Commit 040d9791 authored by kunstler's avatar kunstler
Browse files

start moving from .md to .tex

parent 416d25e3
......@@ -417,10 +417,12 @@ easyPredCI.param <- function(list.res, type, newdata, alpha=0.05) {
## construct 95% Normal CIs on the link scale and
## transform back to the response (probability) scale:
crit <- -qnorm(alpha/2)
if (type %in% c('alphar', 'alphae', 'alphal')) inter <- beta[4]
if (type == 'maxG') inter <- beta[1]
cbind(newdata,
pred = pred,
lwr = pred-crit*pred.se,
upr = pred+crit*pred.se)
pred = pred - inter,
lwr = pred-crit*pred.se - inter,
upr = pred+crit*pred.se - inter)
}
......@@ -440,7 +442,7 @@ return(pred.res)
}
predict.for.one.traits.3params <- function(trait,
predict.for.one.traits.3params <- function(trait,
dir.root, list.res,
alpha = 0.05){
list.var <- get.predict.var.scaled(trait, dir.root)
......@@ -463,19 +465,22 @@ pred.res.al$Tf <- seq(from = list.var[[1]][['ql.o']],
to = list.var[[1]][['qh.o']],
length.out = 100)
pred.res.al$param.type <- 'alphal'
pred.res.al$pred <- -pred.res.al$pred
pred.res.al$lwr <- -pred.res.al$lwr
pred.res.al$upr <- -pred.res.al$upr
pred.res.ae <- easyPredCI.param(list.res, type = 'alphae', new.data, alpha)
pred.res.ae$Tf <- seq(from = list.var[[1]][['ql.o']],
to = list.var[[1]][['qh.o']],
length.out = 100)
pred.res.ae$param.type <- 'alphae'
## pred.res.ae$pred <- -pred.res.ae$pred
## pred.res.ae$lwr <- -pred.res.ae$lwr
## pred.res.ae$upr <- -pred.res.ae$upr
pred.res.ae$pred <- -pred.res.ae$pred
pred.res.ae$lwr <- -pred.res.ae$lwr
pred.res.ae$upr <- -pred.res.ae$upr
return(rbind(pred.res.max, pred.res.ar, pred.res.ae, pred.res.al))
}
# turn pred log(BA.G) in BA.G
inv.link.BA.G <- function(pred, sd.BA.G, mean.BA.G, min.BA.G = 40){
return(exp(pred * sd.BA.G + mean.BA.G) - min.BA.G -1)
......@@ -557,7 +562,7 @@ for (i in traits){
list.temp <- list.res[[paste(data.type, "_", i ,
"_", model,
sep = '')]]
list.df[[i]] <- predict.for.one.traits.3params(trait = i,
list.df[[i]] <- predict.for.one.traits.3params(trait = i,
dir.root, list.temp,
alpha = 0.05)
list.df[[i]]$traits <- i
......@@ -970,22 +975,24 @@ fun.param.descrip <- function(add.param.descrip.TF, x.line = -0.63){
fun.legend <- function(biomes.names, biomes.c, col.vec, pch.vec){
par(mar=c(0, 0, 0, 0))
plot(0:1,0:1,type="n", axes=FALSE, xlab="", ylab="")
points(rep(0.5,length(biomes.c)+1), 0.15+((length(biomes.c)+1):1-1)*0.15,
min.y <- 0.25
step.y <- 0.1
points(rep(0.5,length(biomes.c)+1), min.y+((length(biomes.c)+1):1-1)*step.y,
col = c('black', col.vec[biomes.c]),
pch = c(15, pch.vec[biomes.c]),
cex = 2)
points(rep(0.5,1), 0.15+((length(biomes.c)+1)-1)*0.15,
points(rep(0.5,1), min.y+((length(biomes.c)+1)-1)*step.y,
col = c('black'),
pch = c(15),
cex = 2.5)
segments(rep(0.40,length(biomes.c)+1), 0.15+((length(biomes.c)+1):1-1)*0.15,
rep(0.60,length(biomes.c)+1), 0.15+((length(biomes.c)+1):1-1)*0.15,
segments(rep(0.40,length(biomes.c)+1), min.y+((length(biomes.c)+1):1-1)*step.y,
rep(0.60,length(biomes.c)+1), min.y+((length(biomes.c)+1):1-1)*step.y,
lty =1, lwd = 1.5,col = c('black', col.vec[biomes.c]))
segments(rep(0.40, 1), 0.15+(length(biomes.c)+1-1)*0.15,
rep(0.60, 1), 0.15+(length(biomes.c)+1-1)*0.15,
segments(rep(0.40, 1), min.y+(length(biomes.c)+1-1)*step.y,
rep(0.60, 1), min.y+(length(biomes.c)+1-1)*step.y,
lty =1, lwd = 2,col = 'black')
text(rep(0.5,length(biomes.c)+1), 0.11+((length(biomes.c)+1):1-1)*0.15,
labels = c('mean', biomes.names[biomes.c]), cex= 1.8)
text(rep(0.5,length(biomes.c)+1), min.y-0.04+((length(biomes.c)+1):1-1)*step.y,
labels = c('global', biomes.names[biomes.c]), cex= 1.8)
}
fun.par.mai <- function(i, traits, b){
......@@ -1007,8 +1014,8 @@ plot.param.mean.and.biomes.fixed <- function(list.res,
traits.names = c(Wood.density= 'Wood density',
SLA = 'Specific leaf area',
Max.height = 'Maximum height'),
param.vec = c("Tf", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs"),
param.vec = c("sumTnTfBn.abs", "sumTfBn","sumTnBn",
"sumBn", "Tf"),
param.names = c('Direct trait',
