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\hypersetup{
  pdftitle={From the simulation of forest plantation dynamics to the quantification of bark-stripping damage by ungulates : Analyses},
  pdfauthor={Gauthier Ligot},
  colorlinks=true,
  linkcolor={blue},
  filecolor={Maroon},
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  urlcolor={Blue},
  pdfcreator={LaTeX via pandoc}}

\title{From the simulation of forest plantation dynamics to the
quantification of bark-stripping damage by ungulates : Analyses}
\author{Gauthier Ligot}
\date{}

\begin{document}
\maketitle
\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[sharp corners, frame hidden, borderline west={3pt}{0pt}{shadecolor}, boxrule=0pt, enhanced, interior hidden, breakable]}{\end{tcolorbox}}\fi

\hypertarget{results}{%
\subsection{Results}\label{results}}

\hypertarget{stand-characteristics-over-time}{%
\subsubsection{Stand characteristics over
time}\label{stand-characteristics-over-time}}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-stand-1.pdf}

}

\caption{\label{fig-stand}Changes in in the main characteristics of the
simulated stands}

\end{figure}

Proportion of damaged trees increased with BSR

\begin{longtable}[]{@{}rlrr@{}}
\toprule()
bpr & scenario\_stand & damaged\_prop & damaged\_prop\_sd \\
\midrule()
\endhead
0.00 & Unprotected & 0.0000 & 0.0000000 \\
0.01 & Unprotected & 0.1665 & 0.0000000 \\
0.02 & Unprotected & 0.3153 & 0.0000000 \\
0.03 & Unprotected & 0.4402 & 0.0000000 \\
0.04 & Unprotected & 0.5457 & 0.0000000 \\
0.05 & Unprotected & 0.6334 & 0.0002216 \\
0.06 & Unprotected & 0.7052 & 0.0000000 \\
0.07 & Unprotected & 0.7645 & 0.0000000 \\
0.08 & Unprotected & 0.8125 & 0.0002843 \\
0.09 & Unprotected & 0.8513 & 0.0000000 \\
0.10 & Unprotected & 0.8827 & 0.0000410 \\
\bottomrule()
\end{longtable}

Mean productivity across the simulations

\begin{longtable}[]{@{}rrr@{}}
\toprule()
siteIndex & productivity\_mean & productivity\_sd \\
\midrule()
\endhead
21 & 11.72 & 0.03782 \\
24 & 13.20 & 0.04032 \\
27 & 14.75 & 0.04372 \\
30 & 16.22 & 0.04884 \\
33 & 17.87 & 0.05636 \\
\bottomrule()
\end{longtable}

Statistics of the decay column height

\begin{longtable}[]{@{}rrr@{}}
\toprule()
m & min & max \\
\midrule()
\endhead
2.143 & 0.5516 & 5.576 \\
\bottomrule()
\end{longtable}

\hypertarget{losses-in-timber-volume-and-value}{%
\subsubsection{Losses in timber volume and
value}\label{losses-in-timber-volume-and-value}}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-decayed-1.pdf}

}

\caption{\label{fig-decayed}Importance of the decayed wood across the
simulations}

\end{figure}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-losses-1.pdf}

}

\caption{\label{fig-losses}Undamaged volume and timber value}

\end{figure}

\hypertarget{net-present-value}{%
\subsubsection{Net present value}\label{net-present-value}}

\hypertarget{optimum-rotation-length}{%
\paragraph{Optimum rotation length}\label{optimum-rotation-length}}

\begin{longtable}[]{@{}rrr@{}}
\toprule()
siteIndex & mean\_rotation & sd\_rotation \\
\midrule()
\endhead
21 & 95.3 & 4.117996 \\
33 & 65.6 & 1.846761 \\
\bottomrule()
\end{longtable}

\begin{longtable}[]{@{}lrr@{}}
\toprule()
scenario & mean\_rotation & sd\_rotation \\
\midrule()
\endhead
Unprotected & 76 & 0 \\
Bark-scraping 400 & 76 & 0 \\
Bark-scraping all & 76 & 0 \\
Fence & 82 & 0 \\
\bottomrule()
\end{longtable}

