Table 2 Spatial analysis methods and their geographic interpretation

Kernel Density

\(\lambda (x)=\frac{1}{{mh}}\mathop{\sum }\limits_{i=1}^{n}k(\frac{x-{x}_{i}}{h})\)

k is the kernel function; h is the search radius; (x–x_i) represents the distance from the estimation point x to the feature point xi.

Higher λ(x) values indicate higher concentration of features.

To evaluate the dispersion or clustering characteristics of landscape elements.

Spatial Autocorrelation

\(I={Z}_{i}+\mathop{\sum }\limits_{i=1}^{n}{W}_{{ij}}{Z}_{j}\)

I is Moran’s I; Z_i and Z_j are the standardized values of the observed values for spatial units i and j; W_ij is the spatial weight.

Moran’s I ranges from -1 to 1. Positive values indicate positive spatial autocorrelation (clustering of high or low values), negative values indicate negative spatial autocorrelation (dispersed patterns), and values near zero indicate random spatial distribution.

To reveal the spatial correlation of landscape elements with neighboring elements.

Local Moran’s I

\({I}_{i}=\frac{({x}_{i}-\bar{x}){\sum }_{j=1}^{n}{w}_{i,j}\left({x}_{i}-\bar{x}\right)}{{\sum }_{i=1}^{n}{\left({x}_{i}-\bar{x}\right)}^{2}}\)

xi and xj are the attribute values of features i and j, x̄ is the mean of the attribute values, and w_ij is the spatial weight between features i and j.

Visualizes local clustering patterns of landscape elements.

To identify areas of local spatial clustering in landscape elements.

Getis-Ord Gi* Analysis

\({G}_{i}^{* }=\frac{{\sum }^{{nj}=1}{w}_{{ij}}{x}_{j}-\bar{X}{\sum }_{j=1}^{n}{w}_{{ij}}}{S\sqrt{\frac{n{\sum }_{j=1}^{n}{w}_{{ij}}^{2}-{\left({\sum }_{j=1}^{n}{w}_{{ij}}\right)}^{2}}{n-1}}}\)

x_j is the attribute value at location j, w_ij is the spatial weight between locations i and j, X̄ is the mean of the attribute values, and S is the standard deviation of the attribute values.

High Gi values indicate statistically significant hotspots, whereas low values indicate cold spots.*

To visualize the local hotspots and coldspots distribution of landscape elements.

Standard Deviational Ellipse (SDE)

\({{SDE}}_{y}=\sqrt{\frac{{\sum }_{i=1}^{n}{\left({y}_{i}-\bar{y}\right)}^{2}}{n}}\,{{SDE}}_{x}=\sqrt{\frac{{\sum }_{i=1}^{n}{\left({x}_{i}-\bar{x}\right)}^{2}}{n}}\)

x_i and y_i are the spatial coordinates of the research features.

The long axis and short axis indicate the primary and secondary directional trends of feature distribution. Their lengths represent the degree of dispersion of features along the main and secondary trends relative to the centroid.

To reveal and compare the directional trend and extent of spatial distribution of landscape elements.