Commit f080e0f3 authored by kunstler's avatar kunstler
Browse files

first version in latex and add AIC

parent 040d9791
......@@ -745,9 +745,7 @@ extract.param.sd <- function(trait, list.res,
extract.R2c <- function(trait, list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species',
param.vec = c("logD", "Tf","sumBn", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs")){
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species'){
list.temp <- list.res[[paste("simple_", trait ,
"_", model,
sep = '')]]$lmer.summary
......@@ -755,15 +753,20 @@ extract.R2c <- function(trait, list.res,
}
extract.R2m <- function(trait, list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species',
param.vec = c("logD", "Tf","sumBn", "sumTnBn",
"sumTfBn", "sumTnTfBn.abs")){
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species'){
list.temp <- list.res[[paste("simple_", trait ,
"_", model,
sep = '')]]$lmer.summary
return(list.temp$R2m)
}
extract.AIC <- function(trait, list.res,
model = 'lmer.LOGLIN.ER.AD.Tf.r.biomes.species'){
list.temp <- list.res[[paste("simple_", trait ,
"_", model,
sep = '')]]$lmer.summary
return(list.temp$AIC)
}
## get fixed biomes
fun.get.fixed.biomes <- function(var, list,
......
all: paper.pdf extended_method.pdf extended_data.pdf
paper.pdf: paper.md include.tex refs.bib
pandoc $< metadata.yaml --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
paper.docx: paper.md include.tex refs.bib
pandoc -s -S $< metadata.yaml --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o paper.docx
extended_method.md: extended_method.Rmd
Rscript -e "library(knitr); knit('extended_method.Rmd', output = 'extended_method.md')"
extended_method.pdf: extended_method.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
extended_method.docx: extended_method.md include.tex refs.bib
pandoc -s -S $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o $@
extended_data.md: extended_data.R
Rscript -e "library(sowsear); sowsear('extended_data.R', 'Rmd')"
Rscript -e "library(knitr); knit('extended_data.Rmd', output = 'extended_data.md')"
extended_data.pdf: extended_data.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --standalone --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
SupplMat.md: Suppl_Mat.Rmd
Rscript -e "library(knitr); knit('Suppl_Mat.Rmd', output = 'SupplMat.md')"
SupplMat.pdf: SupplMat.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
clean:
rm -f *.pdf
rm -f *.html
#
......@@ -3,37 +3,42 @@ all: paper_all.pdf SupplMat.pdf extended_data.pdf paper.docx extended_method.doc
paper_all.pdf: paper.pdf extended_method.pdf
gs -dBATCH -dNOPAUSE -q -sDEVICE=pdfwrite -sOutputFile=$@ paper.pdf extended_method.pdf
paper.pdf: paper.md include.tex refs.bib
pandoc $< metadata.yaml --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -s -o $@
paper.pdf: paper.tex ms.sty references.bib
xelatex $<
bibtex paper
xelatex paper.tex
xelatex paper.tex
rm paper.log paper.out paper.aux paper.bbl paper.blg
paper.docx: paper.md include.tex refs.bib
pandoc -s -S $< metadata.yaml --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -s -o paper.docx
paper.docx: paper.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 -s -o paper.docx
extended_method.pdf: extended_method.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
extended_method.pdf: extended_method.tex ms.sty references.bib
xelatex $<
bibtex extended_method
xelatex extended_method.tex
xelatex extended_method.tex
rm extended_method.log extended_method.out extended_method.aux extended_method.bbl extended_method.blg
extended_method.docx: extended_method.md include.tex refs.bib
pandoc -s -S $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o $@
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.md: extended_data.R
extended_data.pdf: 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')"
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 $@
rm extended_data.Rmd extended_data.md
extended_data.pdf: extended_data.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --standalone --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
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 $@
SupplMat.md: Suppl_Mat.Rmd
Rscript -e "library(knitr); knit('Suppl_Mat.Rmd', output = 'SupplMat.md')"
SupplMat.pdf: SupplMat.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
SupplMat.docx: SupplMat.md include.tex refs.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o $@
SupplMat.docx: SupplMat.md SupplMat.pdf include.tex references.bib
pandoc $< --csl=nature.csl --filter pandoc-citeproc --bibliography=references.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt -o $@
clean:
rm -f *.pdf
rm -f *.html
#
#
TARGETS = $(subst md,pdf,$(shell ls *.md))
all: narrative.pdf
narrative.pdf: narrative.md include.tex
pandoc $< --csl=journal-of-applied-ecology.csl --filter pandoc-citeproc --bibliography=refs.bib --template=include.tex --variable mainfont="Times New Roman" --variable sansfont=Arial --variable fontsize=12pt --latex-engine=xelatex -o $@
clean:
rm -f *.pdf
#
This diff is collapsed.
