Commit fee1f548 authored by Kunstler Georges's avatar Kunstler Georges
Browse files

progress on revision two

parent 9797c8f3
......@@ -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,
......
......@@ -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)
}
......
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
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......@@ -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 $@
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xelatex $<
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xelatex extended_data.tex
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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 $@
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% 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].
......
......@@ -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))))