% Appendix A
\chapter{Appendix}

\section{Supplementary material of chapter 2}
\subsection{Study area}
The locations of the sites that were studied in \autoref{ch:rege} are shown in \autoref{fig:A11}.

\begin{figure}[htb]
\includegraphics[width=\textwidth]{figA11}
\caption[Locations of the 23 studied sites.]{Locations of the 23 sites studied in \autoref{ch:rege} and the Belgian Ardennes ecoregion.}
\label{fig:A11}
\end{figure}

\subsection{Assessing light conditions}\label{sec:Aphoto}
We took hemispherical photographs with a Nikon D90 camera and Sigma \SI{4.5}{\milli\metre} fisheye lens that was installed on a self-leveling mount.
 
Hemispherical photographs provide good estimates of light availability under canopy if the thresholding operation correctly classifies the pixels as sky or vegetation. Generally, the operator performs the validation visually. We validated our PACL\textsubscript{photo} estimates by comparing them with sensor measurements (PACL\textsubscript{sensor}) for one day in July 2010. Seventy PAR (Photosynthetically Active Radiation) sensors (Solem S.A., Palaiseau, France) were distributed in plots on 5 sites and in an adjacent open field. Also, the ratio between direct and global radiation ($B/G$) was measured with a BF3 sensor (Delta-T devices, Cambridge, UK). PACL\textsubscript{sensor} was calculated as the ratio of PAR measured under the canopy divided by PAR measured in the open field. We then computed PACL\textsubscript{photo} using the hemispherical photographs for the particular day in July, taking into account the observed $B/G$. We then compared PACL\textsubscript{photo} with PACL\textsubscript{sensor}. This confirmed that PACL\textsubscript{photo} was highly significantly correlated with PACL\textsubscript{sensor} ($r = 0.91$, $P < 0.001$, $n = 70$). The slope of the relationship between PACL\textsubscript{photo} and PACL\textsubscript{sensor} was not significantly different from 1.


\subsection{Modeling procedure}\label{sec:Amodeling}
We selected the models for use in the present study (\autoref{ch:rege}) by following the four steps outlined below. 

\subsubsection[Step 1]{Step 1: Choosing a nonlinear saturated model}
Four commonly used models were tested to express height increment, $iH$, in relation to the percentage of above-canopy light, PACL, and initial height, $H$ (\autoref{tab:A11models}). In these models, maximum growth (asymptote) is a linear expression of the initial height with a random factor ($\alpha_j$) on the intercept.

\begin{table}
\caption[Description of the tested sigmoid models.]{Formulations and interpretations of the tested sigmoid models of the mean annual height increment ($iH_{ij}$) of regeneration in site $j$ and plot $i$.}
\footnotesize
\begin{tabularx}{\textwidth}{llX}
\toprule
 & \textsc{model} & \textsc{interpretation} \\
\midrule
Power & $(\alpha_j + a + b \: H_{ij}) \: PACL^c_{ij}$ & $c=1$, $iH$ increases linearly with PACL; $c<1$, $iH_{ij}$ increases at a decreasing rate with PACL; $c>1$, $iH_{ij}$ increases at an increasing rate with PACL.\\

Michaelis-Menten & $(\alpha_j + a + b \: H_{ij}) \: \frac{PACL^c_{ij}}{c+PACL_{ij}}$ & $iH_{ij}$ increases at a decreasing rate with PACL and $c$ is the value of PACL at which $iH_{ij}$ is half of its maximum.\\

simplified logistic & $(\alpha_j + a + b \: H_{ij}) \: \frac{1}{1+\exp(1-PACL_{ij}/c)}$ & $iH_{ij}$ increases at a decreasing rate with PACL and $c$ is the value of PACL at inflection point.\\

Chapman-Richard & $(\alpha_j + a + b \: H_{ij}) \: \frac{1}{1+\exp(-c \: PACL_{ij})}$ & $c \approx 0$, $iH_{ij}$ increases linearly with PACL; $iH_{ij}$ saturates more rapidly as c increases.\\
\bottomrule
\end{tabularx}
\label{tab:A11models}
\end{table}

Model selection was performed using Akaike’s information criterion (AIC, \autoref{eq:AAIC}). This criterion penalizes models with a high number of parameters ($K$) and a high sums-of-squares residuals (RSS) or a low likelihood. The minimum AIC implies the best fit, but to better interpret their values, we computed the weight of evidence (or an indicative probability) for model $m$ being the best approximating model ($\omega_i$, \autoref{eq:Aweights}), given the data and the set of tested models $r$.

\begin{equation}
\textnormal{AIC} = - 2 \: \ln(\textnormal{likelihood}) + 2 \: k = \ln(\textnormal{RSS}/n) + 2 \: K
\label{eq:AAIC}
\end{equation}

\begin{align}
\label{eq:Aweights}
\Delta_m & = AIC_m - \min(\textnormal{AIC}_r) \\
w_m & = \frac{\exp(-0.5 \: \Delta_m)}{\sum_r \exp(-0.5 \: \Delta_r)} \nonumber
\end{align}