'Compet effect x trait',
'Compet response x trait',
......@@ -1036,6 +1043,8 @@ b <- border.size()
"_", models[1],
sep = '')]]$lmer.summary
param.mean.m <- list.temp.m$fixed.coeff.E[param.vec]
param.mean.m[c("sumTnTfBn.abs", "sumTnBn", "sumBn")] <-
-param.mean.m[c("sumTnTfBn.abs", "sumTnBn", "sumBn")]
param.std.m <- list.temp.m$fixed.coeff.Std.Error
names(param.std.m) <- names(list.temp.m$fixed.coeff.E)
param.std.m <- param.std.m[param.vec]
......@@ -1046,6 +1055,7 @@ b <- border.size()
list.fixed <- fun.get.fixed.biomes(param.vec[n.vars], list.temp,
biomes.vec = biomes)
param.mean <- list.fixed$fixed.biomes
if (param.vec[n.vars] %in% c("sumTnTfBn.abs", "sumTnBn", "sumBn")) param.mean <- -param.mean
param.std <- list.fixed$fixed.biomes.std
seq.jitter <- seq(25, -25, length.out = length(biomes)+1)/120
if(n.vars == 1){
......@@ -1133,3 +1143,232 @@ rm(out)
gc()
}
## param plot
fun.plot.all.param <- function(list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species',
dir.root = '.',
data.type = 'simple',
big.m = 0.6,
small.m = 0.2,
col.vec = fun.col.param()
){
# predict data
data.param <- fun.pred.BA.l.and.h.all.traits.3params(
traits = c('Wood.density', 'SLA', 'Max.height'),
model = model,
dir.root = dir.root,
list.res = list.res,
data.type = data.type)
require(dplyr)
# Layout
m <- matrix(c(1:12), 4, 3)
wid <- c(big.m, 0 , small.m) +
rep((6-big.m-small.m)/3, each= 3)
hei <- c(small.m, 0, 0 , big.m) +
rep((10-big.m-small.m)/4, each= 4)
layout(m, heights=hei, widths= wid )
expr.p.vec <- c(expression(paste('Similarity ', alpha[l] %*% abs(t[f] - t[c]))),
expression(paste('Competitive effect ', alpha[e] %*% t[c])),
expression(paste('Tolerance of competition ', alpha[t] %*% t[f])),
expression(paste('Maximum growth ', m[1] %*% t[f])))
names(expr.p.vec) <- c('alphal', 'alphae', 'alphar', 'maxG')
names.param <- c("Tf","sumTnBn",
"sumTfBn", "sumTnTfBn.abs")
names(names.param) <- c('maxG', 'alphae', 'alphar', 'alphal')
for (t in c('Wood density', 'Specific leaf area', 'Maximum height')){
for (p in c('alphal', 'alphae', 'alphar', 'maxG')){
df.t <- data.param[data.param$traits == t, ]
if(t == 'Wood density'){
if(p == 'alphal'){
par(mai=c(0.1, big.m,small.m,0))
}else{
if(p == 'maxG'){
par(mai=c(big.m, big.m,0.1,0))
}else{
par(mai=c(0.1, big.m,0.1,0))
}
}
}
if(t == 'Specific leaf area'){
if(p == 'alphal'){
par(mai=c(0.1, 0,small.m,0))
}else{
if(p == 'maxG'){
par(mai=c(big.m, 0,0.1,0))
}else{
par(mai=c(0.1, 0,0.1,0))
}
}
}
if(t == 'Maximum height'){
if(p == 'alphal'){
par(mai=c(0.1, 0,small.m,small.m))
}else{
if(p == 'maxG'){
par(mai=c(big.m, 0,0.1,small.m))
}else{
par(mai=c(0.1, 0,0.1,small.m))
}
}
}
if(t == 'Wood density'){
if(p == 'maxG'){
fun.plot.param.tf(df = df.t,
param.sel = p,
xlab = expression(paste('Wood density (mg m', m^-3, ')')),
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], cex.lab = 1.1, cex.axis =0.85, cex = 1)
}else{
fun.plot.param.tf(df = df.t,
param.sel = p,
xaxt= 'n',xlab = NA,
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], cex.lab = 1.1, cex.axis =0.85, cex = 1)
}
}
if(t == 'Specific leaf area'){
if(p == 'maxG'){
fun.plot.param.tf(df = df.t,
param.sel = p, yaxt = 'n',
xlab = expression(paste('Specific leaf area (m', m^2, ' m', g^-1, ')')),
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], add.ylab.TF = FALSE, cex.lab = 1.1, cex.axis =0.85, cex = 1)
}else{
fun.plot.param.tf(df = df.t,
param.sel = p,
xaxt= 'n',xlab = NA,
yaxt = 'n',
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], add.ylab.TF = FALSE, cex.lab = 1.1, cex.axis =0.85, cex = 1)
}
}
if(t == 'Maximum height'){
if(p == 'maxG'){
fun.plot.param.tf(df = df.t,
param.sel = p, yaxt = 'n',
xlab = expression(paste('Maximum height (m)')),
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], add.ylab.TF = FALSE, cex.lab = 1.1, cex.axis =0.85, cex = 1)
}else{
fun.plot.param.tf(df = df.t,
param.sel = p,
xlab = NA,
xaxt= 'n', yaxt = 'n',
col.param = col.vec[names.param[p]],
expr.param = expr.p.vec[p], add.ylab.TF = FALSE, cex.lab = 1.1, cex.axis =0.85, cex = 1)
