## 3 Methodology
### Calculation of Landscape Metrics in R
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Patch Level** & **Formula** & **Ranges of Change** & **Unit** \\ \hline Core area index & \begin{tabular}{l} \(CAI=\left(\frac{a_{ij}^{\text{core}}}{a_{ij}}\right)\times 100\) \\ where \\ \(a_{ij}^{\text{core}}\) Core area in square meters; \\ \(a_{ij}\) Area in square meters; \\ \(CAI\) Core area metric [41]. \\ \end{tabular} & \(0\leq\text{CAI}\leq 100\) & Percent \\ \hline Euclidean nearest-neighbor distance & \begin{tabular}{l} \(ENN=h_{ij}\) \\ where \\ \(h_{ij}\) Distance to the nearest neighbor; \\ \(ENN\) Aggregation metric [42]. \\ \end{tabular} & ENN \textgreater{} 0 & Meters \\ \hline Fractal dimension index & \begin{tabular}{l} \(FRAC=\frac{2 sIn*(0.25*\rho_{ij})}{In\,a_{ij}}\) \\ where \\ \(\rho_{ij}\) Perimeter in meters; \\ \(a_{ij}\) Area in square meters; \\ \(FRAC\) Shape metric [43]. \\ \end{tabular} & \(1\leq\text{FRAC}\leq 2\) & None \\ \hline Related circumscribing circle & \
\begin{tabular}{l} \(CIRCLE=1-\left(\frac{a_{ij}}{a_{ij}^{\text{core}}}\right)\) \\ where \\ \(a_{ij}\) Area in square meters; \\ \(a_{ij}^{\text{circle}}\) Area of the smallest circumscribing circle; \\ \(CIRCLE\) Shape metric [44]. \\ \end{tabular} & \(0\leq\text{CIRCLE}<1\) & None \\ \hline Shape index &
\begin{tabular}{l} \(SHAPE=\frac{P_{ij}}{\min P_{ij}}\) \\ where \\ \(P_{ij}\) Perimeter in terms of cell surfaces; \\ \(\min P_{ij}\) The minimum area of the patch in relation \\ to the cell surfaces; \\ \(SHAPE\) Shape metric [45]. \\ \end{tabular} & SHAPE \(\geq 1\) & None \\ \hline \hline \end{tabular}
\end{table} 
Table 4: List of patch-level landscape metrics. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Class Level** & **Formula** & **Ranges of Change** & **Unit** \\ \hline Aggregation index & \begin{tabular}{l} \(AI=\left[\frac{\delta z}{max-\delta_{z}}\right](100)\) \\ where \\ \(AREA[patch_{ij}]\) Area of each patch in hectares; \\ \(CA\) Area and edge metric [46]. \\ \end{tabular} & \(0\leq\text{AI}\leq 100\) & Percent \\ \hline Total (class) area & \
\begin{tabular}{l} \(CA=sum(AREA[patch_{ij}])\) \\ where \\ \(AREA[patch_{ij}]\) Area of each patch in hectares; \\ \(CA\) Area and edge metric [47]. \\ \end{tabular} & CA \textgreater{} 0 & Hectares \\ \hline Clumpiness index &
\begin{tabular}{l} \(CLUMPY=\left\lfloor\frac{G_{i}-P_{j}}{P_{i}}forG_{i}<P_{i}\&P_{i}<0.5;else \frac{G_{i}-P_{j}}{P_{i}}\right\rfloor\) \\ where \\ \(gti\) Number of like adjacencies; \\ \(gik\) Number of all neighborhoods by class, including the focus class; \\ \(mini\) Minimum size of the overall class based on the cell areas, assuming complete clumping; \\ \(P_{i}\) Proportion of the landscape occupied by each class; \\ \(CLUMPY\) Aggregation metric [48]. \\ \end{tabular} & \(-1\leq\text{CLUMPY}\leq 1\) & None \\ \hline \hline \end{tabular}
\end{table} 
Table 5: List of class-level landscape metrics. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Landscape Level** & **Formula** & **Ranges of Change** & **Unit** \\ \hline Aggregation index & \(AI=\left[\sum\limits_{i=1}^{m}\left(\dfrac{g_{ii}}{max-g_{ii}}\right)p_{i}\right] (100)\) & & \\  & where & & \\ Aggregation index & \(g_{ii}\) Number of like adjacencies; & & \(0\leq\text{AI}\leq 100\) & Percent \\  & \(max-g_{ii}\) Classwise maximum number of like adjacencies; & & \(0\leq\text{AI}\leq 100\) & Percent \\  & \(g_{i}\) Proportion of landscape compromised. & & \\  & \(AI\) Aggregation metric. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: List of landscape-level landscape metrics.