The logistic model provided the best fits for beech, whereas the Chapman-Richard model provided the best fits for oak (\autoref{tab:A12}). Nevertheless, AIC differences were rather weak. In contrast to the power and Michaelis-Menten models, the logistic and Chapman-Richard models are sigmoid models and have an inflection point. These two latter models led to a lower AIC, i.e., better model fits. Due to convergence problems that were faced with the Chapman-Richard model and to ensure consistency between the oak and beech models, we selected the logistic model for both species.

\begin{table}[htbp]
\caption[Comparison of 4 different models of sapling growth.]{Comparison of 4 different models of sapling height growth. A description of these models is given in \autoref{tab:A11models}. The table summarizes the number of plots ($n$), the number of sites ($n_{\textnormal{sites}}$), the Akaike information criterion (AIC), the residual sums-of-squares (RSS), the difference between the model AIC and the lowest AIC ($\Delta_m$), and the weight of evidence for a model being the best model ($\omega_m$).}
\footnotesize
\begin{tabularx}{\textwidth}{llRRRRRR}
\toprule
\textsc{species} & \textsc{model} & $n$ & $n_{\textnormal{sites}}$ & AIC & RSS & $\Delta_m$ & $\omega_m$ \\ \midrule
\multicolumn{1}{l}{Oak} & Chapman-Richard & 174 & 18 & 1206 & 6.961 & 0.000 & 0.492 \\ 
\multicolumn{1}{l}{} & Logistic & 174 & 18 & 1208 & 6.975 & 1.341 & 0.252 \\ 
\multicolumn{1}{l}{}& Michaelis-Menten & 174 & 18 & 1208 & 7.013 & 1.672 & 0.213 \\ 
\multicolumn{1}{l}{} & Power & 174 & 18 & 1211 & 7.116 & 4.880 & 0.043 \\
\multicolumn{ 1}{l}{Beech} & Logistic & 149 & 18 & 1157 & 10.639 & 0.000 & 0.582 \\ 
\multicolumn{1}{l}{} & Chapman-Richard & 149 & 18 & 1158 & 10.695 & 0.923 & 0.367 \\ 
\multicolumn{1}{l}{} & Power & 149 & 18 & 1162 & 10.980 & 4.838 & 0.052 \\ 
\multicolumn{1}{l}{}& Michaelis-Menten & 149 & 18 & 1365 & 21.092 & 208.259 & 0.000 \\ \bottomrule
\end{tabularx}
\label{tab:A12}
\end{table}

\subsubsection[Step 2]{Step 2: Choosing the expression of maximum growth} 
Different expressions of maximum growth were similarly tested. They varied in terms of explanatory variables, number of parameters, and random structure.
 
A comparison of the different fits (\autoref{tab:A13}) indicated that the expressions of maximum height growth were unlikely to be linear. The best fits (lowest AIC) were obtained using the square root and natural logarithm transformations of the initial heights for oak and beech saplings, respectively. This finding justified modeling absolute height growth rather than relative height growth ($iH/H$). The best expression of maximum growth with only one fixed parameter was $\alpha_i + b \: \sqrt{H_{ij}}$ for both species in which $i$ and $j$ are subscripts that refers to the sites and plots, respectively.