\hypertarget{opportunity-cost-of-bark-stripping-damages}{%
\paragraph{Opportunity cost of bark-stripping
damages}\label{opportunity-cost-of-bark-stripping-damages}}

Statistics of the opportunity cost

\begin{verbatim}
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
  -36.27   857.41  1967.48  3601.11  4499.50 19444.99 
\end{verbatim}

\begin{longtable}[]{@{}rlrr@{}}
\toprule()
bpr & scenario & npv & cost \\
\midrule()
\endhead
0.0 & Unprotected & 16491.85 & 0.000 \\
0.1 & Unprotected & 11048.43 & 5443.425 \\
\bottomrule()
\end{longtable}

\begin{longtable}[]{@{}
  >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2537}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1493}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1642}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1493}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2836}}@{}}
\toprule()
\begin{minipage}[b]{\linewidth}\raggedright
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Estimate
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Std. Error
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
t value
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Pr(\textgreater\textbar t\textbar)
\end{minipage} \\
\midrule()
\endhead
bpr & 1.05e+05 & 5.43e+03 & 1.94e+01 & 0e+00 \\
bpr:discountRate & -4.75e+06 & 7.13e+04 & -6.66e+01 & 0e+00 \\
bpr:siteIndex & 3.10e+03 & 1.88e+02 & 1.65e+01 & 0e+00 \\
\bottomrule()
\end{longtable}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-opcost-1.pdf}

}

\caption{\label{fig-opcost}changes in opportunity cost with BSR}

\end{figure}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-opcosta-1.pdf}

}

\caption{\label{fig-opcosta}Changes in cost annuity with BSR}

\end{figure}

\hypertarget{net-present-value-across-treatments}{%
\paragraph{Net present value across
treatments}\label{net-present-value-across-treatments}}

\begin{longtable}[]{@{}
  >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.3659}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1341}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1341}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1341}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2317}}@{}}
\toprule()
\begin{minipage}[b]{\linewidth}\raggedright
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Estimate
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Std. Error
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
t value
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Pr(\textgreater\textbar t\textbar)
\end{minipage} \\
\midrule()
\endhead
(Intercept) & 2.468e+04 & 1.245e+03 & 1.983e+01 & 0.000e+00 \\
scenarioBark-scraping 400 & -1.373e+02 & 7.762e+02 & -1.769e-01 &
8.596e-01 \\
scenarioBark-scraping all & -1.216e+03 & 7.762e+02 & -1.566e+00 &
1.174e-01 \\
scenarioFence & -7.651e+03 & 7.762e+02 & -9.858e+00 & 0.000e+00 \\
siteIndex & 1.463e+03 & 3.457e+01 & 4.231e+01 & 0.000e+00 \\
discountRate & -1.764e+06 & 2.454e+04 & -7.186e+01 & 0.000e+00 \\
bpr & -1.308e+05 & 1.392e+04 & -9.400e+00 & 0.000e+00 \\
discountRate:bpr & 2.596e+06 & 4.149e+05 & 6.258e+00 & 0.000e+00 \\
scenarioBark-scraping 400:bpr & 2.041e+04 & 1.312e+04 & 1.556e+00 &
1.198e-01 \\
scenarioBark-scraping all:bpr & 2.540e+04 & 1.312e+04 & 1.936e+00 &
5.290e-02 \\
scenarioFence:bpr & 6.569e+04 & 1.312e+04 & 5.007e+00 & 6.000e-07 \\
\bottomrule()
\end{longtable}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-npv-1.pdf}

}

\caption{\label{fig-npv}NPV across BSR}

\end{figure}

\hypertarget{discussion}{%
\subsection{Discussion}\label{discussion}}

\hypertarget{model-assumption}{%
\subsubsection{Model assumption}\label{model-assumption}}

