Table 2 The meanings of the selected landscape pattern indexes28
Landscape pattern indexes | Formula | Meaning |
|---|---|---|
Patch Type Area (CA) | \(\mathrm{CA}=\mathop{\sum }\limits_{j=1}^{n}{a}_{{ij}}\times \frac{1}{10,000}\) | (Formula 1) |
In the formula, \({a}_{{ij}}\) refers to the area of patch ij, with a value range of CA > 0. As CA approaches 0, it indicates that the patch type becomes increasingly rare in the landscape; when CA = TA (total landscape area), it means the landscape consists of only one type of patch. | ||
Proportion of Landscape Area Occupied by Patch Type (PLAND) | \(\mathrm{PLAND}={p}_{i}=\frac{{\sum }_{j=1}^{n}{a}_{{ij}}}{A}\times 100\) | (Formula 2) |
PLAND is an indicator used to measure the abundance ratio of a certain patch type in the landscape. In the formula, \({a}_{{ij}}\) refers to the area of patch ij; it is the proportion of patch type i in the entire landscape; A represents the total area of the landscape. | ||
Number of Patch (NP) | \({NP}={n}_{i}\) | (Formula 3) |
The number of patches is a simple description of landscape heterogeneity and fragmentation. | ||
Patch Density (PD) | \({PD}=\frac{{n}_{i}}{A}\times 10,000\times 100\) | (Formula 4) |
PD reflects the number of patches per unit area. | ||
Largest Patch Index (LPI) | \({\rm{LPI}}=\frac{{\max }_{j=1}^{n}\left({a}_{{ij}}\right)}{{\rm{A}}}\times 100\) | (Formula 5) |
In the formula, \({a}_{{ij}}\) represents the area of patch ij; A is the total area of the landscape, including the background within the landscape. LPI represents the proportion of the largest patch area to the total landscape area, with a value range of 0 < LPI ≤ 100. | ||
Total Edge Length (TE) | \({\rm{TE}}=\mathop{\sum }\limits_{k=1}^{m}{e}_{{ik}}\) | (Formula 6) |
In the formula, \({e}_{{ik}}\) represents the total edge length of the corresponding patch type in the landscape, including the landscape boundary line and background part involving the patch type. The unit of TE is meters, and the value range is TE ≥ 0. | ||
Edge Density (ED) | \(\mathrm{ED}=\frac{{\sum }_{k=1}^{m}{e}_{{ik}}}{A}\)×10,000 | (Formula 7) |
In the formula, the unit of ED is m/hm². ED is equal to the total edge length divided by the total landscape area, multiplied by 10,000. | ||
Landscape Shape Index (LSI) | \({\rm{LSI}}=\frac{{e}_{i}}{{{mine}}_{i}}\) | (Formula 8) |
The landscape shape index (LSI) provides a simple description of the aggregation degree of patch types, measured by the edge length of the patch type. In the formula, the value range of LSI is ≥ 1. If LSI = 1, it signifies that there is only one patch of this type in the landscape, and it is square or nearly square. | ||
Aggregation Index (AI) | \({\rm{AI}}=\left[\frac{{g}_{{ij}}}{{{maxg}}_{{ij}}}\right]\times 100\) | (Formula 9) |
In the formula, \({g}_{{ij}}\) represents the number of nodes between patch type i pixels based on the single multiplier method; \({{maxg}}_{{ij}}\) represents the maximum number of nodes between patch type i pixels based on the single multiplier method. When the fragmentation of patch type reaches its maximum, AI = 0. | ||
Landscape Division Index (DIVISION) | \({\rm{DIVISION}}=\left[1-\mathop{\sum }\limits_{j=1}^{m}{\left(\frac{{a}_{{ij}}}{A}\right)}^{2}\right]\) | (Formula 10) |
The separation degree is equal to 1 minus the sum of the squares of the ratio of each patch’s area of a certain patch type to the total landscape area. In the formula, the value range is 0 ≤ DIVISION < 1. When there is only one patch, DIVISION = 0. When the landscape type consists of only one patch with an area equivalent to a single raster, DIVISION = 1. | ||
Patch Cohesion Index (COHESION) | \(\mathrm{COHESION}=\left[1-\frac{{\sum }_{j=1}^{n}{p}_{{ij}}}{{\sum }_{j=1}^{n}{p}_{{ij}}\sqrt{{a}_{{ij}}}}\right]\cdot {\left[1-\frac{1}{\sqrt{A}}\right]}^{-1}\times 100\) | (Formula 11) |
The natural connectivity of related patch types. In the formula, the value range is 0 ≤ COHESION < 100. When the proportion of a certain patch type in the landscape decreases and becomes increasingly fragmented, leading to reduced connectivity, the value of COHESION approaches 0. | ||
Connectivity Index (CONNECT) | \(\mathrm{CONNECT}=\left[\frac{{\sum }_{j=k}^{n}{c}_{{ijk}}}{\frac{{n}_{i}\left({n}_{i}-1\right)}{2}}\right]\times 100\) | (Formula 12) |
In the formula, \({c}_{{ijk}}\) refers to the connectivity between patches j and k related to patch type i within a user-specified critical distance; \({n}_{i}\) represents the number of patches of patch type i in the landscape. | ||
Shannon’s Diversity Index (SHDI) | \({\rm{SHDI}}=-\mathop{\sum }\limits_{i=1}^{m}({p}_{i}\times {\rm{In}}{p}_{i})\) | (Formula 13) |
In the formula, \({p}_{i}\) represents the proportion of patch type i in the landscape; SHDI is the sum of the product of the area proportion of each patch type in the landscape and its natural logarithm, and then the opposite of that sum is taken. The value range is SHDI ≥ 0. | ||
Shanno’s Evenness Index (SHEI) | \(\mathrm{SHEI}=\frac{-{\sum }_{i=1}^{m}\left({p}_{i}\times \mathrm{In}{p}_{i}\right)}{\mathrm{In}m}\) | (Formula 14) |
In the formula, SHEI is the ratio of Shannon’s diversity index to the natural logarithm of the number of patch types. The value range is 0 ≤ SHEI ≤ 1. | ||
Simpson’s Diversity Index (SIDI) | \({\rm{SIDI}}=1-\mathop{\sum }\limits_{i=1}^{m}{p}_{i}^{2}\) | (Formula 15) |
In the formula, SIDI is the sum of the squared area proportions of each patch type in the landscape. The value range is 0 ≤ SIDI ≤ 1. | ||
Modified Simpson’s Diversity Index (MSIDI) | \({\rm{MSIDI}}=-{In}\mathop{\sum }\limits_{i=1}^{m}{p}_{i}^{2}\) | (Formula 16) |
In the formula, MSIDI is the negative natural logarithm of the sum of the squared area proportions of each patch type in the landscape. The value range is MSIDI ≥ 0. | ||
Simpson’s Evenness Index (SIEI) | \({SIEI}=\frac{1-{\sum }_{i=1}^{m}{p}_{i}^{2}}{1-(\frac{1}{m})}\) | (Formula 17) |
In the formula, SIEI is the ratio of Simpson’s diversity index to the difference between 1 and the reciprocal of the number of patch types. The value range is 0 ≤ SIEI ≤ 1. | ||
Modified Simpson’s Evenness Index (MSIEI) | \({MSIEI}=\frac{-{In}{{\sum }}_{{i}{=}{1}}^{{m}}{p}_{i}^{2}}{\mathrm{Inm}}\) | (Formula 18) |
In the formula, MSIEI is the ratio of Simpson’s diversity index to the natural logarithm of the number of patch types in the landscape. The value range is 0 ≤ MSIEI ≤ 1. | ||