\begin{table}[htbp]
\caption[Comparison of expressions of maximum growth.]{Comparison of expressions of maximum height growth. The second column lists the tested expressions of maximum height growth. Also, the table summarizes the number of plots ($n$), the number of sites ($n_{\textnormal{sites}}$), the Akaike information criterion (AIC), the residual sums-of-squares (RSS), the difference between the model AIC and the lowest AIC ($\Delta_m$), and the weight of evidence for a model being the best model ($\omega_m$).}
\footnotesize
\begin{tabularx}{\textwidth}{llRRRRRRR}
\toprule
\textsc{species} & \textsc{maximum height growth} & $n$ & $n_{\textnormal{sites}}$ & $K$ & RSS & AIC & $\Delta_m$ & $w_m$ \\ \midrule
Oak & $\alpha_i + a + b \: \sqrt{H_{ij}}$ & 174 & 18 & 5 & 167919 & 1206 & 0.000 & 0.329 \\ 
 & $\alpha_i +b \: H_{ij}^d$ & 174 & 18 & 5 & 168153 & 1206 & 0.242 & 0.291 \\ 
 & $\alpha_i +a+b \: H_{ij}$ & 174 & 18 & 5 & 169804 & 1208 & 1.943 & 0.124 \\ 
 & $\alpha_i +b \: \sqrt{H_{ij}} $& 174 & 18 & 4 & 171928 & 1208 & 2.105 & 0.115 \\ 
 & $\alpha_i +b \: H_{ij}$ & 174 & 18 & 4 & 171977 & 1208 & 2.154 & 0.112 \\ 
 & $\alpha_i +a+b \: log(H_{ij})$ & 174 & 18 & 5 & 172700 & 1211 & 4.885 & 0.029 \\ 
 & $(\alpha_i +b) \: H_{ij}$ & 174 & 18 & 4 & 182419 & 1218 & 12.411 & 0.001 \\ 
 & $\alpha_i +b \: log(H_{ij})$ & 174 & 18 & 4 & 189818 & 1225 & 19.330 & 0.000 \\ 
 & $(\alpha_i +a) \: H_{ij}^b $& 174 & 18 & 5 & 190158 & 1227 & 21.641 & 0.000 \\ 
 & $\alpha_i +b \: age_i $& 174 & 18 & 4 & 208218 & 1241 & 35.428 & 0.000 \\ 
 & $\alpha_i +a+b \: age_i$ & 174 & 18 & 5 & 207940 & 1243 & 37.195 & 0.000 \\ 
 & $\alpha_i +a $& 174 & 18 & 4 & 219472 & 1250 & 44.587 & 0.000 \\ 
 \addlinespace[2mm]
Beech & $\alpha_i +a+b \: log(H_{ij})$ & 149 & 18 & 5 & 317102 & 1152 & 0.000 & 0.441 \\ 
 & $\alpha_i + b \: H_{ij}^d $& 149 & 18 & 5 & 321400 & 1154 & 2.006 & 0.162 \\ 
 & $\alpha_i +b \: \sqrt{H_{ij}}$ & 149 & 18 & 4 & 326156 & 1154 & 2.195 & 0.147 \\ 
 & $\alpha_i +b \: log(H_{ij})$ & 149 & 18 & 4 & 327180 & 1154 & 2.662 & 0.116 \\ 
 & $\alpha_i +a+b \: \sqrt{H_{ij}}$ & 149 & 18 & 5 & 322998 & 1155 & 2.745 & 0.112 \\ 
 & $\alpha_i +a+b \: H_{ij}$ & 149 & 18 & 5 & 330010 & 1158 & 5.945 & 0.023 \\ 
 & $(\alpha_i +a) \: H_{ij}^b$ & 149 & 18 & 5 & 353393 & 1168 & 16.145 & 0.000 \\ 
 & $\alpha_i +a $& 149 & 18 & 4 & 374125 & 1174 & 22.640 & 0.000 \\ 
 & $\alpha_i +a+b \: age_i $& 149 & 18 & 5 & 372368 & 1176 & 23.938 & 0.000 \\ 
 & $\alpha_i +b \: age_i$ & 149 & 18 & 4 & 381950 & 1178 & 25.724 & 0.000 \\ 
 & $\alpha_i +b \: H_{ij}$ & 149 & 18 & 4 & 384742 & 1179 & 26.809 & 0.000 \\ 
 & $(\alpha_i +b)\: H_{ij}$ & 149 & 18 & 4 & 410148 & 1188 & 36.337 & 0.000 \\ 
 \bottomrule
\end{tabularx}
\label{tab:A13}
\end{table}

\subsubsection[Step 3]{Step 3: Adding the interspecific competition effect}
We computed an index ($HREL$) describing the social status of dominant saplings of each species. For every plot $j$ and species $s$, the social status was computed as the ratio between the heights of species $s$ ($\overline{H09}_{ijs}$) and the maximum height reached by all species that were found in the plot (\autoref{eq:Ahrel}). In the main manuscript, we simplified this index using $SDOM$, which is a dummy variable that enables us to distinguish overtopped species ($HREL<1$) from overtopping species ($HREL=1$).

\begin{equation}
HREL_{ijs} = \frac{\overline{H09}_{ijs}}{\max(\overline{H09}_{ijs})}
\label{eq:Ahrel}
\end{equation}

Next, interspecific competition ($HREL$ or $SDOM$) was included in the expression of the maximum growth, or in the expression of the location of the inflection point. Models were compared with the AIC and whenever they were nested with a model that did not include the competition effect, the significance of the competition effect was tested using the likelihood ratio test \citep{Pinheiro2011}. In addition, we attempted to include in the models additional explanatory variables such as herbaceous cover, height type and regeneration density.

Interspecific competition ($HREL$) was included in the models by adding a parameter that had either a single value ($d$) or two distinct values ($d_{SDOM}$) corresponding to overtopped and overtopping regenerations (\autoref{tab:A14}). Adding the interspecific competition in the models for oak significantly reduced the AIC, but it did not improve the model for beech (\autoref{tab:A14}). For oak, the best fit was obtained either with a reduction in the maximum growth or with a shift in the inflection point. We preferred the latter for its direct biological interpretation. For beech, adding $HREL$ did not improve the fit.
 
Next, the fixed intercept (coefficient $a$ in \autoref{tab:A11models}) was found not to be significant and, therefore, was dropped. We then selected the best maximum growth expression from among those with only one fixed parameter (\autoref{tab:A13}). Furthermore, we attempted to include in the models the effects of sapling density and regeneration composition as well as the effects of herbaceous height and cover (\autoref{fig:A13}). However, these characteristics did not improve significantly model fitting.

