## 2 Materials and Methods
### Forest Map Data and Fragmentation Levels Classification  
Considering the fact that forest cover change may alter the forest fragmentation categories with time, this study requires a temporal stable status of forest cover. In order to exclude the influence from forest coverage change on the accuracy of the classification of forest fragmentation levels, our study only focused on the forest areas in Zhejiang province that have not changed since 2000. We used grids of 500 m in size to calculate the proportion of forest loss between 2000 and 2018 (the ratio of total forest loss pixels to total pixels in a 500 m grid) based on the Global Forest Change dataset [29]; the grids with a forest loss proportion of less than 5% were retained and were representative of unchanged forest landscapes. Moreover, a 50 m resolution forest map from 2010, generated using ALOS PALSAR-2, MODIS, and Landsat-7/8 satellite data [30], was selected as the basic forest cover data to conduct a classification of forest fragmentation levels based on the retained grids (unchanged forest landscapes).  
A forest fragmentation model [20; 21] that is widely used to estimate the status of forest fragmentation based on satellite-derived forest maps was employed in this study to classify forest fragmentation levels. This fragmentation model was developed based on the consideration of causing forest loss as a result of spatial disturbances; it has been widely applied to estimate forest fragmentation by analyzing forest distribution maps [31; 32]. Additionally, forest area density (\(P_{f}\)) and forest connectivity (\(P_{f\!\!f}\)) are two key indicators in this model for defining the fragmentation type of a given \"window\" or \"landscape\" based on a forest/non-forest binary map [20]. The size of the \"window\" reflects different spatial scales in the estimation of forest fragmentation. \(P_{f}\) and \(P_{f\!\!f}\) are calculated using the following equations:  
\[P_{f}=\frac{N_{f}}{N_{w}} \tag{1}\]  
\[P_{ff}=\frac{D_{ff}}{D_{f}} \tag{2}\]  
where \(P_{f}\) is the proportion of forest pixels in a given window, calculated by dividing the number of forest pixels (\(N_{f}\)) by the total number of pixels (\(N_{w}\)) in the window; \(P_{f\!\!f}\) is the forest connectivity, calculated by dividing the pixel pair number that includes at least one forest pixel (\(D_{f\!\!f}\)) by the pixel pair number that includes two forest pixels in cardinal directions (\(D_{f\!\!f}\)).  
A look-up table (Table 1) containing the criteria of the two indicators (\(D_{f\!\!f}\) and \(D_{f\!\!f}\)) was used to conduct the classification of forest fragmentation levels. Six fragmentation types, including patch (PAT), transitional (TRA), perforated (PER), undetermined (UND), edge (EDG), and interior (INT), were obtained. The fragmentation levels of these six types are shown as PAT \(>\) TRA \(>\) PER \(>\) UND \(>\) EDG \(>\) INT. However, UND was excluded from our study due to the fact that it only exists in extreme cases. In addition, in order to match the resolution (\(\sim\)500 m) of the GPP data, a 9 \(\times\) 9 size \"window\" was adopted in this study.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Fragmentation** & **Classification** & **Area** & **Area** \\
**Categories** & **Criteria** & **(10\({}^{4}\) ha)** & **Area Percentage (\%)** \\ \hline PAT & \(P_{f}<0.4\) & 263.0 & 33.7 \\ TRA & \(0.4<P_{f}<0.6\) & 129.5 & 16.6 \\ PER & \(0.6<=P_{f}<1\) and \(P_{f}>P_{f\!\!f}\) & 226.1 & 28.9 \\ UND & \(0.6<=P_{f}<1\) and \(P_{f}=P_{f\!\!f}\) & 0.7 & 0.1 \\ EDG & \(0.6<=P_{f}<1\) and \(P_{f}<P_{f\!\!f}\) & 153.0 & 19.6 \\ INT & \(P_{f\!\!f}=1\) & 9.0 & 1.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Classification criteria, area, and area percentage of each forest fragmentation level of the forest fragmentation model in forest landscapes in Zhejiang, China. PAT: patch forest, TRA: transitional forest, PER: perforated forest, UND: undetermined, EDG: edge forest, and INT: interior forest.