## 3 Materials and Methods
### Method
#### 3.3.2 Determining the Forested Area's Dominant Morphology  
This study chose four indicators, namely, Patch Density (PD), the Largest Patch Index (LPI), the Aggregate Index (AI), and the Landscape shape Index (LSI), for assessing the forested areas' dominating morphology in Thies Region from 2005 to 2020. The ArcGIS and FRAGSTAT.4.2 software were used to compute these four indicators for characterizing the changes in the forested area's dominant morphology in 2005, 2010, 2015, and 2020.  
(a) **Determination method of the Patch Density (PD)**  
As expressed in Equation (4), PD represents the patch number of one specific landscape type per one hundred hectare area [50]. \(PD\) is an \"aggregation metric\" describing forested area fragmentation in this study. The larger the value, the greater the fragmentation of the landscape. So, a low \(PD\) implies fewer patches and the continuity of forested areas, while higher values denote more patches, spatial dispersion, and discontinuity.  
\[PD=\frac{n_{i}}{A} \tag{4}\]  
where \(ni\) is the number of patches of forested areas that change landscape type \(i\) and \(A\) is the total area of the forested areas.  
(b) **Determination method of the Largest Patch Index (LPI)**LPI reflects the dominant patch type in the changing landscape of forested areas and indirectly reflects the direction and magnitude of disturbances to human activity. The calculation method is presented in Equation (5):  
\[LPI=\frac{max(a_{i_{1}...a_{n}})}{A}\times 100 \tag{5}\]  
_LPI_ values are expressed in percentage and range of 0 < _LPI_\(\leq\) 100; a is the patch area and n is the number of patches in the forested areas. The _LPI_ approaches 0 when the largest patch of the corresponding patch type is increasingly small. _LPI_ = 100 when the entire landscape consists of a single patch of the corresponding patch type, and the largest patch comprises 100% of the landscape.  
(c) **Determination method of the Aggregation Index (AI)**  
In forested area change research, spatial pattern aggregation levels must be measured within a single map class and over the same period. So, _AI_ reflects the degree of patch-type clustering in the forested areas that change the landscape. _AI_ assumes that the highest collection level (_AI_ = 100) comprises pixels that share all possible edges. A class whose pixels share no edges (are completely disaggregated) has the lowest level of aggregation (_AI_ = 0). _AI_ reflects the degree of aggregation of patches of forested areas. Low _AI_ values indicate fewer aggregation levels in forested areas and vice versa [52].  
\[AI=2 ln(n)+\sum_{i=l}^{n}\sum_{j=l}^{n}P_{ij}\ ln(P_{ij}\ ) \tag{6}\]  
where \(n\) is the number of classes in the landscape and _pij_ is the total number of times class \(i\) is adjacent to class \(j\), divided by the number of times class i is adjacent to all other classes, including itself. _AI_ ranges from 0 to 100, with 0 indicating the least contagion [53].  
(d) **Determination method of the Landscape shape Index (LSI)**  
_LSI_ quantitatively measures landscape complexity or heterogeneity. _LSI_ is an aggregation metric. Also, it is the ratio between the actual landscape edge length and the hypothetical minimum edge length [54]. The minimum edge length equals the edge length if only one patch is present.  
\[LSI=\frac{E}{min_{E}} \tag{7}\]  
where \(E\) is the total edge length on cell surfaces and \(minE\) is the minimum total edge length on cell surfaces.