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\begin{table}[htbp]
\caption[Comparison of models including different competition effects.]{Comparison of models including different competition effects. The competition effect reduced the maximum growth, shifted the inflection point or reduced growth at all light levels. The parameter $d$ was used to test these effects. Where overtopped saplings were distinguished from overtopping saplings, two estimates ($d_{SDOM}$) were used. In such cases, the first estimate corresponded to the overtopping regeneration, while the second corresponded to overtopped regeneration. The table below includes the number of plots ($n$), the number of sites ($n_{\textnormal{sites}}$), the Akaike information criterion (AIC), the residual sums-of-squares (RSS), the difference between model AIC and the lowest AIC ($\Delta_m$), and the weight of evidence for a model being the best model ($\omega_m$). The likelihood value ($L$) and the corresponding P-value ($P$) of the likelihood ratio test of nested models are also shown.}
\scriptsize
\begin{tabularx}{\linewidth}{lllrrrrRRRRRR}
\toprule
\textsc{reduction in maximum growth} & \textsc{shift of the inflection point} & \textsc{growth reductor} & $n$ & $n_{\textnormal{sites}}$ & $K$ & $d$/$d_{SDOM}$ & RSS & AIC & $L$ & $P$ & $\Delta_m$ & $w_m$ \\ 
\midrule
\textsc{oak}  & & & & & & & & & & & & \\
	\quad $\alpha_i + b \: \sqrt{H_{ij}} + d_{SDOM}$  &  &  & 174 & 18 & 6 & 1.473; -5.27 & 160947 & 1200 & 7.378 & 0.007 & 0.000 & 0.370 \\ 
      & $\exp(-PACL / d_{SDOM} + 1)$ &  & 174 & 18 & 6 & 0.061; 0.097 & 160953 & 1200 & 7.372 & 0.007 & 0.006 & 0.369 \\ 
      & $\exp(-PACL / (c + d \: HREL) + 1)$ &  & 174 & 18 & 6 & -0.096 & 162620 & 1202 & 5.578 & 0.018 & 1.799 & 0.150 \\ 
      &  & $HREL^d$ & 174 & 18 & 6 & 0.238 & 164284 & 1204 & 3.807 & 0.051 & 3.570 & 0.062 \\ 
      &  &  & 174 & 18 & 5 &  & 167918 & 1206 &  &  & 5.378 & 0.025 \\ 
    \quad $\alpha_i + a + b \: \sqrt{H_{ij}} + dHREL$ &  &  & 174 & 18 & 6 & 7.329 & 166095 & 1206 & 1.900 & 0.168 & 5.478 & 0.024 \\ 
      & $\exp(-PACL/(d \: HREL) + 1)$ &  & 174 & 18 & 5 & 0.066 & 178712 & 1217 &  &  & 16.218 & 0.000 \\ 
      &  & $\exp(d \: HREL)$ & 174 & 18 & 6 & 0.929 & 179900 & 1220 & 11.993 & 0.001 & 19.371 & 0.000 \\ 
\addlinespace[2mm]
\textsc{beech}  & & & & & & & & & & & & \\
     & $\exp(-PACL/(d \: HREL) + 1)$ &  & 149 & 18 & 5 & 0.039 & 315724 & 1151 &   &   & 0.000 & 0.224 \\ 
      & $\exp(-PACL/(d_{SDOM}) + 1)$ &  & 149 & 18 & 6 & 0.041; 0.021 & 312349 & 1152 & 2.251 & 0.134 & 0.399 & 0.183 \\ 
      &  &  & 149 & 18 & 5 &  & 317104 & 1152 &  &  & 0.649 & 0.162 \\ 
      &  & $HREL^d$ & 149 & 18 & 6 & 0.138 & 315107 & 1153 & 0.941 & 0.332 & 1.708 & 0.095 \\ 
      &  & $\exp(d \: HREL)$ & 149 & 18 & 6 & -0.138 & 315107 & 1153 & 0.941 & 0.332 & 1.708 & 0.095 \\ 
    \quad $\alpha_i + a + b \: \sqrt{H_{ij}} + d \: HREL$ &  &  & 149 & 18 & 6 & 6.399 & 315326 & 1153 & 0.838 & 0.360 & 1.812 & 0.091 \\ 
    & $\exp(-PACL / (c + d \: HREL) + 1)$ &  & 149 & 18 & 6 & 0.040 & 315724 & 1153 & 5.311 & 0.070 & 2.000 & 0.082 \\ 
    \quad $\alpha_i + a + b \: \sqrt{H_{ij}} + d_{SDOM}$ &  &  & 149 & 18 & 6 & -23.819; 1.835 & 316593 & 1154 & 4.901 & 0.086 & 2.409 & 0.067 \\ 
\bottomrule
\end{tabularx}
\label{tab:A14}
\end{table}

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\subsubsection[Step 4]{Step 4: Check of the residuals}
We verified that the residuals were evenly distributed through the use of scatterplots (\autoref{fig:A13} and \autoref{fig:A12}).


