@@ -294,10 +294,12 @@ Two main data types were used: national forest inventories -- NFI, large permane
# Supplementary Results
## 
## 
pandoc.table(mat.param[c(1,3:5,2,6:14),],caption="Standardized parameters estimates and standard error (in bracket) estimated for each trait, $R^2$* of models and $\\Delta$ AIC of the model and of a model with no trait effect. Best model have a $\\Delta$ AIC of zero. See section Method for explanation of parameters",
pandoc.table(mat.param[c(1:14),],caption="Standardized parameters estimates and standard error (in bracket) estimated for each trait, $R^2$* of models and $\\Delta$ AIC of the model and of a model with no trait effect. Best model have a $\\Delta$ AIC of zero. See section Method for explanation of parameters",
normal distribution of mean 0 and standard deviation $\sigma_{\gamma}${]}
\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
species \(c\) on growth of an individual in species \(f\),
\item
\(B_{i,c,p,s}=0.25\,\pi\,\sum_{j \neq i} w_j \, D_{j,c,p,s,t}^2\) is
the sum of basal area of all individuals competitor trees \(j\) of the species
...
...
@@ -102,7 +100,7 @@ where:
neighboorhood size for tree $j$ depending on the data set (see
below). Note that \(B_{i,c,p,s}\) include all trees of species $c$
in the local neighbourhood excepted the tree
\(i\),
\(i\), and
\item
\(N_i\) is the number of competitor species in the local
neighbourhood of focal tree $i$.
...
...
@@ -141,7 +139,7 @@ and
Previous studies have proposed various decompositions of the competition parameter into key trait-based processes\footnote{There have been different approaches to modeling $\alpha$ from traits. In one of the first studies Uriarte et al.\citep{Uriarte-2010} modelled $\alpha$ as $\alpha=
\alpha_0+\alpha_d \vert t_f-t_c \vert$. Then Kunstler et al.\citep{Kunstler-2012} used two different models: $\alpha=\alpha_0+\alpha_d \vert t_f-t_c \vert$ or $\alpha=
\alpha_0+\alpha_h ( t_f-t_c )$. Finally, Lasky et
al.\citep{Lasky-2014} developped a single model including multiple processes as $\alpha=
al.\citep{Lasky-2014} developed a single model including multiple processes as $\alpha=
where \(\varepsilon_{\alpha_0, f}\sim\mathcal{N}(0,\sigma_{\alpha_0, f})\) and
\(\varepsilon_{\alpha_0, s}\sim\mathcal{N}(0,\sigma_{\alpha_0, s})\){]}. $CON$ is a binary variable taking the value one for $f=c$ (conspecific) and zero for $f \neq c$ (heterospecific),
\(\varepsilon_{\alpha_0, s}\sim\mathcal{N}(0,\sigma_{\alpha_0, s})\){]}. $C$ is a binary variable taking the value one for $f=c$ (conspecific) and zero for $f \neq c$ (heterospecific),
\item
\(\alpha_t\) is the \textbf{tolerance of competition} by the focal
species, i.e.~change in competition tolerance due to traits \(t_f\) of
Estimating separate $\alpha_0$ for intra and interspecific competition allows to account for traitindependant differences in interactions with conspecific or with heterospecific.
Estimating separate $\alpha_0$ for intra and interspecific competition allowed us to account for trait-independent differences in interactions with conspecifics and heterospecifics.
We also explored a simpler version of the model where only one $\alpha_0$ was included in the model of$\alpha_{c,f}$ as most previous studies have generally not make this distinction which may lead into an overestimation of the trait dissimilarity effect. In this alternative model the equation was:
We also explored a simpler version of the model where trait-independent competitive effects were pooled (i.e. there was a single value for$\alpha_0$), as most previous studies have generally not make this distinction which may lead into an overestimation of the trait dissimilarity effect. In this alternative model the equation was:
