to a few particular
 locations, restricting our ability to find general mechanisms that link traits and competition in the main vegetation types
 of the world.
 
@@ -208,14 +211,14 @@ unprecedented scale covering all the major forest biomes on Earth (Fig.
 \ref{ilustr}a), and (ii) the influence of traits on competition is
 partitioned among four fundamental mechanisms (Fig. \ref{ilustr}b,c) as
 follows. A competitive advantage for trees with some trait values compared to
-others can arise through: (1) permitting faster maximum growth in absence
+others can arise through: (1) permitting faster maximum growth in the absence
 of competition\citep{Wright-2010}; (2) exerting a stronger
 competitive
 effect\citep{Goldberg-1996, Gaudet-1988},
 meaning that competitor species possessing those traits suppress more strongly the
 growth of their neighbours; or (3) permitting a better tolerance of
-competition (also referred to as competitive `response' in
-Goldberg\citep{Goldberg-1996}), \textit{i.e.} growth
+competition (or competitive `response' in
+Goldberg\citep{Goldberg-1996}), meaning that growth
 of species possessing those traits is less affected by competition
 from neighbours. Finally, (4) competition can promote trait
 diversification, if increasing trait dissimilarity between species
@@ -223,123 +226,121 @@ reduces interspecific competition compared to intraspecific competition \citep{M
 four mechanisms are connected to three key traits that describe plant
 strategies
 worldwide\citep{Westoby-2002, Wright-2004, Chave-2009}. These traits are
-wood density (an indicator of a trade-off between stem construction cost
-and strength), specific leaf area (SLA, an indicator of a trade-off
-between leaf construction cost and leaf longevity), and maximum height
-(an indicator of a trade-off between access to light and early
+wood density (an indicator of a trade-off in stems between growth
+and strength), specific leaf area (SLA, an indicator of a trade-off in
+leaves between cheap construction cost and leaf longevity), and maximum height
+(an indicator of a trade-off between sustained access to light and early
 reproduction). We analyse basal area growth (annual increase in the
 area of the cross section of tree trunk at 1.3 m height) of more than 3
 million trees from more than 2500
-species, across all major forested biomes of the earth (Fig. \ref{ilustr}). Species mean trait values were extracted from the global TRY
-data base\citep{Kattge-2011, Niinemets-2001} and local
-data bases (see Methods). We analysed how basal area growth of each
+species, across all major forested biomes of the earth (Fig. \ref{ilustr}). Species mean trait values were extracted from local
+data bases and the global TRY
+data base\citep{Kattge-2011} (see Methods). We analysed how basal area growth of each
 individual tree was reduced by the abundance of competitors in its local
 neighbourhood\citep{Uriarte-2004} (measured as the sum of
 basal areas of competitors in m$^2$ ha$^{-1}$), accounting for traits of both
 the focal tree and its competitors. This analysis allowed effect sizes
-to be estimated for each of the four pathways outlined above (Fig. \ref{ilustr}c).
+to be estimated for each of the four mechanisms outlined above (Fig. \ref{ilustr}c).
 
 Across all biomes the strongest driver of individual growth was the
 total abundance of neighbours,
 irrespective of their traits (parameters $\alpha_{0 intra}$
-and $\alpha_{0 inter}$ in Fig. \ref{res1}). Values were strongly positive, indicating neighbours were reductions in growth due to competition
-rather than facilitative effect. The main effects of traits were that some trait values led
+and $\alpha_{0 inter}$ in Fig. \ref{res1}). Values were strongly
+positive, indicating neighbours had competitive rather than facilitative effects. The main effects of traits were that some trait values led
 to a competitive advantage compared to others through two main
-mechanisms. First, traits of the focal species had direct influences on its
+mechanisms. First, traits of the focal species had influences on its
 maximum growth -- \emph{i.e.} in the absence of competition -- (parameter $m_1$ in Fig.
 \ref{res1} and Extended Data Table 3). The fastest growing species
 had low wood density and high SLA, though the confidence interval
-spanned zero in two out of five biomes for SLA (Fig. \ref{res1}). This is in agreement with previous studies\citep{Wright-2010} of
+intercepted zero in two out of five biomes for SLA (Fig. \ref{res1}). This
+is in agreement with previous studies\citep{Poorter-2008, Wright-2010} of
 adult trees reporting a strong link between maximum growth and wood
-density but a weak correlation for SLA. Second,
+density but a weaker link for SLA. Second,
 some trait values were associated with species having stronger
 competitive effects, or better tolerance of competition (Fig.
 \ref{res1}; Extended
 Data Table 3). High wood density was correlated with better tolerance of
-competition from neighbours and with stronger competitive effect upon
-neighbours, whereas low SLA was correlated only with stronger
+competition from neighbours and with a stronger competitive effect upon
+neighbours, whereas low SLA was correlated only with a stronger
 competitive effect. This agrees with studies reporting that high wood density species are
 more shade-tolerant\citep{Wright-2010} and have deeper and wider
-crowns\citep{Poorter-2006a, Aiba-2009} hence potentially
-higher light interception (further detail in Supplementary Discussion). It has been proposed that that
-shorter leaf lifespan associated with high SLA results in lower standing
-leaf area and lower light interception\citep{Niinemets-2010}, that may explained the influence of
-SLA on competitive effect, but this pattern is still unclear. We found
-no correlation of maximum height with any mechanisms linked to
-competitive advantage. Current height of an individual is of course an influence on light interception, a key process in competition\citep{Mayfield-2010}, but maximum
-height of a species reflects something more strategic. Possibly
-maximum height would have stronger effects on long-term
-population level outcomes than it did on short-term basal area growth\citep{Adams-2007}.
-After separating trait independent difference between intraspecific
-competition \textit{vs.} interspecific competition, trait dissimilarity
-had little effect on competition between species (Fig. \ref{res1}). Only maximum height dissimilarity between focal and
-neighbour species led to a weak decrease in competitive suppression of
+crowns\citep{Poorter-2006a, Aiba-2009}, hence potentially
+higher light interception (further detail in Supplementary Discussion). The
+shorter leaf lifespan associated with high SLA results in lower
+leaf mass fraction\citep{Niinemets-2010}. The low competitive effect
+associated with high SLA species could thus result from a lower light
+interception but few data are available on this link\citep{Niinemets-2010}. Maximum height was weakly
+negatively correlated with tolerance to competition in three out of
+five biomes, supporting the idea that sub-canopy trees are more
+shade-tolerant\citep{Poorter-2006a}. We found however no correlation
+between maximum height and competitive effect. Current height of an
+individual has of course an influence on light interception, a key
+process in competition\citep{Mayfield-2010}. But maximum
+height of a species reflects its long-term strategy and
+would possibly have stronger effects on long-term
+population level competition outcomes than it did on short-term basal area
+growth\citep{Adams-2007}.
+
+After separating trait-independent differences between intraspecific \textit{vs.} interspecific competition, trait dissimilarity
+had little effect on competition between species
+(Fig. \ref{res1}). Only dissimilarity in maximum height between focal and
+neighbour species led to a weak, but consistent, decrease in competitive suppression of
 tree growth (Fig. \ref{res1}). Mechanisms explaining this effect are
-unknown, but could possibly result from complementary 
-architectures\citep{Sapijanskas-2014, Jucker-2015}. Ratios of interspecific over intraspecific competition between
-pairs of species -- a key indicator of processes stabilising coexistence -- were thus
-only weakly related to trait dissimilarity (see Extended Data Fig
-3). Trait dissimilarity effects have often been considered as a key
-mechanism by which traits might affect competition. But this has
-rarely supported with
-field data\citep{Mayfield-2010}, and our analysis confirms at
-global scale that trait dissimilarity effect are weak or
-absent. It remains unclear why the trait-independent  
-competitive effects (per unit basal area) of conspecifics is higher than 
-that of heterospecifics. Higher loads of shared specialised
-pathogens\citep{Bagchi-2014} could plausibly contribute. We emphasise that
-other traits may show stronger trait dissimilarity effects, but we do not
-currently have trait data that might capture such an effect.  
-
-Analyses that allowed for different effects among biomes did not show
-strong evidence for any particular biome behaving consistently
+poorly understood, but could possibly result from complementary
+crown architectures\citep{Sapijanskas-2014, Jucker-2015}. The average differences in strength of interspecific \textit{vs.} intraspecific competition between two species -- a key indicator of processes that could stabilise coexistence -- were thus
+only weakly related to trait dissimilarity (Extended Data Fig.
+3). Trait dissimilarity effects are widely considered to be a key
+mechanism by which traits affect competition\citep{Mayfield-2010}, but our analysis shows at
+global scale that trait dissimilarity effects are weak or
+absent. It remains unclear why the trait-independent competitive effects are higher within species than
+between species. Higher loads of shared specialised
+pathogens\citep{Bagchi-2014} could plausibly contribute. Other traits or combinations of traits (see Kraft \textit{et al.}\citep{Kraft-2015} may show stronger trait dissimilarity effects, but we
+currently lack the trait data to capture such effects.
+
+Analyses allowing for different effects among biomes did not show
+any particular biome behaving consistently
 differently from the others (Fig. \ref{res1}). This lack of context
-dependence in trait effects may seem surprising, but on the other hand
-competition for light is important in forests everywhere, and it is
-satisfying to find consistency across forest types (further details in Supplementary Discussion).
+dependence in trait effects may seem surprising, but reinforces the idea that competition for light is important in most forests, and this may
+explain why we find consistency across such diverse forest types (further details in Supplementary Discussion).
 
 Our global study supports the hypothesis that trait values
 favouring high tolerance of competition or high competitive effects also
 render species slow growing in the absence of competition across all
-forested biomes (Fig. \ref{res3}). This trait-based trade-off is a key ingredient in the classical model for successional
-coexistence of species in forests, where fast-growing species are more abundant
-in early successional stages where competitors are absent, and are
+forested biomes (Fig. \ref{res3}). This trait-based trade-off is a key
+ingredient in the classical model of successional
+coexistence in forests, where fast-growing species are more abundant
+in early successional stages where competitors are absent or rare, and are
 later replaced by slow-growing species in late successional stages where
 competitors become more abundant\citep{Rees-2001}. Human or
-natural disturbances are conspicuous in all the forests analysed, and
-so successional
-dynamics are likely to be on going in all these sites (see
-data description in Supplementary Methods). These trade-offs were present for wood
+natural disturbances are conspicuous in all the forests analysed, hence successional
+dynamics are likely to be present in all these sites (see Supplementary Methods). This trade-off was strongest for wood
 density, with high wood density associated with slow potential
 growth rate but high tolerance to competition and strong competitive effect
 (Fig. \ref{res3}). A similar pattern was present, though less clear, for SLA. High SLA was
-correlated with low competitive effect and marginally correlated with fast maximum
+correlated with low competitive effect but fast maximum
 growth (confidence intervals not spanning zero in three
-biomes, Fig. \ref{res1} and \ref{res3}). To the extent that long-term
-outcomes of competition at the population level are more influenced by
+biomes, Fig. \ref{res1} and \ref{res3}). Given that long-term
+outcomes of competition at the population level may be more influenced by
 tolerance of competition than by competitive effect\citep{Goldberg-1996}, SLA
 might be less influential in succession.
 
-Coordination between trait values conferring high competitive effect and
+Coordination between trait values conferring strong competitive effect and
 trait values conferring high tolerance of competition has
 been widely expected\citep{Goldberg-1996, Kunstler-2012}, but rarely
 documented\citep{Goldberg-1996, Wang-2010}.
-Wood density showed such coordination, with the
-same direction for its competitive effect and tolerance of competition
-parameters, but it was not the case for the two other traits (Fig. \ref{res1}).
+Only wood density showed such coordination, as it was correlated with both competitive effect and tolerance of competition in the same direction (Fig. \ref{res1}).
 
 The globally consistent links that we report here between traits and
 competition have considerable promise for predicting species
-interactions governing forest communities across different vegetation
-types and different continents of the globe. The analysis presented
-here demonstrates that trait dissimilarity is not the major determinant of
+interactions governing forest communities across different forest
+biomes and continents of the globe. Our analysis demonstrates that trait dissimilarity is not the major determinant of
 local-scale competitive impacts on tree growth, at least for these three
 traits. In contrast, the trait-based trade-off in performance with \textit{vs.} without
-competition, that we report, could promote
+competition, reported here, could promote
 coexistence of species with diverse traits, provided disturbances
 create a mosaic of successional stages. A challenge for the
-future is moving beyond tree growth to analyse all key demographic rates
-and life history stages of trees, to analyse how traits influence
+future is to move beyond growth to analyse all key demographic rates
+and life history stages, to analyse how traits influence
 competitive outcomes at the population
 level and control stable coexistence.
 
@@ -361,7 +362,7 @@ The authors declare no competing financial interests.
 
 \newpage
 
-\section{FIGURES}\label{figures}
+\section{MAIN FIGURES}\label{figures}
 
 \begin{figure}[htbp]
 \centering
@@ -380,15 +381,15 @@ trait values of the focal tree ($t_f$), and the abundance (measured as
 the sum of their basal areas) and traits values of competitor species ($t_c$)
 influenced basal area growth of the focal tree. Species maximum growth (red) was
 influenced by trait of the focal tree ($m_0 + m_1 \, t_f$, with $m_0$
-maximum growth independent of trait). Reduction
-in growth per unit basal area of competitors ($-\alpha_{c,f}$, black) was
-modelled as the sum of growth reduction independent of trait (blue) by conspecific
-($\alpha_{0 \, intra}$) and heterospecific ($\alpha_{0 \, inter}$), the effect of competitor traits ($t_c$) on their
+maximum growth independent of the trait). Reduction
+in growth per unit basal area of competitors ($-\alpha_{f,c}$, black) was
+modelled as the sum of growth reduction independent of the trait (blue) by conspecific
+($\alpha_{0 \, intra}$) and heterospecific ($\alpha_{0 \, inter}$) competitors, the effect of competitor traits ($t_c$) on their
 competitive effect ($\alpha_e$), the effect of the focal tree's traits
 ($t_f$) on its tolerance of competition ($\alpha_t$), and the effect
 of trait dissimilarity between the focal tree and its competitors
 ($\vert t_c-t_f \vert$) on competition ($\alpha_d$). The parameters $m_0, m_1, \alpha_{0 \, intra}, \alpha_{0 \, inter}, \alpha_e, \alpha_t$ and
-$\alpha_d$ are fitted from data using maximum likelihood method.
+$\alpha_d$ are fitted from data using a maximum likelihood method.
 \label{ilustr}}
 \end{figure}
 
@@ -400,7 +401,8 @@ $\alpha_d$ are fitted from data using maximum likelihood method.
 \caption{\textbf{Trait-dependent and trait-independent effects on
 maximum growth and competition across the globe and their variation among biomes.}
 Standardized regression coefficients for growth models, fitted
-separately for each trait (points: mean estimates and lines: 95\%
+separately for wood density (a), specific
+leaf area (b) and maximum height (c) (points: mean estimates and lines: 95\%
 confidence intervals). Black points and lines represent global estimates
 and coloured points and lines represent the biome level estimates. The
 parameter estimates represent: effect of focal tree's trait value on maximum
@@ -414,7 +416,7 @@ trait dissimilarity between the focal tree and its competitors \(\alpha_d\)
 (negative values indicate that higher trait dissimilarity leads to a
 lower reduction of the growth of the focal tree), and the
 trait-independent competitive effect of conspecific
-$\alpha_{0 \, intra}$ and heterospecific $\alpha_{0 \, inter}$, . Tropical rainforest
+$\alpha_{0 \, intra}$ and heterospecific $\alpha_{0 \, inter}$. Tropical rainforest
 and tropical seasonal forest were merged together as tropical forest,
 tundra was merged with taiga, and desert was not included as too few
 plots were available (see Fig 1a. for biomes definitions).
@@ -426,9 +428,9 @@ plots were available (see Fig 1a. for biomes definitions).
 \begin{figure}[htbp]
 \centering
 \includegraphics{../../figs/figres4t_TP_intra.pdf}
-\caption{\textbf{Trade offs between maximum growth and competitive
-effects or competitive tolerance parameters of wood density and specific
-leaf area predicted by the global traits models.} Variation of maximum growth
+\caption{\textbf{Variation of maximum growth, competitive
+effects and competitive tolerance with wood density (a, b and c) and specific
+leaf area (d, e and f) predicted by global traits models.} Variation of maximum growth
 (\(m_1 \, t_f\)), tolerance of competition (\(\alpha_t \, t_f\)) and
 competitive effect ($\alpha_e \, t_c$)
 parameters with wood density (first column) and specific leaf area
@@ -443,9 +445,309 @@ area represents the 95\% confidence interval of the prediction
 \newpage
 \clearpage
 