\begin{figure}[htb]
\includegraphics[width=\textwidth]{figA13}
\caption[Residual dispersion versus potential explanatory variables.]{Residual scatterplots with other potential explanatory variables (\autoref{eq:3beechmodel} and \autoref{eq:3oakmodel}).}
\label{fig:A13}
\end{figure}

\begin{figure}[htb]
\includegraphics[width=\textwidth]{figA12}
\caption[Residual dispersion versus fitted values and explanatory variables.]{Residual dispersion versus fitted values and explanatory variables of the full models using \autoref{eq:3beechmodel} and \autoref{eq:3oakmodel}. The model for oak saplings fitted better with our observations than the model for beech saplings. We observed that residuals were evenly distributed, indicating no clear evidence of model bias.}
\label{fig:A12}
\end{figure}

\section{Height to the largest crown extension}\label{sec:Ahlce}
Height to largest crown cross-section ($H_{lcc}$) defines the height of the center of ellipsoid sections. This parameter is useful for defining upper and lower sections of different lengths, i.e., different values of $c$ parameter (\autoref{eq:4ellipsoid} and \autoref{fig:44crownshape}). We did not measure $H_{lcc}$ in the study plots. Nevertheless, Dr. Mathieu Jonard (2012, pers. comm.) had measured it in mixed forests of oak and beech that were located in the Belgian Ardennes. Next, he adjusted the following models to predict the height to the largest crown extension for oak trees (\autoref{eq:AjonardOak}, $R^2=$ \SI{64.7}{\percent}):

\begin{equation}
\label{eq:AjonardOak}
H_{lcc} = H_{cb} + 0.4209 \: (H - H_{cb})
\end{equation}

And, for beech trees (\autoref{eq:AjonardBeech}, $R^2 =$ \SI{75.1}{\percent}):

\begin{equation}
\label{eq:AjonardBeech}
H_{lcc} = H_{cb} + (0.1126 + 0.0129 \: H / 100) \: (H - H_{cb})
\end{equation}

For other broadleaved species, we can assume that $H_{lcc}$ corresponds to the mid-height of the crown, i.e., $H_{lcc} = H_{cb} + 0.5 \: (H - H_{cb})$; for coniferous trees, we can assume that the crown has a parabolic crown shape, i.e., $H_{lcc} = H_{cb}$.

\section[Light predictions of SamsaraLight and SORTIE-ND]{Comparison of light predictions of SamsaraLight and SORTIE-ND}\label{sec:comparison}
We compared predictions of the percentage of above-canopy light (PACL) that were made by the two radiative transfer models with PACL measures. The two tested models are SamsaraLight and SORTIE-ND. SamsaraLight is the radiative transfer model that was used in this thesis and is implemented in the Capsis platform, whereas SORTIE-ND is a stand dynamic simulator that contains a radiative transfer model \citep{Canham2011}.
 
Both radiative transfer models are ray-tracing models but differences are expected due to different calibration methods, ray sampling, and algorithm implementation. We attempted to verify whether the use of a common dataset for both models would provide similar predictions.

\subsection{Method}
\subsubsection{Datasets}
We used two datasets. The first corresponds to the dataset used for this thesis, with 19 plots in mixed uneven-aged forests of oak (\textit{Quercus Petraea} (Matt.) Liebl.) and beech (\textit{Fagus sylvatica} L.). Understory light was measured with 310 hemispherical photographs. The second dataset has been provided by Dr. Aitor Ameztegui and contains 24 plots in even-aged forests of silver fir (\textit{Abies alba} Miller), Scots pine (\textit{Pinus sylvestris} L.), and mountain pine (\textit{Pinus uncinata} Ram.) in the Pyrenees \citep{Ameztegui2012}. In this latter dataset, understory light was measured with 216 hemispherical photographs.

\subsubsection{Calibration}
We set both models to model crowns with cylinders. The radius of these cylinders corresponded to the measured radius multiplied by $\sqrt{2/3}$ or $\sqrt{1/3}$ for broadleaved species or conifers, respectively (\autoref{tab:A31}). With this correction, the volume of the cylinders is closer to the volume of the measured crowns, which are assumed to have ellipsoid or conic shapes. Both the turbid medium and the porous envelope approaches were used. Other calibrations could be used but this study was performed for exploratory purposes and, consequently, we use calibrations that were as similar as possible between the two models and calibrations that do not involve further programming work.