}
}
}
}
}
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))
}
fun.plot.param.tf <- function(df, param.sel, xlab,
col.param, expr.param,
add.ylab.TF = TRUE,
cex.lab = 1.3, cex.axis = 1,
cex = 1.3, ...){
df.t <- df[df$param.type == param.sel, ]
plot(df.t[ , 'Tf'],
df.t[, 'pred'],
xlab = xlab, ylab = NA,
lwd = 3, cex.lab = cex.lab, cex.axis = cex.axis,
col = col.param, ylim = range(df.t[, c('upr', 'lwr')]), type = 'l',...)
polygon(c(df.t[, 'Tf'],
rev(df.t[, 'Tf'])),
c(df.t[, 'upr'],
rev(df.t[, 'lwr'])),
col = add.alpha(col.param, 0.5), border = NA)
if(add.ylab.TF){
mtext(expr.param,
side=2, cex =cex,
line = 2.5, col = col.param)
}
}
## plot only wd and sla
fun.plot.wd.sl.param <- function(list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species',
dir.root = '.',
data.type = 'simple',
big.m = 1.0,
small.m = 0.42
){
# predict data
data.param <- fun.pred.BA.l.and.h.all.traits.3params(
traits = c('Wood.density', 'SLA'),
model = model,
dir.root = dir.root,
list.res = list.res,
data.type = data.type)
require(dplyr)
# Layout
m <- matrix(c(1:4), 2, 2)
wid <- c(small.m , big.m) +
rep((6-big.m-small.m)/2, each= 2)
layout(m, heights=wid)
par(mai=c(0.2, big.m,small.m,0.1), xpd = TRUE)
fun.plot.param.tf(df = filter(data.param,
traits == "Wood density"),
param.sel = 'maxG', xlab = NA, xaxt= 'n',
col.param = "#e41a1c",
expr.param = expression(paste('Max growth ',
(m[1] %*% t[f]))))
par(mai=c(big.m , big.m,0.2,0.1), xpd = TRUE)
fun.plot.param.tf(df = filter(data.param,
traits == "Wood density"),
param.sel = 'alphar',
xlab = expression(
paste('Wood density (mg m', m^-3, ')')),
col.param = "#4daf4a",
expr.param = expression(paste(
'Tolerance of competition ',
(alpha[t] %*% t[f]))))
par(mai=c(0.2, big.m,small.m,0.1), xpd = TRUE)
fun.plot.param.tf(df = filter(data.param,
traits == "Specific leaf area"),
param.sel = 'maxG',xlab = NA, xaxt= 'n',
col.param = "#e41a1c",
expr.param = expression(paste('Max growth ',
(m[1] %*% t[f]))))
par(mai=c(big.m , big.m,0.2,0.1), xpd = TRUE)
fun.plot.param.tf(df = filter(data.param,
traits == "Specific leaf area"),
param.sel = 'alphae',
xlab = expression(
paste('Specific leaf area (m', m^2, ' m', g^-1, ')')) ,
col.param = "#984ea3",
expr.param = expression(paste(
'Competitive effect ',
(alpha[e] %*% t[c]))))
}
% Supplementary Information
# Supplementary methods
We developed the equation of $\alpha_{c,f} = \alpha_{0,f} + \alpha_r \, t_f + \alpha_i \, t_c + \alpha_s \, \vert t_c-t_f \vert$ along with the basal area of each competitive species in the competition index to show the parameters are directly related to community weighted means of the different traits variables as:
We developed the equation of $\alpha_{c,f} = \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert$ along with the basal area of each competitive species in the competition index to show the parameters are directly related to community weighted means of the different traits variables as:
\begin{equation} \label{alphaBA}
\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} + \alpha_r \, t_f \, B_{i,tot} + \alpha_i \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}
\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} - \alpha_t \, t_f \, B_{i,tot} + \alpha_e \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}
\end{equation}
Where:
......@@ -328,7 +328,7 @@ SLA was positively correlated with maximum basal area growth (growth without com
Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@poorter_architecture_2006; @poorter_are_2008; @wright_functional_2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might be expected to select for slower growth in long-lived plants[@poorter_are_2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@poorter_architecture_2006]. There was however a tendency for species with tall maximum height to have stronger competitive effect (though with wider confidence intervals intercepting zero), that might be explained by greater light interception from taller trees.