-\section{References}\label{references-max-30}
+\section{METHODS}\label{methods}
+
+\subsection{Model and analysis}\label{model-and-analysis}
+
+To examine the link between competition and traits we used a
+neighbourhood modelling
+framework\citep{Canham-2006, Uriarte-2010, Ruger-2012, Kunstler-2012, Lasky-2014}
+to model the growth of a focal tree of species \(f\) as a product of its
+maximum growth (determined by its traits and size) together with
+reductions due to competition from individuals growing in the local
+neighbourhood (see definition below). Specifically, we assumed a relationship of the form
+
+\begin{equation} \label{G1}
+G_{i,f,p,s,t} = G_{\textrm{max} \, f,p,s} \, D_{i,f,p,s,t}^{\gamma_f} \,  \exp\left(\sum_{c=1}^{N_i} {-\alpha_{f,c} B_{i,c,p,s}}\right),
+\end{equation}
+where:
+\begin{itemize}
+\itemsep1pt\parskip0pt\parsep0pt
+\item
+  \(G_{i,f,p,s,t}\) and \(D_{i,f,p,s,t}\) are the annual basal area
+  growth and diameter at breast height of individual \(i\) from species
+  \(f\), plot or quadrat (see below) \(p\), data set \(s\), and census $t$,
+\item
+  \(G_{\textrm{max} \, f,p,s}\) is the maximum basal area growth for species \(f\) on plot or quadrat \(p\) in data set \(s\), i.e.~in
+  absence of competition,
+\item
+  \(\gamma_f\) determines the rate at which growth changes with size for
+  species \(f\), modelled with a normally distributed random effect of
+  species \(\varepsilon_{\gamma, f}\) {[}as
+  \(\gamma_f = \gamma_0 + \varepsilon_{\gamma, f}\) where
+  \(\varepsilon_{\gamma, f} \sim \mathcal{N} (0,\sigma_{\gamma})\) -- a
+  normal distribution of mean 0 and standard deviation $\sigma_{\gamma}${]}
+\item
+  \(\alpha_{f,c}\) is the per unit basal area effect of individuals from
+  species \(c\) on growth of an individual in species \(f\),
+\item
+  \(B_{i,c,p,s}= 0.25\, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s,t}^2\) is
+  the sum of basal area of all individuals competitor trees \(j\) of the species
+  \(c\) within the local neighbourhood
+  of the tree $i$ in
+  plot \(p\), data
+  set \(s\) and census $t$, where \(w_j\) is a constant based on
+  neighboorhood size for tree $j$ depending on the data set (see
+  below). Note that \(B_{i,c,p,s}\) include all trees of species $c$
+  in the local neighbourhood excepted the tree
+  \(i\), and
+\item
+  \(N_i\) is the number of competitor species in the local
+  neighbourhood of focal tree $i$.
+\end{itemize}
+
+Values of \(\alpha_{f,c}> 0\) indicate competition, whereas
+\(\alpha_{f,c}\) \textless{} 0 indicates facilitation.
+
+Log-transformation of equ. \ref{G1} leads to a linearised model of the
+form
+
+\begin{equation} \label{logG1}
+\log{G_{i,f,p,s,t}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s,t}} +  \sum_{c=1}^{N_i} {-\alpha_{f,c} B_{i,c,p,s}}.
+\end{equation}
+
+To include the effects of traits on the parameters of the growth model we build on previous studies that explored the role of traits for tree performances and tree competition\citep{Uriarte-2010, Kunstler-2012, Lasky-2014}. We modelled the effect of traits, one trait at a time.
+The effect of a focal species' trait value, \(t_f\), on its
+maximum growth was included as:
+
+\begin{equation} \label{Gmax}
+\log{G_{\textrm{max} \, f,p,s}} = m_{0} + m_1 \, t_f + m_2 \, MAT +
+m_3 \, MAP + \varepsilon_{G_{\textrm{max}}, f} + \varepsilon_{G_{\textrm{max}}, p} + \varepsilon_{G_{\textrm{max}}, s}.
+\end{equation}
+
+Here \(m_0\) is the average maximum growth, \(m_1\) gives the effect of
+the focal species trait, $m_2$ and $m_3$ the effects of mean annual temperature
+$MAT$ and sum of annual precipitation $MAP$ respectively, and \(\varepsilon_{G_{\textrm{max}}, f}\),
+\(\varepsilon_{G_{\textrm{max}}, p}\), \(\varepsilon_{G_{\textrm{max}}, s}\)
+are normally distributed random effects for species \(f\), plot or
+quadrat \(p\) (see below), and data set \(s\) {[}where
+\(\varepsilon_{G_{\textrm{max}, f}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, f}})\);
+\(\varepsilon_{G_{\textrm{max}, p}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, p}})\)
+and
+\(\varepsilon_{G_{\textrm{max}, s}} \sim \mathcal{N} (0,\sigma_{G_{\textrm{max}, s}})\){]}.
+
+Previous studies have proposed various decompositions of the competition parameter into key trait-based processes\footnote{Different approaches have been proposed to model $\alpha$ from traits. In one of the first studies Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha =
+\alpha_0 + \alpha_d \vert t_f-t_c \vert$. Then Kunstler et al.\citep{Kunstler-2012} used two different models: $\alpha = \alpha_0 + \alpha_d \vert t_f-t_c \vert$ or $\alpha =
+\alpha_0 + \alpha_h ( t_f-t_c )$. Finally, Lasky et
+al.\citep{Lasky-2014} developed a single model including multiple processes as $\alpha =
+\alpha_0 + \alpha_t t_f +\alpha_h ( t_f-t_c ) + \alpha_d \vert t_f-t_c
+\vert$. In our study, we extended this last model. We considered that it was clearer to split
+$\alpha_h (t_f - t_c)$ into $\alpha_t t_f + \alpha_e t_c$, which is
+equivalent to the hierarchical distance if $\alpha_t = - \alpha_e$
+(thus avoiding replication of $t_f$ effect through both $\alpha_h$ and
+$\alpha_t$). We also included two $\alpha_0$, one for intra and one for
+interspecific
+competition.}, and here we extended the approach of the most recent study\citep{Lasky-2014}. As presented in Fig. 1, competitive
+interactions were modelled using an equation of the form\footnote{For
+  fitting the model, the equation of \(\alpha_{f,c}\) was developed with
+  species basal area in term of community weighted means of (i) trait values of competitors and (i) absolute trait distance between focal species and its competitors.}:
+
+\begin{equation} \label{alpha}
+\alpha_{f,c}= \alpha_{0,f,intra} \, C + \alpha_{0,f,inter} \, (1-C) - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
+\end{equation}
+
+where:
+
+\begin{itemize}
+\itemsep1pt\parskip0pt\parsep0pt
+\item
+  $\alpha_{0,f,intra}$ and $\alpha_{0,f,inter}$ are respectively
+  \textbf{intraspecific and average interspecific trait independent competition} for the focal
+  species \(f\), modelled with a normally distributed random effect of
+  species \(f\) and each with normally distributed random effect of data set
+  \(s\) {[}as
+  \(\alpha_{0,f} = \alpha_0 + \varepsilon_{\alpha_0, f}+ \varepsilon_{\alpha_0, s}\),
+  where \(\varepsilon_{\alpha_0, f} \sim \mathcal{N} (0,\sigma_{\alpha_0, f})\) and
+  \(\varepsilon_{\alpha_0, s} \sim \mathcal{N} (0,\sigma_{\alpha_0, s})\){]}. $C$ is a binary variable taking the value one for $f=c$ (conspecific) and zero for $f \neq c$ (heterospecific),
+\item
+  \(\alpha_t\) is the \textbf{tolerance of competition} by the focal
+  species, i.e.~change in competition tolerance due to traits \(t_f\) of
+  the focal tree with a normally distributed random effect of data set
+  \(s\) included
+  {[}\(\varepsilon_{\alpha_t,s} \sim \mathcal{N} (0,\sigma_{\alpha_t})\){]},
+\item
+  \(\alpha_{e}\) is the \textbf{competitive effect}, i.e.~change in
+  competition effect due to traits \(t_c\) of the competitor tree with a
+  normally distributed random effect of data set \(s\) included
+  {[}\(\varepsilon_{\alpha_i,s} \sim \mathcal{N} (0,\sigma_{\alpha_i})\){]}, and
+\item
+  \(\alpha_d\) is the effect of \textbf{trait dissimilarity}, i.e.~change
+  in competition due to absolute distance between traits
+  \(\vert{t_c-t_f}\vert\) with a normally distributed random effect of
+  data set \(s\) included
+  {[}$\varepsilon_{\alpha_d,s} \sim \mathcal{N} (0,\sigma_{\alpha_d})${]}.
+\end{itemize}
+
+Estimating separate $\alpha_0$ for intra and interspecific competition allowed us to account for trait-independent differences in interactions with conspecifics and heterospecifics. We also explored a simpler version of the model where trait-independent competitive effects were pooled (i.e. there was a single value for $\alpha_0$), as most previous studies have generally not made this distinction, using the following equation:
+
+\begin{equation} \label{alpha2}
+\alpha_{f,c}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_d \, \vert t_c-t_f \vert
+\end{equation}
+
+In this alternative model any differences between intra and interspecific competition do enter into trait dissimilarity effects, with a trait dissimilarity of zero attached to them. This may lead to an overestimation of the trait dissimilarity effect. Results for this model
+are presented in Supplementary Results.
+
+Eqs. \ref{logG1}-\ref{alpha} were then fitted to empirical estimates of
+growth based on change in diameter between census $t$
+and $t+1$ (respectively at year $y_t$ and $y_{t+1}$), given by
+
+\begin{equation} \label{logGobs} G_{i,f,p,s,t} = 0.25 \pi
+  \left(D_{i,f,p,s,t+1}^2 - D_{i,f,p,s,t}^2\right)/(y_{t+1} - y_t).
+\end{equation}
+
+To estimate standardised coefficients (one type of standardised effect
+size)\citep{Schielzeth-2010}, response and explanatory variables
+were standardized (divided by their standard deviations) prior to
+analysis. Trait and diameter were also centred to facilitate
+convergence. The models were fitted using the \(lmer\) routine in
+the lme4 package \citep{Bates-2014}
+in the R statistical environment\citep{RTeam-2014}. We fitted two
+versions of each model. In the first
+version parameters \(m_{0}, m_1, \alpha_0,\alpha_t,\alpha_i,\alpha_d\)
+were estimated as constant across all biomes. In the second version, we
+allowed
+different fixed estimates of these parameters for each biome. This
+enabled us to explore variation among biomes. Because some biomes had
+few observations, we merged those with biomes with similar climates. Tundra was
+merged with taiga, tropical rainforest and tropical seasonal forest were
+merged into tropical forest, and deserts were not included in this final
+analysis as too few plots were available. To evaluate whether our results
+were robust to the random effect structure we also explored a model
+with a random effect
+attached to parameters both for the data set and for a local ecoregion using
+the K{\"o}ppen-Geiger ecoregion\citep{Kriticos-2012} (see
+Supplementary Results).
+
+\subsubsection{Estimating the effect of traits on the average differences between intra and interspecific competition}\label{intrainter}
+
+Differences between inter and intraspecific competition have long been considered key to community assembly and species coexistence\citep{Connell-1983, Chesson-2000, Chesson-2012, Kraft-2015, Godoy-2014}. Our estimated growth model allowed us to estimate the average inter and intraspecific competition from trait-independent and trait-dependent processes. Using eqn. \ref{alpha}, we can predict for any combination of two values of trait $t_i$ and $t_j$ the interspecific
+($\alpha_{t_i,t_j}$ and $\alpha_{t_j,t_i}$) and
+intraspecific ($\alpha_{t_i,t_i}$ and $\alpha_{t_j,t_j}$)
+competition competition of typical (or mean) species (thus leaving out the random species effects). We can then estimate the average differences between interspecific and intraspecific competition over the two combinations using the following expression:
+
+\begin{equation} \label{rhoequ}
+\frac{(\alpha_{t_i,t_j} - \alpha_{t_i,t_i}) + (\alpha_{t_j,t_i} - \alpha_{t_j,t_j})}{2}
+\end{equation}
+
+Substituting in from eqn. \ref{alpha} (leaving out the species random
+effect) this simplifies as:
+\begin{equation} \label{rhoequ2}
+\alpha_{0,inter} - \alpha_{0,intra} + \alpha_d \vert t_j - t_i \vert
+\end{equation}
+
+Thus, the average differences between inter and intraspecific competition are affected only by the difference between $\alpha_{0, intra}$ and $\alpha_{0, inter}$ and by trait dissimilarity via $\alpha_d$ (see Figure 3. in Extended Data for the results).
+
+
+\subsection{Data}\label{data}
+
+\subsubsection{Growth data}\label{growth-data}
+
+Our main objective was to collate data sets spanning the dominant forest
+biomes of the world. Data sets were included if they (i) allowed both
+growth of individual trees and the local abundance of competitors
+to be estimated, and (ii) had good (\textgreater{}40\%) coverage for at
+least one of the traits of interest (SLA, wood density, and maximum
+height).
+
+The data sets collated fell into two broad categories: (1) national
+forest inventories (NFI), in which trees above a given diameter were
+sampled in a network of small plots (often on a regular grid) covering
+the country (references for NFI data used\citep{-b, Kooyman-2012, -e, Wiser-2001, -c, Villaescusa-1998, Villanueva-2004, Fridman-2001, -a, -d}); (2) large permanent plots (LPP) ranging in size from
+0.5-50ha, in which the x-y coordinates of all trees above a given
+diameter were recorded (references for LPP data used\citep{Condit-2013, Condit-1993, Lasky-2013, Ishihara-2011, Thompson-2002, Ouedraogo-2013, Herault-2010, Herault-2011} ). LPP were mostly located in tropical
+regions. The minimum diameter of recorded trees varied among sites from
+1-12cm. To allow comparison between data sets, we restricted our
+analysis to trees greater than 10cm. Moreover, we excluded from the
+analysis any plots with harvesting during the growth measurement period,
+that were identified as plantations, or that overlapped a forest edge.
+Finally, we randomly selected only two consecutive census dates per
+plot or quadrat to
+avoid having to account for repeated measurements (less than a third
+of the data had repeated measurements). Because human and natural disturbances are present in all these forests (see Supplementary Methods), they probably all experience successional dynamics (as indicated by the forest age distribution available in some of these sites in Supplementary Methods). See Supplementary Methods and
+Extended Data Table 1 for more details on individual data sets.
+
+Basal area growth was estimated from diameter measurements recorded
+between the two censuses. For the French NFI, these data were
+obtained from short tree cores. For all other data sets, diameter at
+breast height (\(D\)) of each individual was recorded at multiple census
+dates. We excluded trees (i) with extreme positive or negative diameter
+growth measurements, following criteria developed at the BCI site
+\citep{Condit-1993} (see the R package
+\href{http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/}{CTFS R}),
+(ii) that were palms or tree ferns, or (iii) that were
+measured at different heights in two consecutive censuses.
+
+For each individual tree, we estimated the local abundance of competitor
+species as the sum of basal area for all individuals \textgreater{} 10cm
+diameter within a specified neighbourhood. For LPPs, we defined the
+neighbourhood as being a circle with 15m radius. This value was selected
+based on previous studies showing the maximum radius of interaction to
+lie in the range
+10-20m\citep{Uriarte-2004, Uriarte-2010}. To avoid
+edge effects, we also excluded trees less than 15m from the edge of a
+plot. To account for variation of abiotic conditions within the LPPs, we
+divided plots into regularly spaced 20x20m quadrats and included a
+random quadrat effect in the model (see above).
+
+For NFI data coordinates of individual trees within plots were generally
+not available, thus neighbourhoods were defined based on plot size. In
+the NFI from the United States, four sub-plots of 7.35m located within
+20m of one another were measured. We grouped these sub-plots to give a
+single estimate of the local competitor abundance. Thus, the
+neighbourhoods used in the competition analysis ranged in size from
+10-25 m radius, with most plots 10-15 m radius. We included variation in
+neighbourhood size in the constant $w_j$ to compute competitor basal
+area in $m^2/ha$.
+
+We extracted mean annual temperature (MAT) and mean annual sum of
+precipitation (MAP) from the \href{http://www.worldclim.org/}{worldclim}
+data base \citep{Hijmans-2005}, using the plot latitude and
+longitude. MAT and MAP data were then used to classify plots into
+biomes, using the diagram provided by Ricklefs\citep{Ricklefs-2001}
+(after Whittaker).
+
+\subsubsection{Traits}\label{traits}
+
+Data on species functional traits were extracted from existing sources.
+We focused on wood density, species specific leaf area (SLA) and maximum
+height, because these traits have previously been related to competitive
+interactions and are available for large numbers of species
+\citep{Wright-2010, Uriarte-2010, Ruger-2012, Kunstler-2012, Lasky-2014}
+(see Extended Data Table 2 for trait coverage). Where available we used
+data collected locally (references for the local trait data used in this analysis\citep{Wright-2010, Swenson-2012, Gourlet-Fleury-2011, Lasky-2013, Baraloto-2010}); otherwise we sourced data from the
+\href{http://www.try-db.org/}{TRY} trait data base
+\citep{Kattge-2011} (references for the data extracted from the TRY database used in this analysis\citep{Ackerly-2007, Castro-Diez-1998, Chave-2009, Cornelissen-1996, Cornelissen-1996a, Cornelissen-1997, Cornelissen-2004, Cornelissen-2003, Cornwell-2009, Cornwell-2006, Cornwell-2007, Cornwell-2008, Diaz-2004, Fonseca-2000, Fortunel-2009, Freschet-2010, Freschet-2010a, Garnier-2007, Green-2009, Han-2005, He-2006, He-2008, Hoof-2008, Kattge-2009, Kleyer-2008, Kurokawa-2008, Laughlin-2010, Martin-2007, McDonald-2003, Medlyn-1999a, Medlyn-1999, Medlyn-2001, Messier-2010, Moles-2005b, Moles-2005a, Moles-2004, Niinemets-2001, Niinemets-1999, Ogaya-2003, Ogaya-2006, Ogaya-2007, Ogaya-2007a, Onoda-2011, Ordonez-2010, Ordonez-2010a, Pakeman-2008, Pakeman-2009, Penuelas-2010, Penuelas-2010a, Poorter-2006, Poorter-2009, Poorter-2009a, Preston-2006, Pyankov-1999, Quested-2003, Reich-2008, Reich-2009, Sack-2004, Sack-2005, Sack-2006, Sardans-2008, Sardans-2008a, Shipley-2002, Soudzilovskaia-2013, Willis-2010, Wilson-2000, Wright-2007, Wright-2006, Wright-2010, Wright-2004, Zanne-2010}).
+ Local data were available for most tropical
+sites and species (see Supplementary Methods). Several of the NFI data
+sets also provided tree height measurements, from which we computed a
+species' maximum height as the 99\% quantile of observed values (for
+France, US, Spain, Switzerland). For Sweden we used the estimate from
+the French data set and for Canada we used the estimate from the US data
+set. Otherwise, we extracted height measurements from the TRY database. We were
+not able to account for trait variability within species.
+
+For each focal tree, our approach required us to also account for the
+traits of all competitors present in the neighbourhood. Most of our
+plots had good coverage of competitors, but inevitably there were some
+trees where trait data were lacking. In these cases we estimated trait
+data as follows. If possible, we used the genus mean, and if no genus
+data was available, we used the mean of the species present in the
+country. However, we restricted our analysis to plots where (i) the
+percentage of basal area contributed by trees with no species level trait data was
+less than 10\%, and (ii) the
+percentage of basal area of trees with neither species nor genus level trait data was
+less than 5\%.
+
+\newpage
+\clearpage
+
 