......@@ -50,35 +50,27 @@ list.t <- dlply(dat, 1, paste_name_data)
writeLines(unlist(list.t[dat[["Country"]]]))
```
## References for the data extracted from the TRY database used in this analysis
```{r refs data, echo = FALSE, results='asis'}
data.refs <-read.csv(file.path("../..", 'output', 'refsTRYtidy.csv'), stringsAsFactors = FALSE)
list.t <- lapply(as.list(data.refs$refs), function(x) paste("- ",x))
writeLines(unlist(list.t))
```
# Supplementary discussion
## 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 drivers of tree growth[@stephenson_rate_2014; @enquist_allometric_1999]. Then there was a consistent negative effect of the total basal area of neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height > 10cm), agree well with the idea that facilitation processes are generally limited to the regeneration phase rather than at the adult stage [@callaway_competition_1997].
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 drivers of tree growth[@Stephenson-2014; @Enquist-1999]. Then there was a consistent negative effect of the total basal area of neighbouring competitors across all biomes. The dominance of a competitive effect for the growth of adult trees (diameter at breast height > 10cm), agree well with the idea that facilitation processes are generally limited to the regeneration phase rather than at the adult stage [@Callaway-1997].
In term of traits effects, Wood density (WD) was strongly negatively associated with maximum growth, in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (in full light conditions) than shade tolerant species[@nock_wood_2009; @wright_functional_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 a low wood density species will have a higher basal area increment than a high wood density species[@enquist_allometric_1999]. Other advantages of light wood may include higher xylem conductivity[@chave_towards_2009], though for angiosperms this is a correlated trait rather than an automatic consequence. A countervailing advantage for high wood density species was their better tolerance to 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_towards_2009; @nock_wood_2009; @wright_functional_2010]. This has generally been related to the higher survival associated with high wood density[@kraft_relationship_2010], via resistance to mechanical damage, herbivores and pathogens[@chave_towards_2009; @kraft_relationship_2010], but may also be connected to a lower maintenance respiration[@larjavaara_perspective_2010]. For growth, the lower respiration may lead to a direct advantage in deep shade, but the correlation might also arise through correlated selection for high survival rate and for high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effect, especially in tropical forest where the confidence interval did not span zero. This might possibly have been mediated by larger crowns (both in depth and radius)[@poorter_architecture_2006; @aiba_architectural_2009], casting a deeper shade.
In term of traits effects, Wood density (WD) was strongly negatively associated with maximum growth, in agreement with the idea that shade-intolerant species with low wood density have faster growth in absence of competition (in 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 a low wood density species will have a higher basal area increment than a high wood density species[@Enquist-1999]. Other advantages of light wood may include higher xylem conductivity[@Chave-2009], though for angiosperms this is a correlated trait rather than an automatic consequence. A countervailing advantage for high wood density species was their better tolerance to 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 generally 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], but may also be connected to a lower maintenance respiration[@Larjavaara-2010]. For growth, the lower respiration may lead to a direct advantage in deep shade, but the correlation might also arise through correlated selection for high survival rate and for high growth in shade. Finally, high wood density was also weakly correlated with stronger competitive effect, especially in tropical forest where the confidence interval did not span zero. This might possibly have been mediated by larger crowns (both in depth and radius)[@Poorter-2006a; @Aiba-2009], casting a deeper shade.
SLA was positively correlated with maximum basal area growth (growth without competition). This agrees well with previous studies that reported a positive correlation between SLA and nitrogen and phosphorus concentration, and gas exchange (the 'leaf economic spectrum'[@wright_worldwide_2004]). As in previous studies[@poorter_are_2008; @wright_functional_2010], this direct effect of SLA was smaller than the effect size of wood density and had wider confidence intervals. 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_review_2010].
SLA was positively correlated with maximum basal area growth (growth without competition). This agrees well with previous studies that reported a positive correlation between SLA and nitrogen and phosphorus concentration, and gas exchange (the 'leaf economic spectrum'[@Wright-2004]). As in previous studies[@Poorter-2008; @Wright-2010], this direct effect of SLA was smaller than the effect size of wood density and had wider confidence intervals. 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_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.