\begin{table}[htbp]
  \caption[Calibration of the radiative transfer models.]{Calibration summary of the tested radiative transfer models.}
  \centering
  \footnotesize
    \begin{tabularx}{\textwidth}{lXXXXX}
    \toprule
   	 & \textsc{beech} & \textsc{sessile oak} & \textsc{silver fir} & \textsc{scots pine} & \textsc{mountain pine} \\
    \midrule
\textsc{SamsaraLight} & & & & & \\
	\quad crown shape & cylinder & cylinder & cylinder & cylinder & cylinder \\
    \quad crown radius & $\cdot \sqrt{2/3}$ & $\cdot \sqrt{2/3}$ & $\cdot \sqrt{1/3}$ & $\cdot \sqrt{1/3}$ & $\cdot \sqrt{1/3}$ \\
    \quad LAD   & \multicolumn{2}{c}{Model, see \autoref{tab:412LAD}} &  -     &    -   & - \\
    \quad Crown openness &  -     &   -    & 0.086 & 0.205 & 0.116 \\
     \addlinespace[2mm]  
\textsc{SORTIE-ND}& & & & & \\
 	\quad crown shape & cylinder & cylinder & cylinder & cylinder & cylinder \\
	\quad crown radius & $\cdot \sqrt{2/3}$ & $\cdot \sqrt{2/3}$ & $\cdot \sqrt{1/3}$ & $\cdot \sqrt{1/3}$ & $\cdot \sqrt{1/3}$ \\
    \quad LAD   &  -     &    -   &   -    &    -   &  -\\
  	\quad Crown openness & 0.0345 & 0.122 & 0.086 & 0.205 & 0.116 \\
    \bottomrule
    \end{tabularx}%
  \label{tab:A31}%
\end{table}%

\subsection{Results and discussion}
Both models provided similar predictions of the percentage of above canopy light with the two datasets (\autoref{fig:A31}). Predictions were poorer with the Belgian plots and especially with SORTIE-ND, i.e., in uneven-aged broadleaf forests versus in even-aged coniferous forests. Further work is required to determine whether predictions of PACL in heterogeneous forests require a more complex radiative transfer model than predictions of PACL in homogeneous forests. Such a study should use more than two datasets to disentangle the effects of calibration from the effects of canopy complexity. 

\begin{figure}[htb]
\centering
\includegraphics[width=0.8 \textwidth]{figA31}
\caption[Measures versus predictions of PACL.]{Predictions versus observed measures of percentage above canopy light (PACL). The coefficients of determination ($R^2$) of the linear least-squares regressions indicate the quality of model predictions.}
\label{fig:A31}
\end{figure}

\clearpage

\section{Activity list}
\subsection[Peer reviewed articles]{Articles published in peer reviewed journals}
\noindent Ligot, G., Balandier, P., Courbaud, B., Jonard, M., Kneeshaw, D. \& Claessens, H. (2014). Managing understory light to maintain a mixture of species with different shade tolerance. \textit{For. Ecol. Manage.}, 327:189-200. \href{http://hdl.handle.net/2268/163600}{handle: 2268/163600}\\

\noindent Ligot, G., Balandier, P., Courbaud, B. \& Claessens, H. (2014). Forest radiative transfer models: which approach for which application? \textit{Can. J. For. Res.}, 44(5):385-397. \href{http://hdl.handle.net/2268/163600}{handle: 2268/163600}\\
 
\noindent Ligot, G., Balandier, P., Fayolle, A., Lejeune, P. \& Claessens, H. (2013). Height competition between \textit{Quercus petraea} and \textit{Fagus sylvatica} natural regeneration in mixed and uneven-aged stands. \textit{For. Ecol. Manage.}, 304:391-398. \href{http://hdl.handle.net/2268/151307}{handle: 2268/151307}\\
 
\noindent Ligot, G., Gheysen, T., Lehaire, F., Hebert, J., Licoppe, A., Lejeune, P. \& Brostaux, Y. (2013). Modeling recent bark stripping by red deer (Cervus elaphus) in South Belgium coniferous stands. \textit{Ann. For. Sci.}, 70(3):309-318. \href{http://hdl.handle.net/2268/138556}{handle: 2268/138556}\\
 
\noindent Ligot, G., Lejeune, P., Rondeux, J. \& Hebert, J. (2012). Assessing and harmonizing lying deadwood volume with regional forest inventory data in Wallonia (southern region of Belgium). \textit{Open For. Sci. J.}, 5:15-22. \href{http://hdl.handle.net/2268/129624}{handle: 2268/129624}\\
 
\noindent Lehaire, F., Ligot, G., Morelle, K. \& Lejeune, P. (2014). Les indicateurs de la pression du cerf élaphe sur la végétation du sous-bois en forêts feuillues tempérées : synthèse bibliographique. \textit{Biotechnol., Agron., Soc. Environ.}, 18(2):262-272. \href{http://hdl.handle.net/2268/166921}{handle: 2268/166921}\\
 
\noindent Gheysen, T., Brostaux, Y., Hebert, J., Ligot, G., Rondeux, J. \& Lejeune, P. (2011). A Regional Inventory and Monitoring Setup to Evaluate Bark Peeling Damage by Red Deer (Cervus elaphus) in Coniferous Plantations in Southern Belgium. \textit{Environ. Monit. Assess.}, 181(1-4):335-45. \href{http://hdl.handle.net/2268/78072}{handle: 2268/78072}\\
 
\subsection[Non-peer reviewed articles]{Articles published in non-peer reviewed journals}
\noindent Ligot, G., Balandier, P., Mackels, B., Lehaire, F. \& Claessens, H. (2014). Suivi scientifique de vingt-sept régénérations naturelles de chêne sessile et de hêtre en Ardenne: retour d’expérience. \textit{Forêt Wallonne}, 128:3-13. \href{http://hdl.handle.net/2268/151800}{handle: 2268/151800}\\
 
