Suppl_Mat.Rmd 3.98 KB
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% Supplementary Information 

# Supplementary methods
The log transformed growth model is:
\begin{equation} \label{logG1}
\log{G_{i,f,p,s}} = \log{G_{\textrm{max} \, f,p,s}} + \gamma_f \, \log{D_{i,f,p,s}} +  \sum_{c=1}^{N_p} {\alpha_{c,f} B_{c,p,s}}.
\end{equation}

To include traits effects on competition presented in Fig. 1 (main text), competitive interactions were modelled using an equation of the form:
\begin{equation} \label{alpha}
\alpha_{c,f} = \alpha_{0,f} + \alpha_r \, t_f + \alpha_i \, t_c + \alpha_s \, \vert t_c-t_f \vert
\end{equation}
where:

- $\alpha_{0,f}$ is the trait independent competition for the focal species $f$, modelled with a normally distributed random effect of species $f$ and a normally distributed random effect of data set $s$ (as $\alpha_{0,f} = \alpha_0 + \epsilon_{0, f}+ \epsilon_{\alpha_0, s}$),
- $\alpha_r$ is the **competitive response** of the focal species, i.e. change in competition response due to traits $t_f$ of the focal tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_r,s}$),
- $\alpha_{i}$ is the **competitive impact**, i.e. change in competition impact due to traits $t_c$ of the competitor tree and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_i,s}$), and
- $\alpha_s$ is the effect of **trait similarity**,  i.e. change in competition due to absolute distance between traits  $\vert{t_c-t_f}\vert$ and include a normally distributed random effect of data set $s$ ($\epsilon_{\alpha_s,s}$).


When the equation \label{alpha} is developed in the competition index of equation \label{logG1} 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_{c,p,s}} = \alpha_{0,f} \, B_{tot} + \alpha_r \, t_f \, B_{tot} + \alpha_i \, B_{t_c} + \alpha_s \, B_{\vert t_c - t_f \vert}
\end{equation}

Where:

$B_{tot} = \sum_{c=1}^{C_p} {B_{c}}$,

$B_{t_c} = \sum_{c=1}^{C_p} {t_c \times B_{c}}$,

and $B_{\vert t_c - t_f \vert} = \sum_{c=1}^{C_p} {\vert t_c - t_f \vert \times B_{c}}$.


## Details on sites

```{r kable, echo = FALSE, results="asis"}
library(plyr)
dat <- read.csv('../../data/metadata/sites/sites_description.csv', check.names=FALSE, stringsAsFactors=FALSE)
# reorder so references column is last
i <- match("References", names(dat))
dat <- dat[,c(seq_len(ncol(dat))[-c(i)], i)]

refs <- read.csv('../../data/metadata/sites/references.csv', check.names=FALSE, stringsAsFactors=FALSE)

replace_refs <- function(x){
	ids <- as.numeric(unlist(strsplit(x,",")))
	if(length(ids>0))
		ret <-	paste0("\n\t- ", refs$citation[match(ids, refs$id)], collapse="")
	else
		ret <- ""
}

dat$References <- sapply(dat$References, replace_refs)

paste_name_data <- function(df){
	sprintf("## %s\n\n%s\n\n", df[["Data set name"]],
		paste0(
			llply(names(df)[-c(1)], function(x) sprintf("- %s: %s", x, df[[x]])), collapse="\n")
		)
}

writeLines(unlist(dlply(dat, 1, paste_name_data)))
```

# Supplementary discussion

## Variations between biomes

The results were more variable for SLA than for other traits (Fig. 2 main text). The different sign for the parameter $\alpha_r$ related to the link between trait and competitive response in temperate forest biome, may be related to the high abundance of deciduous species in this biomes (see Extended data Table 1). Previous studies[@lusk_why_2008]  has reported a different link between shade-tolerance and SLA for deciduous and evergreen species. The only other important differences between biomes was taiga for which the parameter relating wood density to competitive impact was positive whereas this parameter was negative in the other biomes (Fig 2 main text). We have ne satisfactory explanation for this discrepancy. The number of species in this biomes is relatively limited in comparison with the other biomes and there is a high dominance of conifer species for which the range of wood density is much narrow than for the angiosperm (see Extended data Table 1). 


# References