Maximum height was weakly positively correlated with maximum growth rate (confidence intervals spanned zero except for temperate rain forest). Previous studies[@Poorter-2006a; @Poorter-2008; @Wright-2010] found mixed support for this relationship. Possible mechanisms are contradictory: maximum height may be associated with greater access to light and thus faster growth, but at the same time life history strategies might be expected to select for slower growth in long-lived plants[@Poorter-2008]. Maximum height was negatively correlated with tolerance to competition (confidence intervals spanned zero except for temperate rain forest and taiga), in line with the idea that sub-canopy trees are more shade-tolerant[@Poorter-2006a]. There was however a tendency for species with tall maximum height to have stronger competitive 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 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.
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-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-1990; @Goldberg-1991; @Wang-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-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-2012; @Kraft-2014; @Lasky-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].
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-2014].
## 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 (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).
Overall most results were rather consistent across biomes (Fig 2 main text), but some exceptions deserve comment.
Only for SLA, the sign of the effect size parameters were changing a lot between biomes (Fig. 2 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-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 2 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
......
% Functional traits have globally consistent effects on plant competition
% Georges Kunstler; David A Coomes; Daniel Falster; Francis Hui;
Rob Kooyman; Daniel Laughlin Lourens Poorter; Mark Vanderwel;
Ghislain Vieilledent; Joe Wright; Masahiro Aiba; John Caspersen;
Sylvie Gourlet-Fleury; Marc Hanewinkel; Bruno Herault; Hiroko Kurokawa;
Yusuke Onoda; Maria Uriarte; Sarah Richardson; Paloma Ruiz;
I-Fang Sun; Goran Ståhl; Nathan Swenson; Jill Thompson; Miguel Zavala;
Hongcheng Zeng; Jess Zimmerman; Niklaus E Zimmermann; and Mark Westoby.
% BES-SFE Annual Meeting
Competition is a very important type of ecological interaction, especially in terrestrial vegetation where plants greatly modify the local environment for each other. Competitive interactions influence the growth and survival of individuals, and thereby change community composition over time into the future. However firm generalizations have yet to be established about outcomes of competition among species. Here we show that key species’ traits have consistent influences on growth and competition. Our analysis synthesize individuals tree growth data for more than 3-millions trees across a global set of national forest inventories plus also several large forest-monitoring plots. Some traits have a strong effect on the growth rate of the species. Then traits in part determine the tolerance to competition and the impact of competitor’s on a focal tree. A notable generalization is that trait values that favour tolerance to competition also render species slow growing in absence of competition. There is also a small but detectable benefit in reducing competition from trait-dissimilarity between a focal plant and its competitors. The trait-based picture that emerges is much simpler and more general than a quantification of competition coefficients between each pair of species, which is intractable at the global scale. Our results demonstrate that traits may be used to predict competitive interactions in forests at a large scale. We also anticipate our results to have a profound influence on trait-based-models of community.
# Extend data
```{r options-chunk, echo = FALSE, results = 'hide', message=FALSE}
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
``` {r This deals with some path issues, echo = FALSE, results = 'hide'}
git.root <- function() {
system("git rev-parse --show-toplevel", intern=TRUE)
}
source.root <- function(filename) {
source(file.path(git.root(), filename), chdir=TRUE)
}
readRDS.root <- function(filename) {
readRDS(file.path(git.root(), filename))
}
```
``` {r Load script, echo = FALSE, results = 'hide', message=FALSE}
path.root <- git.root()
```
# Data description
``` {r kable2, echo = FALSE, results="asis", message=FALSE}
library(pander)
data.set <-read.csv(file.path(path.root, 'output', 'data.set.csv'), stringsAsFactors = FALSE)
dat.2 <- data.set[, -(2)]
dat.2[dat.2$set == 'NVS',1] <- 'New Zealand'
dat.2[dat.2$set == 'NSW',1] <- 'Australia'
dat.2[dat.2$set == 'Swiss',1] <- 'Switzerland'
dat.2[dat.2$set == 'BCI',1] <- 'Panama'
dat.2[dat.2$set == 'Fushan',1] <- 'Taiwan'