\noindent Ligot, G., Lehaire, F., Gheysen, T., Licoppe, A. \& Lejeune, P. (2013). Analyse spatio-temporelle des dégâts d’écorcement dans les plantations résineuses en Région Wallonne. \textit{Forêt Wallonne}, 126:29-39. \href{http://hdl.handle.net/2268/158633}{handle: 2268/158633}\\
 
\noindent Petit, S., Claessens, H. \& Ligot, G. (2013). Quel type de peuplement pour un renouvellement naturel du douglas? \textit{Forêt Wallonne}, 122:3-12. \href{http://hdl.handle.net/2268/144343}{handle: 2268/144343}\\

\noindent Alderweireld, M., Ligot, G., Latte, N. \& Claessens, H. (2010). Le chêne en forêt ardennaise, un atout à préserver. \textit{Forêt Wallonne}, 109:10-24. \href{http://hdl.handle.net/2268/79321}{handle: 2268/79321}\\
 
\subsection{Presentations}
\noindent Ligot, G. (2014, April 29). Dynamique des forêts irrégulières et mélangées: de la modélisation aux recommandations sylvicoles. Colloque du centre d’étude de la forêt 2014, Montréal, QC, Canada. \href{http://hdl.handle.net/2268/166562}{handle: 2268/166562}\\

\noindent Ligot, G. (2014, February 18). Modélisation de la dynamique des peuplements irréguliers, Rimouski, QC, Canada. \href{http://hdl.handle.net/2268/163560}{handle: 2268/163560}\\

\noindent Ligot, G. (2013, April 09). Compétition entre le chêne sessile et le hêtre en régénération naturelle de peuplements irréguliers et mélangés. Journées CAQ-Capsis, Prenovel, France. \href{http://hdl.handle.net/2268/147108}{handle: 2268/147108}\\

\noindent Ligot, G., Jonard, M., de Coligny, F. \& Courbaud, B. (2013, April 08). Modélisation du transfert radiatif en forêts feuillues ardennaises: adaptation de la librairie Samsaralight, Journées CAQ-Capsis, Prenovel, France. \href{http://hdl.handle.net/2268/147109}{handle: 2268/147109}\\
 
\noindent Ligot, G. (2011, January 25). Prémices de modélisation de la dynamique des hêtraies-chênaies irrégulières ardennaises (Belgique). TR sedyvin, Avignon, France. \href{http://hdl.handle.net/2268/88487}{handle: 2268/88487}\\

\noindent Ligot, G. (2012, April 04). Quergus, un modèle CAPSIS de la dynamique des peuplements irréguliers et mélangés de chênes et de hêtres. Journées CAQ-Capsis, Nogent-sur-Vernisson, France. \href{http://hdl.handle.net/2268/116405}{handle: 2268/116405}\\

\noindent Ligot, G., Vallet, P., Perin, J., Cerisier, F., Lisein, J. \& Bauwens, S. (2012, April 02). Simuler la ressource forestière à l’échelle d’un massif : application de SIMMEM et GYMNOS. Journées CAQ-Capsis, Nogent-sur-Vernisson, France. \href{http://hdl.handle.net/2268/118076}{handle: 2268/118076}\\

\noindent Ligot, G., Perin, J. \& de Pierpont, A. (2011, April 06). Le DouglasModel et nos futurs projets CAPSIS. Journées CAQ-Capsis, Aix-En-Provence, France. \href{http://hdl.handle.net/2268/90140}{handle: 2268/90140}\\

\subsection{Posters}
\noindent Ligot, G. \& Rondeux, J. (2010, May 12). L’inventaire du bois mort à terre. Poster session presented at: \textit{Les inventaires forestiers nationaux, observatoires et tableaux de bord permanents des espaces boisées}, Gembloux, Belgique. \href{http://hdl.handle.net/2268/76152}{handle: 2268/76152}\\
 
\noindent Lehaire, F., Morelle, K., Ligot, G. \& Lejeune, P. (2013, August). Bioindicators for measurement of red deer pressure on understory vegetation in temperate deciduous forests. Poster session presented at: \textit{International Union of Game Biologists - Congress IUGB 2013}, Brussels, Belgium. \href{http://hdl.handle.net/2268/155182}{handle: 2268/155182}\\

\noindent Perin, J., Ligot, G., Cerisier, F., Claessens, H., Hebert, J., Lejeune, P. \& de Pierpont, A. (2012, March 02). Harmonized Growth Models and Simulations of the Evolution of Pure Stands of Norway spruce, Larches and Douglas-fir for Southern Belgium (Wallonia). Poster session presented at: \textit{COST FP0603 Final meeting: Forest models for research and decision support in sustainable forest management}, Bordeaux, France. \href{http://hdl.handle.net/2268/117125}{handle: 2268/117125}\\
 