Our results raised the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and response are the two central elements of the species competitive ability[@goldberg_competitive_1991]. One may expect that because of intra-specific competition, species with strong competitive effect should have evolved a high tolerance to competition. However, in agreement with previous studies[@goldberg_components_1990; @goldberg_competitive_1991; @wang_are_2010], we found little evidence for such coordination. It was present only for wood density, where high density conferred better competitive response and also stronger competitive effect (but with wide confidence intervals). For SLA there was no clear coordinations. For maximum height as explained above there was a tendency for short maximum height to lead to high tolerance to competition but to low competitive effect. This interesting because a trade-off between competitive tolerance and maximum height has been proposed as fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@kohyama_stratification_2009]. Finally the lack of support for coordination between response and effect is important because it means that competitive interaction is not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_r$ as in @kunstler_competitive_2012; @kraft_functional_2014; @lasky_trait-mediated_2014). Traits of competitors alone or of focal plants alone may convey more information. If traits are strongly linked to either competitive effect or competitive response, this still means that some trait values will have an advantage in competitive interactions.
Our results raised the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of the species competitive ability[@goldberg_competitive_1991]. One may expect that because of intra-specific competition, species with strong competitive effect should have evolved a high tolerance to competition. However, in agreement with previous studies[@goldberg_components_1990; @goldberg_competitive_1991; @wang_are_2010], we found little evidence for such coordination. It was present only for wood density, where high density conferred better competitive tolerance and also stronger competitive effect (but with wide confidence intervals). For SLA there was no clear coordinations. For maximum height as explained above there was a tendency for short maximum height to lead to high tolerance to competition but to low competitive effect. This interesting because a trade-off between competitive tolerance and maximum height has been proposed as fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@kohyama_stratification_2009]. Finally the lack of support for coordination between tolerance and effect is important because it means that competitive interaction is 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_competitive_2012; @kraft_functional_2014; @lasky_trait-mediated_2014). Traits of competitors alone or of focal plants alone may convey more information. If traits are strongly linked to either competitive effect or competitive tolerance, this still means that some trait values will have an advantage in competitive interactions.
Given that the effect sizes we report for effects of traits on competitive interaction are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that if traits measured at the individual level were available, rather than species averages, this might strengthen predictive power[@kraft_functional_2014].
......@@ -336,7 +336,7 @@ Given that the effect sizes we report for effects of traits on competitive inter
## Variations between biomes
Overall most results were rather consistent across biomes (Fig 3 main text), but some exceptions deserve comment.
Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 3 main text). High SLA species tended to be more competition-tolerant (competitive response parameter $\alpha_r$) in temperate forests (confidence interval only marginally intercepted zero) while low SLA species were more competition-tolerant in tropical forests. These different outcomes may trace to the prevalence of deciduous species in temperate forests (see Extended data Table 1), because the link between shade-tolerance and SLA is different for deciduous and evergreen species[@lusk_why_2008]. In tropical forests shade-tolerant species often have long leaf lifespans, associated with low SLA. On the other hand in temperate deciduous forests the length of the growing season is fixed by temperature. Shade tolerant species cannot increase leaf longevity and instead reduce the cost of leaf production (high SLA) to offset the reduced income due to low light availability. The other noticeable difference between biomes was for taiga where the parameter relating wood density to competitive impact was positive, versus negative in the other biomes (Fig 3 main text). We do not have a mechanistic explanation to suggest for this discrepancy, but can observe that taiga has relatively few species many of which are conifers where the range of wood density is narrower than for angiosperms (see Extended data Table 1).
Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 3 main text). High SLA species tended to be more competition-tolerant (tolerance to competition parameter $\alpha_t$) in temperate forests (confidence interval only marginally intercepted zero) while low SLA species were more competition-tolerant in tropical forests. These different outcomes may trace to the prevalence of deciduous species in temperate forests (see Extended data Table 1), because the link between shade-tolerance and SLA is different for deciduous and evergreen species[@lusk_why_2008]. In tropical forests shade-tolerant species often have long leaf lifespans, associated with low SLA. On the other hand in temperate deciduous forests the length of the growing season is fixed by temperature. Shade tolerant species cannot increase leaf longevity and instead reduce the cost of leaf production (high SLA) to offset the reduced income due to low light availability. The other noticeable difference between biomes was for taiga where the parameter relating wood density to competitive impact was positive, versus negative in the other biomes (Fig 3 main text). We do not have a mechanistic explanation to suggest for this discrepancy, but can observe that taiga has relatively few species many of which are conifers where the range of wood density is narrower than for angiosperms (see Extended data Table 1).
# References
......
% Supplementary Information
# Supplementary methods
We developed the equation of $\alpha_{c,f} = \alpha_{0,f} + \alpha_r \, t_f + \alpha_i \, t_c + \alpha_s \, \vert t_c-t_f \vert$ along with the basal area of each competitive species in the competition index to show the parameters are directly related to community weighted means of the different traits variables as:
We developed the equation of $\alpha_{c,f} = \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert$ along with the basal area of each competitive species in the competition index to show the parameters are directly related to community weighted means of the different traits variables as:
\begin{equation} \label{alphaBA}
\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} + \alpha_r \, t_f \, B_{i,tot} + \alpha_i \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}
\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}} = \alpha_{0,f} \, B_{i,tot} - \alpha_t \, t_f \, B_{i,tot} + \alpha_e \, B_{i,t_c} + \alpha_s \, B_{i,\vert t_c - t_f \vert}
\end{equation}
Where:
......@@ -70,7 +70,7 @@ SLA was positively correlated with maximum basal area growth (growth without com
Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@poorter_architecture_2006; @poorter_are_2008; @wright_functional_2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might be expected to select for slower growth in long-lived plants[@poorter_are_2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@poorter_architecture_2006]. There was however a tendency for species with tall maximum height to have stronger competitive effect (though with wider confidence intervals intercepting zero), that might be explained by greater light interception from taller trees.
Our results raised the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and response are the two central elements of the species competitive ability[@goldberg_competitive_1991]. One may expect that because of intra-specific competition, species with strong competitive effect should have evolved a high tolerance to competition. However, in agreement with previous studies[@goldberg_components_1990; @goldberg_competitive_1991; @wang_are_2010], we found little evidence for such coordination. It was present only for wood density, where high density conferred better competitive response and also stronger competitive effect (but with wide confidence intervals). For SLA there was no clear coordinations. For maximum height as explained above there was a tendency for short maximum height to lead to high tolerance to competition but to low competitive effect. This interesting because a trade-off between competitive tolerance and maximum height has been proposed as fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@kohyama_stratification_2009]. Finally the lack of support for coordination between response and effect is important because it means that competitive interaction is not well described as a trait hierarchy relating a focal species to its competitors (measured as $t_c -t_f$ and thus assuming $\alpha_e = \alpha_r$ as in @kunstler_competitive_2012; @kraft_functional_2014; @lasky_trait-mediated_2014). Traits of competitors alone or of focal plants alone may convey more information. If traits are strongly linked to either competitive effect or competitive response, this still means that some trait values will have an advantage in competitive interactions.
Our results raised the question whether there is a coordination between trait values conferring strong competitive effect and trait values conferring high competitive tolerance. Competitive effect and tolerance are the two central elements of the species competitive ability[@goldberg_competitive_1991]. One may expect that because of intra-specific competition, species with strong competitive effect should have evolved a high tolerance to competition. However, in agreement with previous studies[@goldberg_components_1990; @goldberg_competitive_1991; @wang_are_2010], we found little evidence for such coordination. It was present only for wood density, where high density conferred better competitive tolerance and also stronger competitive effect (but with wide confidence intervals). For SLA there was no clear coordinations. For maximum height as explained above there was a tendency for short maximum height to lead to high tolerance to competition but to low competitive effect. This interesting because a trade-off between competitive tolerance and maximum height has been proposed as fundamental mechanisms of coexistence of species in size-structured population in the stratification theory of species coexistence[@kohyama_stratification_2009]. Finally the lack of support for coordination between tolerance and effect is important because it means that competitive interaction is 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_competitive_2012; @kraft_functional_2014; @lasky_trait-mediated_2014). Traits of competitors alone or of focal plants alone may convey more information. If traits are strongly linked to either competitive effect or competitive tolerance, this still means that some trait values will have an advantage in competitive interactions.