dat.2[dat.2$set == 'Luquillo',1] <- 'Puerto Rico'
dat.2[dat.2$set == 'Mbaiki',1] <- 'Central African Republic'
var.names <- colnames(dat.2)
var.names[2] <- '# of trees'
var.names[3] <- '# of species'
var.names[4] <- '# of plots/quadrats'
var.names[5] <- '% of angiosperm'
var.names[6] <- '% of evergreen'
var.names[7] <- '% cover Leaf N'
var.names[8] <- '% cover Seed mass'
var.names[9] <- '% cover SLA'
var.names[10] <- '% cover Wood density'
var.names[11] <- '% cover Max height'
colnames(dat.2) <- var.names
dat.2 <- as.data.frame(dat.2)
rownames(dat.2) <- NULL
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 tree, species and plot in NFI data and quadrat in LPP data, and 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 sites. 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)
```
``` {r Describe data, echo = FALSE, results = 'hide', message=FALSE}
source.root("R/analysis/lmer.output-fun.R")
source.root("R/analysis/lmer.run.R")
source.root("R/utils/plot.R")
```
# Model results
``` {r ComputeTable_Effectsize, echo = FALSE, results = 'hide', message=FALSE}
list.all.results <-
readRDS.root('output/list.lmer.out.all.NA.simple.set.rds')
library(pander)
mat.param <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.param, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species',
param.vec = c("(Intercept)", "logD", "Tf","sumBn",
"sumTnBn","sumTfBn", "sumTnTfBn.abs")))
mat.param.sd <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.param.sd, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species',
param.vec = c("(Intercept)", "logD", "Tf","sumBn",
"sumTnBn","sumTfBn", "sumTnTfBn.abs")))
mat.R2c <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.R2c, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
mat.R2m <- do.call('cbind', lapply(c('Wood.density', 'SLA', 'Max.height'),
extract.R2m, list.res = list.all.results,
model = 'lmer.LOGLIN.ER.AD.Tf.r.set.species'))
bold.index <- which(((mat.param - 1.96*mat.param.sd) >0 & mat.param > 0) |
((mat.param + 1.96*mat.param.sd) <0 & mat.param <0),
arr.ind = TRUE)
mat.param.mean.sd <- matrix(paste0(round(mat.param, 3),
' (',
round(mat.param.sd, 3),
')'), ncol = 3)
mat.param <- rbind(mat.param.mean.sd,
round(mat.R2m, 4),
round(mat.R2c, 4))
colnames(mat.param) <- c('Wood density', 'SLA', 'Maximum height')
row.names(mat.param) <- c('$m_0$', '$\\gamma$', '$m_1$', '$\\alpha_0$',
'$\\alpha_i$', '$\\alpha_r$',
'$\\alpha_s$', '$R^2_m$*', '$R^2_c$*')
```
``` {r Table2_Effectsize, echo = FALSE, results='asis', message=FALSE}
pandoc.table(mat.param[c(1,3,2,4:9), ], caption = "Standaridized parameters estimates and standard error (in bracket) estimated for each traits and $R^2$* of models. See Fig 1. in main text for explanation of parameters",
digits = 3, justify = c('left', rep('right', 3)),
emphasize.strong.cells = bold.index, split.tables = 200)
```
\* We report the conditional and marginal $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133142 (2013), modified by Johnson, P. C. D. Extension of Nakagawa and Schielzeths R2GLMM to random slopes models. Methods in Ecology and Evolution 5, 944946 (2014).
# Extend data
![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
# Data description
-------------------------------------------------------------------------------------------------------------
set # of trees # of species # of plots/quadrats % of angiosperm % of evergreen
------------------------ ------------ -------------- --------------------- ----------------- ----------------
Sweden 202519 26 22552 27.0 73.0
New Zealand 53775 117 1415 94.0 99.1
US 1370481 493 59840 63.4 37.2
Canada 495008 75 14983 34.4 64.9
Australia 906 101 63 99.9 92.4
France 184316 127 17611 74.1 28.5
Switzerland 28301 61 2597 36.4 55.2
Spain 418805 122 36462 34.7 81.6
Panama 27028 238 2033 99.8 77.6
Paracou 46513 716 2157 100.0 83.5
Japan 4619 140 318 72.7 70.4
Taiwan 14701 72 623 92.0 75.3
Puerto Rico 14011 82 399 100.0 99.0
Central African Republic 17591 204 989 99.5 72.4
-------------------------------------------------------------------------------------------------------------
Table: Data description, with number of individual tree, species and plot in NFI data and quadrat in LPP data, and percentage of angiosperm and evergreen species.
----------------------------------------------------------------------------------
set % cover SLA % cover Wood density % cover Max height
------------------------ ------------- ---------------------- --------------------
Sweden 100 100 98
New Zealand 100 100 100
US 91 94 100
Canada 99 99 100
Australia 0 99 100
France 99 99 100
Switzerland 97 95 100
Spain 97 99 100
Panama 93 93 95
Paracou 73 73 63
Japan 100 100 100
Taiwan 100 99 96
Puerto Rico 99 99 99
Central African Republic 40 47 0
----------------------------------------------------------------------------------
Table: Traits coverage in each sites. Percentage of species with species level trait data.