\subsection{Reports}
\noindent Ligot, G., Mackels, B., Lehaire, F. \& Claessens, H. (2013). Suivi de 27 régénérations de chêne sessile et de hêtre : résultats pour la période de 2007 à 2012. Gembloux, Belgique: Unité de gestion des ressources forestières et des milieux naturels, ULg. \href{http://hdl.handle.net/2268/151800}{handle: 2268/151800}\\

\noindent Ligot, G., Courbaud, B., de Coligny, F., and Jonard, M., 2013. SamsaraLight: {\footnotesize \url{http://capsis.cirad.fr/capsis/help_en/samsaralight}}\\
 
\noindent Ligot,G. \& Mackels, B (2011) Photographies hémisphériques, rapport de recherche interne. Ulg, Gembloux. \href{http://hdl.handle.net/2268/168676}{handle: 2268/168676}\\

\noindent Ligot, G. (2011). R en 30 minutes. ULg, Gembloux. \href{http://hdl.handle.net/2268/91708}{handle: 2268/91708}\\

\subsection{Courses, conferences and training}
\noindent From Reasearch To Business (2012), 56h, cycle de formation avec le soutien du Fonds social européen et de la Région wallonne.\\

\noindent RDCT0002-1 - Introduction à la modélisation bayesienne (2012), 9h, Christophe Abraham, Ulg.\\

\noindent Journée d’étude sur le mécanisme REDD+ (2012), Gembloux Agro-Bio Tech et AWAC.\\

\noindent STAT 1210-2 - Logiciels statistiques et calculs statistiques sur ordinateur (2011), 24h Th, 24h Pr, Yves Brostaux, ULg.\\

\noindent STAT 1216-1 - Modèles linéaires et modélisation statistique (2011), 36h Pr, 36h Th, Rodolphe Palm, ULg.\\

\noindent Structurer son document écrit par Jean-Luc Doumont (2011), 2h, Jean-Luc Doumont, ULg.\\

\noindent RDCT0557-1 - Introduction à Quantum GIS (2011), 2h, Stephanie Bonnet, ULg.\\

\noindent L'antartique dans tous ses états: La reconstruction et les prédictions climatiques en Antarctique à différentes échelles (2011), 1h, Hugues Goose et Wim Vyverman, Collège de Belgique.\\

\noindent From scientific questions to experimental design in the study of tree and stand functioning (2011), 1h, John King, UCL.\\

\noindent Formation à Java et Capsis (2010), 2 jours, François de Coligny, AMAP-CIRAD, Montpelier, France.\\

\noindent Ecosystèmes, CO$_2$ et climat: risques et opportunités (2010), 2h, Marc Aubinet, Collège de Belgique.\\

\noindent RDCT0556-1 - GF217 – cynégétique (2009), 24h, Cédric Vermeulen, ULg.\\

\subsection{Research mobility}
\noindent Stage de recherche (2013), 1 an, Centre d’étude de la forêt, Université du Québec à Montréal, Montréal, QC, Canada.\\

\noindent Réunion de travail et implémentation de la librairie SamsaraLight de Capsis (2012), 2 jours, Mountain Ecosystems Research Unit, IRSTEA, Grenoble, France.\\

\noindent Réunion de travail et implémentation de la librairie Régénération de Capsis (2012), 2 jours, PIAF, IRSTEA, Clermont-Ferrand, France.\\

\noindent COST: Forest models for research and decision support in sustainable forest (2012), 4 days, INRA Pierroton, Bordeaux, France.\\

\noindent Réunion de travail et implémentation des modules SIMMEM, GYMNOS, QUERGUS (2011), 2 jours, AMAP-CIRAD, Montpelier, France.\\

\noindent IUFRO: ecology and sylviculture of Beech (2011), 5 days, Institute of Silviculture and Forest Protection, Dresden – Gottingen, Germany.\\

\noindent 7\textsuperscript{th} IUFRO international conference on uneven-aged silviculture: integrating ecologically-based uneven-aged silviculture with increased demands for forests (2010), 3 days, Biotechnical Faculty, Ljubljana, Slovenia.\\

\noindent Journées CAQ (2010), 2 jours, CEMAGREF, Grenoble, France.\\

\noindent Réunion de travail (2010), 2 jours, CEMAGREF, Clermont-Ferrand, France.\\

\subsection{Supervision of master’s thesis}
\noindent Sebastien Petit, 2012.\\

\subsection{Review of scientific articles}
\noindent Yang, J., Zhang G., Liu, W. \& Liu Q. Forest composition and light dynamics mediate the regeneration of Korean pine (\textit{Pinus koraiensis} Siebold \& Zucc.) at different succession stages in northeast China, \textit{Plos One}.\\

\noindent Forrester, D., Guisasola, R., Tang, X., Albrecht A.T., Lam Dong, T. \& le Maire, G. Using a stand-level model to predict light absorption in stands with vertically and horizontally heterogeneous canopies, \textit{For. Ecosyst.}.\\

\noindent Vilhar, U., Ro\v{z}enbergar, D., Simon\v{c}i\v{c}, P. \& Diaci, D. Variation in light availability, edaphic factors, and regeneration patterns in experimental canopy gaps - a case study, \textit{Ann. For. Sci}.\\