 \bibliographystyle{naturemag}
 \bibliography{references}
 
+\newpage
+\clearpage
+
+
+
 \end{document}
diff --git a/docs/paper/references.bib b/docs/paper/references.bib
index a2bd75b0209a8b7bb40fc29afa452f853a8c3d45..049e739b6754d7d8005261e290c5ca6fab8daabb 100644
--- a/docs/paper/references.bib
+++ b/docs/paper/references.bib
@@ -109,6 +109,16 @@
 }
 
 
+@article{Chesson-2000,
+  title = {Mechanisms of maintenance of species diversity},
+  volume = {31},
+  journal = {Annual Review of Ecology, Evolution, and Systematics},
+  author = {Chesson, P},
+  year = {2000},
+  pages = {343--366}
+}
+
+
 @incollection{Chesson-2012,
   title = {Species competition and predation},
   booktitle = {Ecological Systems},
@@ -1079,6 +1089,15 @@
   Volume                   = {89}
 }
 
+
+@article{Poorter-2015,
+	title = {How does biomass distribution change with size and differ among species? {An} analysis for 1200 plant species from five continents},
+	issn = {0028646X},
+	journal = {New Phytologist},
+	author = {Poorter, Hendrik and Jagodzinski, Andrzej M. and Ruiz-Peinado, Ricardo and Kuyah, Shem and Luo, Yunjian and Oleksyn, Jacek and Usoltsev, Vladimir A. and Buckley, Thomas N. and Reich, Peter B. and Sack, Lawren},
+	year = {2015},
+}
+
 @Article{Preston-2006,
   Title                    = {Wood density and vessel traits as distinct correlates of ecological strategy in 51 {California} coast range angiosperms},
   Author                   = {Preston, Katherine A and Cornwell, William K and {DeNoyer}, Jeanne L},
@@ -1268,9 +1287,6 @@
   pages = {806--810}
 }
 
-
-
-
 @Article{Soudzilovskaia-2013,
   Title                    = {Functional traits predict relationship between plant abundance dynamic and long-term climate warming},
   Author                   = {Soudzilovskaia, Nadejda A and Elumeeva, Tatiana G and Onipchenko, Vladimir G and Shidakov, Islam I and Salpagarova, Fatima S and Khubiev, Anzor B and Tekeev, Dzhamal K and Cornelissen, Johannes {HC}},
@@ -1291,6 +1307,21 @@
   Volume                   = {507}
 }
 
+
+
+@Article{South-2011,
+author = {Andy South},
+title = {rworldmap. A New R package for Mapping Global Data},
+journal = {The R Journal},
+year = {2011},
+volume = {3},
+number = {1},
+pages = {35-43},
+month = {June},
+issn = {2073-4859},
+}
+
+
 @Article{Swenson-2012,
   Title                    = {Temporal turnover in the composition of tropical tree communities: functional determinism and phylogenetic stochasticity},
   Author                   = {Swenson, Nathan G. and Stegen, James C. and Davies, Stuart J. and Erickson, David L. and Forero-Monta{\~n}a, Jimena and Hurlbert, Allen H. and Kress, W. John and Thompson, Jill and Uriarte, Mar{\'\i}a and Wright, S. Joseph},
@@ -1317,6 +1348,27 @@
   Volume                   = {12}
 }
 