Given that the effect sizes we report for effects of traits on competitive interaction are modest, the question arises whether the three traits available to us (wood density, SLA, and maximum height) were the best candidates. It is possible that traits more directly related to mechanisms of competition -- for instance for competition for light, the leaf area index of the competitors or the compensation point at leaf or whole-plant level -- may be more powerful. It is also possible that if traits measured at the individual level were available, rather than species averages, this might strengthen predictive power[@kraft_functional_2014].
......@@ -78,7 +78,7 @@ Given that the effect sizes we report for effects of traits on competitive inter
## Variations between biomes
Overall most results were rather consistent across biomes (Fig 3 main text), but some exceptions deserve comment.
Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 3 main text). High SLA species tended to be more competition-tolerant (competitive response parameter $\alpha_r$) in temperate forests (confidence interval only marginally intercepted zero) while low SLA species were more competition-tolerant in tropical forests. These different outcomes may trace to the prevalence of deciduous species in temperate forests (see Extended data Table 1), because the link between shade-tolerance and SLA is different for deciduous and evergreen species[@lusk_why_2008]. In tropical forests shade-tolerant species often have long leaf lifespans, associated with low SLA. On the other hand in temperate deciduous forests the length of the growing season is fixed by temperature. Shade tolerant species cannot increase leaf longevity and instead reduce the cost of leaf production (high SLA) to offset the reduced income due to low light availability. The other noticeable difference between biomes was for taiga where the parameter relating wood density to competitive impact was positive, versus negative in the other biomes (Fig 3 main text). We do not have a mechanistic explanation to suggest for this discrepancy, but can observe that taiga has relatively few species many of which are conifers where the range of wood density is narrower than for angiosperms (see Extended data Table 1).
Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 3 main text). High SLA species tended to be more competition-tolerant (tolerance to competition parameter $\alpha_t$) in temperate forests (confidence interval only marginally intercepted zero) while low SLA species were more competition-tolerant in tropical forests. These different outcomes may trace to the prevalence of deciduous species in temperate forests (see Extended data Table 1), because the link between shade-tolerance and SLA is different for deciduous and evergreen species[@lusk_why_2008]. In tropical forests shade-tolerant species often have long leaf lifespans, associated with low SLA. On the other hand in temperate deciduous forests the length of the growing season is fixed by temperature. Shade tolerant species cannot increase leaf longevity and instead reduce the cost of leaf production (high SLA) to offset the reduced income due to low light availability. The other noticeable difference between biomes was for taiga where the parameter relating wood density to competitive impact was positive, versus negative in the other biomes (Fig 3 main text). We do not have a mechanistic explanation to suggest for this discrepancy, but can observe that taiga has relatively few species many of which are conifers where the range of wood density is narrower than for angiosperms (see Extended data Table 1).
# References
......
......@@ -7,6 +7,11 @@
## ![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 comprise both a 50ha plot and a network of 1ha plots).](image/worldmapB.png)
## \newpage
## ![Variation of the four parameters linking the three studied traits with maximum growth and competition - maximum growth ($t_f \, m_1$), tolerance to competition ($t_f \, \alpha_t$), competitive effect ($t_c \, \alpha_e$) and limiting similarity ($|t_f - t_c| \, \alpha_l$, $t_c$ fixed at the lowest value and $t_f$ varying from quantile 5 to 95\%). The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$).](../../figs/figres4b.pdf)
## \newpage
......
......@@ -7,6 +7,11 @@ opts_chunk$set(dev= c('pdf','svg'), fig.width= 10, fig.height = 5)
![Map of the plot locations of all data sets analysed. LPP plots are represented with a large points and NFI plots with small points (The data set of Panama comprise both a 50ha plot and a network of 1ha plots).](image/worldmapB.png)
\newpage
![Variation of the four parameters linking the three studied traits with maximum growth and competition - maximum growth ($t_f \, m_1$), tolerance to competition ($t_f \, \alpha_t$), competitive effect ($t_c \, \alpha_e$) and limiting similarity ($|t_f - t_c| \, \alpha_l$, $t_c$ fixed at the lowest value and $t_f$ varying from quantile 5 to 95\%). The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$).](../../figs/figres4b.pdf)
\newpage
......