Tree size at initialization

\begin{longtable}[]{@{}rrr@{}}
\toprule()
siteIndex & dg\_m & dg\_sd \\
\midrule()
\endhead
21 & 3.201355 & 0.0177672 \\
24 & 3.896765 & 0.0228595 \\
27 & 4.604541 & 0.0253597 \\
30 & 5.316467 & 0.0282973 \\
33 & 6.028286 & 0.0343851 \\
\bottomrule()
\end{longtable}

\hypertarget{how-much-does-bark-stripping-alter-timber-production-and-profitability}{%
\subsubsection{How much does bark-stripping alter timber production and
profitability?}\label{how-much-does-bark-stripping-alter-timber-production-and-profitability}}

Loss at clear-cut :

\begin{longtable}[]{@{}rrrr@{}}
\toprule()
bpr & siteIndex & loss\_rel & peeled\_prop \\
\midrule()
\endhead
0.05 & 27 & 8.724550 & 0.5017007 \\
0.05 & 33 & 7.776958 & 0.5051669 \\
0.10 & 27 & 16.558257 & 0.8624242 \\
0.10 & 33 & 15.125089 & 0.8583275 \\
\bottomrule()
\end{longtable}

mean cost for the study area

\begin{longtable}[]{@{}rrrr@{}}
\toprule()
siteIndex & cost & cost\_rel & annuity \\
\midrule()
\endhead
21 & 2391.358 & 35.11016 & 47.82717 \\
27 & 2647.054 & 19.12818 & 52.94108 \\
33 & 3879.772 & 17.40202 & 77.59544 \\
\bottomrule()
\end{longtable}

\begin{longtable}[]{@{}rrrr@{}}
\toprule()
bpr & siteIndex & npv & pc \\
\midrule()
\endhead
0.0 & 33 & 4123.2113 & \\
0.1 & 33 & 1714.8095 & 0.5841083 \\
0.0 & 27 & 719.8228 & \\
0.1 & 27 & -839.1817 & 2.1658171 \\
0.0 & 21 & -1695.0691 & \\
0.1 & 21 & -2690.6348 & -0.5873305 \\
\bottomrule()
\end{longtable}

\begin{longtable}[]{@{}rrrrrrr@{}}
\toprule()
bpr & siteIndex & discountRate & npv & cost & loss & annuity \\
\midrule()
\endhead
0.00 & 27 & 0.02 & 16491.85 & & & \\
0.04 & 27 & 0.02 & 13844.80 & 2647.054 & 16.05068 & 52.94108 \\
\bottomrule()
\end{longtable}

\hypertarget{supplementary-material}{%
\subsection{Supplementary material}\label{supplementary-material}}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-rotation-1.pdf}

}

\caption{\label{fig-rotation}Optimum rotation across simulation}

\end{figure}

\begin{longtable}[]{@{}
  >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2537}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1493}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1642}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1493}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2836}}@{}}
\toprule()
\begin{minipage}[b]{\linewidth}\raggedright
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Estimate
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Std. Error
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
t value
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
Pr(\textgreater\textbar t\textbar)
\end{minipage} \\
\midrule()
\endhead
bpr & 7.20e+04 & 2.19e+03 & 3.29e+01 & 0e+00 \\
bpr:discountRate & -2.22e+06 & 2.87e+04 & -7.74e+01 & 0e+00 \\
bpr:siteIndex & 1.00e+03 & 7.57e+01 & 1.33e+01 & 0e+00 \\
\bottomrule()
\end{longtable}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-Ndamaged-si-1.pdf}

}

\caption{\label{fig-Ndamaged-si}changes in density of damaged trees, the
effect of site index.}

\end{figure}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-npvall-1.pdf}

}

\caption{\label{fig-npvall}Changes in NPV across all simulations}

\end{figure}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-ct-1.pdf}

}

\caption{\label{fig-ct}density of protected and damages trees}

\end{figure}

\begin{figure}[H]

{\centering \includegraphics{2_generate-results_files/figure-pdf/fig-opcostrel-1.pdf}

}

\caption{\label{fig-opcostrel}Variability of the opportunity cost}

\end{figure}



\end{document}