+
+@article{Tilman-1977,
+	title = {Resource {Competition} between {Plankton} {Algae}: {An} {Experimental} and {Theoretical} {Approach}},
+	volume = {58},
+	number = {2},
+	journal = {Ecology},
+	author = {Tilman, David},
+	year = {1977},
+	pages = {338},
+}
+
+
+@incollection{Tilman-1990,
+	title = {Mechanisms of plant competition for nutrients: the elements of a predictive theory of competition.},
+	booktitle = {Perspectives on plant competition.},
+	author = {Tilman, David},
+	editor = {Grace, J. B.},
+	year = {1990},
+	pages = {117--141},
+}
+
 @Article{Uriarte-2004,
   Title                    = {A neighborhood analysis of tree growth and survival in a hurricane-driven tropical forest},
   Author                   = {Uriarte, Mar{\'\i}a and Canham, Charles D. and Thompson, Jill and Zimmerman, Jess K.},
diff --git a/scripts/analysis/results.biomes.map.R b/scripts/analysis/results.biomes.map.R
index 66abd171f3f2524724c3dc624788cf5c3c71cb35..b8d10cd0e9ec1a94490f48924c0c0f010a5c6180 100644
--- a/scripts/analysis/results.biomes.map.R
+++ b/scripts/analysis/results.biomes.map.R
@@ -60,6 +60,9 @@ dev.off()
 ## WORLD MAP
 source("R/utils/plot.R")
 source("R/utils/maps.R")
+
+
+## WORLD MAP
 col.vec <- fun.col.pch.set()$col.vec
 cols.vec <- fun.col.pch.set()$col.vec
 names.set <-  names(cols.vec)
@@ -67,37 +70,28 @@ names.set[1] <- 'Panama'
 names.set[4] <- 'Taiwan'
 names.set[6] <- 'Puerto Rico'
 names.set[7] <- 'Central African Republic'
+names.set[8] <- 'Australia'
 names.set[9] <- 'New Zealand'
 names.set[10] <- 'French Guiana'
 names.set[13] <- 'Switzerland'
+names.set[14] <- 'US'
+
 set.order.i <-  c(2, 3, 8, 9, 11, 12, 13, 14)
 set.order.b <-  c(1, 4, 5, 6, 7, 10)
 
-pdf(file.path('figs/world_map.pdf'),  width = 7, height = 5)
+pdf(file.path('figs','world_map.pdf'),  width = 8, height = 4)
 world.map.all.sites(clim,
                     add.legend=FALSE,
                     cols =  fun.col.pch.set()$col.vec)
-legend(-187, -0, xjust = 0, yjust = 0, legend =names.set[set.order.i] , col = cols.vec[set.order.i],
+legend(-187, -0, xjust = 0, yjust = 0, legend =names.set[set.order.i] , col = cols.vec[set.order.i], 
        pt.bg =  cols.vec[set.order.i] ,
        box.col = "white",bg = "white",
        pt.cex = 0.5, pch = 21, cex = 0.7, title = 'NFI')
-legend(-187, -50, xjust = 0, yjust = 0, legend =names.set[set.order.b] , col = cols.vec[set.order.b],
+legend(-187, -60, xjust = 0, yjust = 0, legend =names.set[set.order.b] , col = cols.vec[set.order.b],
        pch = 21,
        pt.bg =  cols.vec[set.order.b], pt.cex = 1.2,
        box.col = "white",bg = "white", cex = 0.7, title = 'LPP', title.adj = 0.3)
 text(67,-80, '> 3 million trees & > 2500 species', col = 'red', cex = 1.2)
-## text(-40,50, 'Canada', col = col.vec['Canada'], cex = 0.7)
-## text(-68,35, 'US', col = col.vec['US'], cex = 0.7)
-## text(-45,22, 'Puerto Rico', col = col.vec['Luquillo'], cex = 0.7)
-## text(-95,8, 'Panama', col = col.vec['BCI'], cex = 0.7)
-## text(-27,3, 'French Guiana', col = col.vec['Paracou'], cex = 0.7)
-## text(-19,40, 'Spain', col = col.vec['Spain'], cex = 0.7)
-## text(-17,48, 'France', col = col.vec['France'], cex = 0.7)
-## text(2,-7, 'Central African \nRepublic', col = col.vec['Mbaiki'], cex = 0.7)
-## text(0,70, 'Sweden', col = col.vec['Sweden'], cex = 0.7)
-## text(25,48, 'Switzerland', col = col.vec['Swiss'], cex = 0.7)
-## text(157,40, 'Japan', col = col.vec['Japan'], cex = 0.7)
-## text(137,18, 'Taiwan', col = col.vec['Fushan'], cex = 0.7)
-## text(171,-30, 'Australia', col = col.vec['NSW'], cex = 0.7)
-## text(173,-51, 'New Zealand', col = col.vec['NVS'], cex = 0.7)
 dev.off()
+
+
diff --git a/scripts/analysis/results.fig.R b/scripts/analysis/results.fig.R
index cb38c082e674ac9e34bc6bf05caf6164523b9566..1fa22af1789f036c32f2692b026876f89a2218af 100644
--- a/scripts/analysis/results.fig.R
+++ b/scripts/analysis/results.fig.R
@@ -15,8 +15,8 @@ names.biomes <- c('Desert', 'Desert', 'Woodland/shrubland', 'Temperate forest',
 list.all.results.set <-
     readRDS('output/list.lmer.out.all.NA.simple.set.rds')
 
-## list.all.results.ecocode <-
-##     readRDS('output/list.lmer.out.all.NA.simple.ecocode.koppen.rds')
+list.all.results.ecocode <-
+    readRDS('output/list.lmer.out.all.NA.simple.ecocode.koppen.rds')
 
 list.all.results.intra <-
     readRDS('output/list.lmer.out.all.NA.intra.set.rds')
@@ -42,51 +42,6 @@ vec.rel.grad.set < 0.001
 
 
 ## plots
-pdf('figs/figres12.pdf', height = 14, width = 16)
-plot.param.mean.and.biomes.fixed(list.all.results.set , data.type = "simple",
-               models = c('lmer.LOGLIN.ER.AD.Tf.r.set.species',
-                   'lmer.LOGLIN.ER.AD.Tf.r.set.fixed.biomes.species'),
-               traits = c('Wood.density' , 'SLA', 'Max.height'),
-               param.vec = c("sumTnTfBn.abs", "sumTfBn","sumTnBn",
-                   "sumBn", "Tf"),
-               param.print = 1:5,
-               param.names = c(expression('Trait dissim '(alpha['d'])),
-                               expression('Tolerance '(alpha['t'])),
-                               expression('Effect '(alpha['e'])),
-                               expression('Trait indep'(alpha[0])),
-                               expression("Direct trait "(m[1])),
-                              expression("Size "(gamma %*% log('D'))) ) ,
-               col.vec =  fun.col.pch.biomes()$col.vec,
-               pch.vec =  fun.col.pch.biomes()$pch.vec,
-               names.bio = names.biomes ,
-               xlim = c(-0.30, 0.35))
-dev.off()
-
-
-pdf('figs/figres12_intra.pdf', height = 14, width = 16)
-plot.param.mean.and.biomes.fixed(list.all.results.intra , data.type = "intra",
-               models = c('lmer.LOGLIN.ER.AD.Tf.intra.r.set.species',
-                   'lmer.LOGLIN.ER.AD.Tf.intra.r.set.fixed.biomes.species'),
-               traits = c('Wood.density' , 'SLA', 'Max.height'),
-               param.vec = c("sumTnTfBn.abs", "sumTfBn","sumTnBn",
-                   "sumBn.intra", "sumBn.inter", "Tf"),
-               param.print = 1:6,
-               param.names = c(expression('Trait dissim '(alpha['d'])),
-                               expression('Tolerance '(alpha['t'])),
-                               expression('Effect '(alpha['e'])),
-                               expression('Trait indep'(alpha['0 intra'])),
-                               expression('Trait indep'(alpha['0 inter'])),
-                               expression("Direct trait "(m[1])),
-                              expression("Size "(gamma %*% log('D'))) ) ,
-               col.vec =  fun.col.pch.biomes()$col.vec,
-               pch.vec =  fun.col.pch.biomes()$pch.vec,
-               names.bio = names.biomes ,
-               xlim = c(-0.30, 0.35),
-               intra.TF =TRUE)
-dev.off()
-
-
-
 pdf('figs/figres12_TP.pdf', height = 14, width = 16)
 plot.param.mean.and.biomes.fixed(list.all.results.set , data.type = "simple",
                models = c('lmer.LOGLIN.ER.AD.Tf.MAT.MAP.r.set.species',
@@ -99,7 +54,7 @@ plot.param.mean.and.biomes.fixed(list.all.results.set , data.type = "simple",
                                expression('Dissim '(alpha['d'])),
                                expression('Tolerance '(alpha['t'])),
                                expression('Effect '(alpha['e'])),
-                               expression("Direct trait "(m[1])),
+                               expression("Trait link"(m[1])),
                               expression("Size "(gamma %*% log('D'))) ) ,
                col.vec =  fun.col.pch.biomes()$col.vec,
                pch.vec =  fun.col.pch.biomes()$pch.vec,
@@ -122,7 +77,7 @@ plot.param.mean.and.biomes.fixed(list.all.results.intra , data.type = "intra",
                                expression('Dissim '(alpha['d'])),
                                expression('Tolerance '(alpha['t'])),
                                expression('Effect '(alpha['e'])),
-                               expression("Direct trait "(m[1])),
+                               expression("Trait link "(m[1])),
                               expression("Size "(gamma %*% log('D'))) ) ,
                col.vec =  fun.col.pch.biomes()$col.vec,
                pch.vec =  fun.col.pch.biomes()$pch.vec,
@@ -133,27 +88,6 @@ dev.off()
 