......@@ -5,6 +5,11 @@
![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 comprise both a 50ha plot and a network of 1ha plots).](image/worldmapB.png)
\newpage
![Variation of the four parameters linking the three studied traits with maximum growth and competition - maximum growth ($t_f \, m_1$), tolerance to competition ($t_f \, \alpha_t$), competitive effect ($t_c \, \alpha_e$) and limiting similarity ($|t_f - t_c| \, \alpha_l$, $t_c$ fixed at the lowest value and $t_f$ varying from quantile 5 to 95\%). The shaded area represents the 95% confidence interval of the prediction (including uncertainty associated with $\alpha_0$ or $m_0$).](../../figs/figres4b.pdf)
\newpage
......@@ -94,27 +99,27 @@ Table: Traits coverage in each sites. Percentage of species with species level t
-------------------------------------------------------------------------
&nbsp; Wood density SLA Maximum height
---------------- ------------------ ------------------ ------------------
**$m_0$** **0.218 (0.099)** 0.115 (0.099) **0.247 (0.072)**
------------------------------------------------------------------------
&nbsp; Wood density SLA Maximum height
---------------- ----------------- ------------------ ------------------
**$m_0$** 0.191 (0.101) 0.083 (0.1) **0.186 (0.082)**
**$m_1$** **-0.121 (0.039)** **0.115 (0.051)** **0.067 (0.044)**
**$m_1$** **-0.131 (0.04)** **0.118 (0.055)** **0.045 (0.04)**
**$\gamma$** **0.441 (0.014)** **0.409 (0.014)** 0.429 (0.013)
**$\gamma$** **0.419 (0.011)** **0.395 (0.011)** 0.419 (0.011)
**$\alpha_0$** **-0.308 (0.058)** **-0.259 (0.069)** **-0.349 (0.066)**
**$\alpha_0$** **-0.161 (0.03)** **-0.135 (0.034)** **-0.159 (0.033)**
**$\alpha_i$** -0.019 (0.017) **0.076 (0.025)** -0.025 (0.026)
**$\alpha_i$** -0.022 (0.015) **0.079 (0.025)** -0.017 (0.029)
**$\alpha_r$** **0.056 (0.022)** -0.007 (0.037) **-0.088 (0.039)**
**$\alpha_r$** **0.061 (0.023)** -0.013 (0.032) -0.062 (0.037)
**$\alpha_s$** **0.042 (0.015)** **0.065 (0.028)** **0.064 (0.016)**
**$\alpha_s$** **0.039 (0.012)** **0.058 (0.022)** **0.049 (0.016)**
**$R^2_m$*** 0.1242 0.1355 0.1203
**$R^2_m$*** 0.1214 0.1368 0.123
**$R^2_c$*** 0.717 0.7373 0.7168
-------------------------------------------------------------------------
**$R^2_c$*** 0.7057 0.7322 0.7026
------------------------------------------------------------------------
Table: Standaridized parameters estimates and standard error (in bracket) estimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters
......
......@@ -5,7 +5,7 @@
To examine the link between competition and traits we used a neighbourhood modelling framework[@canham_neighborhood_2006; @uriarte_trait_2010; @ruger_functional_2012; @kunstler_competitive_2012; @lasky_trait-mediated_2014] to model the growth of a focal tree of species $f$ as a product of its maximum growth rate (determined by its traits and size) together with reductions due to competition from individuals growing in the local neighbourhood. Specifically, we assumed a relationship of the form
\begin{equation} \label{G1}
G_{i,f,p,s} = G_{\textrm{max} \, f,p,s} \, D_{i}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}}\right),
G_{i,f,p,s} = G_{\textrm{max} \, f,p,s} \, D_{i}^{\gamma_f} \, \exp\left(\sum_{c=1}^{N_p} {-\alpha_{c,f} B_{i,c,p,s}}\right),
\end{equation}
where:
......@@ -18,11 +18,11 @@ where:
- $B_{i,c,p,s}= 0.25\, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s}^2$ is the sum of basal area of all individuals trees $j$ of the species $c$ competiting with the tree $i$ within the plot $p$ and data set $s$, where $w_j$ is a constant based on subplot size where tree $j$ was measured. Note that $B_{i,c,p,s}$ include all trees in the plot excepted the tree $i$.
Values of $\alpha_{c,f}< 0$ indicate competition, whereas $\alpha_{c,f}$ > 0 indicates facilitation.
Values of $\alpha_{c,f}> 0$ indicate competition, whereas $\alpha_{c,f}$ < 0 indicates facilitation.
Log-transformation of eq. \ref{G1} leads to a linearised model of form
Log-transformation of eq. \ref{G1} leads to a linearised model of the form
\begin{equation} \label{logG1}
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} + \sum_{c=1}^{N_p} {\alpha_{c,f} B_{i,c,p,s}}.
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} + \sum_{c=1}^{N_p} {-\alpha_{c,f} B_{i,c,p,s}}.