# Model results
------------------------------------------------------------------------
&nbsp; Wood density SLA Maximum height
---------------- ----------------- ------------------ ------------------
**$m_0$** 0.191 (0.101) 0.083 (0.1) **0.186 (0.082)**
**$m_1$** **-0.131 (0.04)** **0.118 (0.055)** **0.045 (0.04)**
**$\gamma$** **0.419 (0.011)** **0.395 (0.011)** 0.419 (0.011)
**$\alpha_0$** **-0.161 (0.03)** **-0.135 (0.034)** **-0.159 (0.033)**
**$\alpha_i$** -0.022 (0.015) **0.079 (0.025)** -0.017 (0.029)
**$\alpha_r$** **0.061 (0.023)** -0.013 (0.032) -0.062 (0.037)
**$\alpha_s$** **0.039 (0.012)** **0.058 (0.022)** **0.049 (0.016)**
**$R^2_m$*** 0.1214 0.1368 0.123
**$R^2_c$*** 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
\* We report the conditional and marginal $R^2$ of the models using the methods of Nakagawa, S. & Schielzeth, H. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4, 133–142 (2013), modified by Johnson, P. C. D. Extension of Nakagawa and Schielzeth’s R2GLMM to random slopes models. Methods in Ecology and Evolution 5, 944–946 (2014).
\documentclass[a4paper,11pt]{article}
\usepackage{lmodern}
\usepackage{amssymb,amsmath}
\usepackage{ifxetex,ifluatex}
\usepackage{fixltx2e} % provides \textsubscript
\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\else % if luatex or xelatex
\ifxetex
\usepackage{mathspec}
\usepackage{xltxtra,xunicode}
\else
\usepackage{fontspec}
\fi
\defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase}
\newcommand{\euro}{}
\fi
\usepackage{ms}
% use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
% use microtype if available
\IfFileExists{microtype.sty}{%
\usepackage{microtype}
\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\usepackage[numbers,sort&compress]{natbib}
\ifxetex
\usepackage[setpagesize=false, % page size defined by xetex
unicode=false, % unicode breaks when used with xetex
xetex]{hyperref}
\else
\usepackage[unicode=true]{hyperref}
\fi
\hypersetup{breaklinks=true,
bookmarks=true,
pdfauthor={Kunstler},
pdftitle={Methods},
colorlinks=true,
citecolor=blue,
urlcolor=blue,
linkcolor=magenta,
pdfborder={0 0 0}}
\urlstyle{same} % don't use monospace font for urls
\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt plus 2pt minus 1pt}
\setlength{\emergencystretch}{3em} % prevent overfull lines
\setcounter{secnumdepth}{0}
\usepackage{fancyhdr}
\pagestyle{fancy}
\rhead{Methods}
\title{Methods (1497-without refs /max 3000 words)}
\date{}
\begin{document}
\maketitle
\section{Model and analysis}\label{model-and-analysis}
To examine the link between competition and traits we used a
neighbourhood modelling
framework\citep{Canham-2006, Uriarte-2010, Ruger-2012, Kunstler-2012, Lasky-2014}
to model the growth of a focal tree of species \(f\) as a product of its
maximum growth 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),
\end{equation}
where:
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
\(G_{i,f,p,s}\) and \(D_{i,f,p,s}\) are the the annual basal area
growth and diameter at breast height of individual \(i\) from species
\(f\), plot \(p\) and data set \(s\),
\item
\(G_{\textrm{max} \, f,p,s}\) is the potential growth rate in basal
area growth for species \(f\) on plot \(p\) in data set \(s\), i.e.~in
absence of competition,
\item
\(\gamma_f\) determines the rate at which growth changes with size for
species \(f\), modelled with a normally distributed random effect of
species \(\epsilon_{\gamma, f}\) (as
\(\gamma_f = \gamma_0 + \epsilon_{\gamma, f}\) where
\(\epsilon_{\gamma, f} \sim N(0,\sigma_{\gamma})\))
\item
\(N_p\) is the number of competitor species on plot \(p\) ,
\item
\(\alpha_{c,f}\) is the per unit basal area effect of individuals from
species \(c\) on growth of an individual in species \(f\), and
\item
\(B_{i,c,p,s}= 0.25\, \pi \, \sum_{j \neq i} w_j \, D_{j,c,p,s}^2\) 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 \(i\).
\end{itemize}
Values of \(\alpha_{c,f}> 0\) indicate competition, whereas
\(\alpha_{c,f}\) \textless{} 0 indicates facilitation.
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}}.
\end{equation}
To include the effect of a focal trees' traits, \(t_f\), on its growth,
we let:
\begin{equation} \label{Gmax}