 
 
-pdf('figs/figres12_ecocode.pdf', height = 14, width = 16)
-plot.param.mean.and.biomes.fixed(list.all.results.ecocode ,
-                                 data.type = "simple",
-               models = c('lmer.LOGLIN.ER.AD.Tf.r.ecocode.species',
-                   'lmer.LOGLIN.ER.AD.Tf.r.ecocode.fixed.biomes.species'),
-               traits = c('Wood.density' , 'SLA', 'Max.height'),
-               param.vec = c("sumTnTfBn.abs", "sumTfBn","sumTnBn",
-                   "sumBn", "Tf"),
-               param.print = 1:5,
-               param.names = c(expression('Trait dissim '(alpha['d'])),
-                               expression('Tolerance '(alpha['t'])),
-                               expression('Effect '(alpha['e'])),
-                               expression('Trait indep'(alpha[0])),
-                               expression("Direct trait "(m[1])),
-                              expression("Size "(gamma %*% log('D'))) ) ,
-               col.vec =  fun.col.pch.biomes()$col.vec,
-               pch.vec =  fun.col.pch.biomes()$pch.vec,
-               names.bio = names.biomes ,
-               xlim = c(-0.3, 0.27))
-dev.off()
-
 
 pdf('figs/figres12_ecocode_TP_intra.pdf', height = 14, width = 16)
 plot.param.mean.and.biomes.fixed(list.all.results.intra ,
@@ -170,7 +104,7 @@ plot.param.mean.and.biomes.fixed(list.all.results.intra ,
                                expression('Dissim '(alpha['d'])),
                                expression('Tolerance '(alpha['t'])),
                                expression('Effect '(alpha['e'])),
-                               expression("Direct trait "(m[1])) ) ,
+                               expression("Trait link "(m[1])) ) ,
                col.vec =  fun.col.pch.biomes()$col.vec,
                pch.vec =  fun.col.pch.biomes()$pch.vec,
                names.bio = names.biomes ,
@@ -182,10 +116,7 @@ dev.off()
 
 
 
-### PLOT TRADE OFF param
-
-
-
+### PLOT TRADE OFF and parameters
 
 pdf('figs/figres4t_TP_intra.pdf', width = 8, height = 7)
 fun.plot.trade.param(list.all.results.intra,
@@ -205,11 +136,6 @@ fun.plot.all.param(list.all.results.intra,
 dev.off()
 
 
-pdf('figs/rho_set_TP.pdf')
-fun.plot.all.rho(list.all.results.set,
-                 model = 'lmer.LOGLIN.ER.AD.Tf.MAT.MAP.r.set.species',
-                 MAT.MAP.TF = TRUE)
-dev.off()
 
 pdf('figs/rho_set_TP_intra.pdf', width = 9, height = 3)
 fun.plot.all.rho(list.all.results.intra,
@@ -219,128 +145,3 @@ dev.off()
 
 
 
-fun.plot.rho <- function(i, mat.param, T = seq(0.1, 1, length.out = 50)){
-param <- mat.param[, i]    
-exp((param['sumBn.inter'] - param['sumBn.intra'] +param['sumTnTfBn.abs'] *abs(T -min(T))))
-}
-
-generate.random.param <- function(trait,
-                                  list.res, n = 500,
-                                  model= 'lmer.LOGLIN.ER.AD.Tf.MAT.MAP.intra.r.set.species',
-                                  data.type = 'intra',
-                                  param.name = c('sumBn.inter', 'sumBn.intra',
-                                                 'sumTfBn', 'sumTnBn', 'sumTnTfBn.abs')){
-    
-require(mvtnorm)
-mean.param <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$lmer.summary$fixed.coeff.E
-vcov <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$vcov
-mean.param.s <- mean.param[param.name]
-vcov.s <- as.matrix(vcov[param.name, param.name])
-res <- rmvnorm(n, mean=mean.param.s, sigma=vcov.s, method="chol")
-return(res)
-}
-
-
-ratio.dan <- function(i, T1, T2, mat.param,list.sd){
-param <- mat.param[i, ]
-aer <- param['sumBn.inter']/list.sd[['sd.sumBn.inter']]
-ara <- param['sumBn.intra']/list.sd[['sd.sumBn.intra']]
-at <- param['sumTfBn']/list.sd[['sd.sumTfBn']]
-ae <- param['sumTnBn']/list.sd[['sd.sumTnBn']]
-ad <- param['sumTfTnBn.abs']/list.sd[['sd.sumTfTnBn.abs']]
-
-dan <-(aer at *T1 + ae *T2 + ad *abs(T2 -T1))*
-   (aer +at *T2 + ae *T1 + ad *abs(T2 -T1))/
-((ara +at *T1 + ae *T1) *
- (ara + at *T2 + ae *T2))
-return(dan)
-
-}
-
-fun.plot.dan <- function(i, mat.param, T1 = 0.1,
-                         T2 = seq(0.1, 1, length.out = 50)){
-
-list.sd <- list.res[[paste0(data.type, "_", trait ,
-                                 "_", model)]]$list.sd
-dan <- outer(T1, T2, ratio.dan, i, mat.param, list.sd)
-return(dan)
-}
-
-fun.dan.ci <- function(trait, list.res, alpha= 0.05, T1 = 1,
-                         T2 = seq(0.1, 1, length.out = 50), n = 500){
-mat.param.r <- generate.random.param(trait, n = n, list.res = list.all.results)
-res.ci <- sapply(1:n, ratio.dan, T1, T2, mat.param.r)
-mean.p <- apply(res.ci, MARGIN = 1, median)
-ci.p <- apply(res.ci, MARGIN = 1, quantile, probs = c(alpha/2, 1-alpha/2))
-return(cbind(mean.p, t(ci.p)))
-}
-
-
-get.predict.var.scaled <- function(trait, dir.root='../..', log.TF = FALSE, N.pred = 100){
-if(log.TF) {file.type <- ''}
-else{file.type <- 'no.log'}
-dir.read <- 'output/processed'
-sd.traits <-
-    readRDS(file.path(dir.root, dir.read,
-                      paste0('data.sd.traits.', file.type, '.rds')))
-quant.data <-
-    readRDS(file.path(dir.root, dir.read,
-                      paste0('data.quant.traits.', file.type, '.rds')))
-trait.quant <-fun.std.quant.trait(trait, dat.q = quant.data
-       , dat.sd = sd.traits)
-seq.BATOT <- seq(from = 0,
-                 to = quant.data[['qh.BATOT']],
-                 length.out = N.pred)
-return(list(trait.quant, seq.BATOT))
-}
-
-
-fun.plot.rho.dan <- function(trait, list.res, fun.tf = max){
-qa <- get.predict.var.scaled(trait)[[1]]
-T2 <- seq(qa[['ql']], qa[['qh']], length.out = 50)
-T1 <-  fun.tf(T2)
-T <- seq(qa[['ql.o']], qa[['qh.o']], length.out = 50) - qa[['ql.o']]
-mat.p <- fun.dan.ci(trait,  list.res, T1=T1, T2=T2)
-plot(T, mat.p[,1],type = 'l', lwd = 2, ylim =range(mat.p), col = '#018571')
-    polygon(c(T,
-          rev(T)),
-        c(mat.p[, 2],
-          rev(mat.p[, 3])),
-       col = add.alpha('#018571', 0.5), border = NA)
-lines(T,mat.p[,2], lty= 2)
-lines(T,mat.p[,3], lty= 2)
-}
-
-add.alpha <- function(col, alpha=0.5){
-  if(missing(col))
-    stop("Please provide a vector of colours.")
-  apply(sapply(col, col2rgb)/255, 2,
-                     function(x)
-                       rgb(x[1], x[2], x[3], alpha=alpha))
-}
-
-x11()
-par(mfcol = c(1,3))
-fun.plot.rho.dan('Wood.density', list.all.results)
-fun.plot.rho.dan('SLA', list.all.results)
-fun.plot.rho.dan('Max.height', list.all.results)
-
-
-
-plot(T,1-fun.plot.dan(1, mat.param))
-plot(T,1-fun.plot.dan2(1, mat.param))
-plot(T,1- fun.plot.rho(2, mat.param))
-plot(T,1-fun.plot.dan(2, mat.param))
-plot(T,1-fun.plot.dan2(2, mat.param))
-plot(T,1- fun.plot.rho(3, mat.param))
-plot(T,1-fun.plot.dan(3, mat.param))
-plot(T,1-fun.plot.dan2(3, mat.param))
-
-
-
-par(mfrow= c(1,3))
-image(fun.plot.dan(1, mat.param, T1 = seq(0.1, 1, length.out = 50)))
-image(fun.plot.dan(2, mat.param, T1 = seq(0.1, 1, length.out = 50)))
-image(fun.plot.dan(3, mat.param, T1 = seq(0.1, 1, length.out = 50)))
diff --git a/scripts/maps/biomemap.R b/scripts/maps/biomemap.R
index 3b009faafdb92f67912aea0afa2aa2a3e6e54504..7ed5aa3e5eb74d2ecabd7e524dd7e5d04f0e0fa7 100644
--- a/scripts/maps/biomemap.R
+++ b/scripts/maps/biomemap.R
@@ -68,7 +68,8 @@ names.set[7] <- 'Central African Republic'
 names.set[8] <- 'Australia'
 names.set[9] <- 'New Zealand'
 names.set[10] <- 'French Guiana'
-names.set[14] <- 'USA'
+names.set[13] <- 'Switzerland'
+names.set[14] <- 'US'
 