\end{equation}
......@@ -32,18 +32,18 @@ To include the effect of a focal trees' traits, $t_f$, on its growth, we let:
\end{equation}
Here $m_0$ is the average maximum growth, $m_1$ gives the effect of the focal trees trait, and $\epsilon_{G_{\textrm{max}}, f}$, $\epsilon_{G_{\textrm{max}}, p}$, $\epsilon_{G_{\textrm{max}}, s}$ are normally distributed random effect for species $f$, plot or quadrat $p$ (see below), and data set $s$ (where $\epsilon_{G_{\textrm{max}, f}} \sim N(0,\sigma_{G_{\textrm{max}, f}})$; $\epsilon_{G_{\textrm{max}, p}} \sim N(0,\sigma_{G_{\textrm{max}, p}})$ and $\epsilon_{G_{\textrm{max}, s}} \sim N(0,\sigma_{G_{\textrm{max}, s}})$).
Here $m_0$ is the average maximum growth, $m_1$ gives the effect of the focal trees trait, and $\epsilon_{G_{\textrm{max}}, f}$, $\epsilon_{G_{\textrm{max}}, p}$, $\epsilon_{G_{\textrm{max}}, s}$ are normally distributed random effect for species $f$, plot or quadrat $p$ (see below), and data set $s$ \[where $\epsilon_{G_{\textrm{max}, f}} \sim N(0,\sigma_{G_{\textrm{max}, f}})$; $\epsilon_{G_{\textrm{max}, p}} \sim N(0,\sigma_{G_{\textrm{max}, p}})$ and $\epsilon_{G_{\textrm{max}, s}} \sim N(0,\sigma_{G_{\textrm{max}, s}})$].
To include trait effects on competition presented in Fig. 1, competitive interactions were modelled using an equation of the form[^note]:
\begin{equation} \label{alpha}
\alpha_{c,f}= \alpha_{0,f} + \alpha_r \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert
\alpha_{c,f}= \alpha_{0,f} - \alpha_t \, t_f + \alpha_e \, t_c + \alpha_s \, \vert t_c-t_f \vert
\end{equation}
where:
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{\alpha_0, f}+ \epsilon_{\alpha_0, s}$, where $\epsilon_{\alpha_0, f} \sim N(0,\sigma_{\alpha_0, f})$ and $\epsilon_{\alpha_0, s} \sim N(0,\sigma_{\alpha_0, s})$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree with a normally distributed random effect of data set $s$ included ($\epsilon_{\alpha_r,s} \sim N(0,\sigma_{\alpha_r})$),
- $\alpha_{e}$ is the **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 ($\epsilon_{\alpha_i,s} \sim N(0,\sigma_{\alpha_i})$), and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ with a normally distributed random effect of data set $s$ included ($\epsilon_{\alpha_s,s} \sim N(0,\sigma_{\alpha_s})$).
- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ \[as $\alpha_{0,f} = \alpha_0 + \epsilon_{\alpha_0, f}+ \epsilon_{\alpha_0, s}$, where $\epsilon_{\alpha_0, f} \sim N(0,\sigma_{\alpha_0, f})$ and $\epsilon_{\alpha_0, s} \sim N(0,\sigma_{\alpha_0, s})$],
- $\alpha_t$ is the **tolerance to competition** of 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 \[$\epsilon_{\alpha_t,s} \sim N(0,\sigma_{\alpha_t})$],
- $\alpha_{e}$ is the **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 \[$\epsilon_{\alpha_i,s} \sim N(0,\sigma_{\alpha_i})$], and
- $\alpha_s$ is the effect of **trait similarity**, i.e. change in competition due to absolute distance between traits $\vert{t_c-t_f}\vert$ with a normally distributed random effect of data set $s$ included \[$\epsilon_{\alpha_s,s} \sim N(0,\sigma_{\alpha_s})$].
[^note]:For fitting the model the equation of $\alpha_{c,f}$ was developped with species basal area in term of community weighted mean of the trait, see Supplementary methods for more details.
......@@ -57,9 +57,9 @@ size)[@schielzeth_simple_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 $lmer$ in
lme4[@lme4; @lme4_b] with R[@RCRAN]. We fitted two versions of this
lme4[@lme4] with R[@RCRAN]. We fitted two versions of this
model. In the first version parameters $m_{0}, m_1,
\alpha_0,\alpha_r,\alpha_i,\alpha_s$ were estimated as constant across
\alpha_0,\alpha_t,\alpha_i,\alpha_s$ were estimated as constant across
all biomes. In the second version, we repeated the same analysis as
the first version but provided for different fixed estimates of these parameters for each biome. This enabled us to explore variation between biomes. Because some biomes had few observations, we merged some biomes with similar climate. 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 data were available.
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title: Plant functional traits have globally consistent effects on competition
author:
- name: Georges Kunstler
affiliation: 1, 2
affiliation: 1, 2, 3
- name: David A. Coomes
affiliation: 3
affiliation: 4
- name: Daniel Falster
affiliation: 2
affiliation: 3
- name: Francis Hui
affiliation: 4
affiliation: 5
- name: Robert M. Kooyman