 set.order.i <-  c(2, 3, 8, 9, 11, 12, 13, 14)
 set.order.b <-  c(1, 4, 5, 6, 7, 10)
@@ -86,64 +87,5 @@ legend(-187, -60, xjust = 0, yjust = 0, legend =names.set[set.order.b] , col = c
        pt.bg =  cols.vec[set.order.b], pt.cex = 1.2,
        box.col = "white",bg = "white", cex = 0.7, title = 'LPP', title.adj = 0.3)
 text(67,-80, '> 3 million trees & > 2500 species', col = 'red', cex = 1.2)
-## text(-40,50, 'Canada', col = col.vec['Canada'], cex = 0.7)
-## text(-68,35, 'US', col = col.vec['US'], cex = 0.7)
-## text(-45,22, 'Puerto Rico', col = col.vec['Luquillo'], cex = 0.7)
-## text(-95,8, 'Panama', col = col.vec['BCI'], cex = 0.7)
-## text(-27,3, 'French Guiana', col = col.vec['Paracou'], cex = 0.7)
-## text(-19,40, 'Spain', col = col.vec['Spain'], cex = 0.7)
-## text(-17,48, 'France', col = col.vec['France'], cex = 0.7)
-## text(2,-7, 'Central African \nRepublic', col = col.vec['Mbaiki'], cex = 0.7)
-## text(0,70, 'Sweden', col = col.vec['Sweden'], cex = 0.7)
-## text(25,48, 'Switzerland', col = col.vec['Swiss'], cex = 0.7)
-## text(157,40, 'Japan', col = col.vec['Japan'], cex = 0.7)
-## text(137,18, 'Taiwan', col = col.vec['Fushan'], cex = 0.7)
-## text(171,-30, 'Australia', col = col.vec['NSW'], cex = 0.7)
-## text(173,-51, 'New Zealand', col = col.vec['NVS'], cex = 0.7)
 dev.off()
 
-pdf(file.path('figs/world_mapold.pdf'))
-col.vec <- fun.col.pch.set()$col.vec
-world.map.all.sites(clim,
-                    cols =  col.vec)
-text(67,-80, '> 7 million trees & > 2500 species', col = 'red', cex = 1.2)
-text(-40,50, 'Canada', col = col.vec['Canada'], cex = 0.7)
-text(-68,35, 'US', col = col.vec['US'], cex = 0.7)
-text(-52,22, 'Puerto Rico', col = col.vec['Luquillo'], cex = 0.7)
-text(-95,8, 'Panama', col = col.vec['BCI'], cex = 0.7)
-text(-32,2, 'French Guiana', col = col.vec['Paracou'], cex = 0.7)
-text(-19,40, 'Spain', col = col.vec['Spain'], cex = 0.7)
-text(-17,48, 'France', col = col.vec['France'], cex = 0.7)
-text(2,-5, 'CAR', col = col.vec['Mbaiki'], cex = 0.7)
-text(0,70, 'Sweden', col = col.vec['Sweden'], cex = 0.7)
-text(25,48, 'Swiss', col = col.vec['Swiss'], cex = 0.7)
-text(157,40, 'Japan', col = col.vec['Japan'], cex = 0.7)
-text(137,18, 'Taiwan', col = col.vec['Fushan'], cex = 0.7)
-text(167,-30, 'NSW', col = col.vec['NSW'], cex = 0.7)
-text(167,-30, 'NSW', col = col.vec['NSW'], cex = 0.7)
-text(178,-50, 'NZ', col = col.vec['NVS'], cex = 0.7)
-dev.off()
-
-
-
-png(file.path('figs/world_map.png'),  width = 2000, height = 1425)
-world.map.all.sites(clim,
-                    add.legend=FALSE,
-                    cols =  fun.col.pch.set()$col.vec)
-text(67,-80, '> 7 million trees & > 2500 species', col = 'red', cex = 1.2)
-text(-40,50, 'Canada', col = col.vec['Canada'], cex = 0.7)
-text(-68,35, 'US', col = col.vec['US'], cex = 0.7)
-text(-45,22, 'Puerto Rico', col = col.vec['Luquillo'], cex = 0.7)
-text(-95,8, 'Panama', col = col.vec['BCI'], cex = 0.7)
-text(-27,2, 'French Guiana', col = col.vec['Paracou'], cex = 0.7)
-text(-19,40, 'Spain', col = col.vec['Spain'], cex = 0.7)
-text(-17,48, 'France', col = col.vec['France'], cex = 0.7)
-text(2,-5, 'CAR', col = col.vec['Mbaiki'], cex = 0.7)
-text(0,70, 'Sweden', col = col.vec['Sweden'], cex = 0.7)
-text(25,48, 'Swiss', col = col.vec['Swiss'], cex = 0.7)
-text(157,40, 'Japan', col = col.vec['Japan'], cex = 0.7)
-text(137,18, 'Taiwan', col = col.vec['Fushan'], cex = 0.7)
-text(167,-30, 'NSW', col = col.vec['NSW'], cex = 0.7)
-text(167,-30, 'NSW', col = col.vec['NSW'], cex = 0.7)
-text(178,-50, 'NZ', col = col.vec['NVS'], cex = 0.7)
-dev.off()