• Spatial Correlation Analysis

Spatial autocorrelation can be defined as the coincidence of value similarity with location similarity, and is used to detect patterns of spatial association [63]. In this study, the global Moran's I index [64,65] (Equation (3)) was adopted to analyze the spatial autocorrelation of each landscape metric in its characteristic scale interval (500~1200 m), providing appropriate spatial scales for launching the bivariate spatial correlation analysis between each landscape metric and the influencing factors (Appendix A Table A2).

$$\mathbf{I} = \frac{\mathbf{n}}{\sum\_{\mathbf{i}} \sum\_{\mathbf{j}} \mathbf{w}\_{\mathbf{ij}}} \times \frac{\sum\_{\mathbf{i}} \sum\_{\mathbf{j}} \mathbf{w}\_{\mathbf{ij}} (\mathbf{x\_i} - \bar{\mathbf{x}})}{\sum\_{\mathbf{i}} \left(\mathbf{x\_i} - \bar{\mathbf{x}}\right)^2} \tag{3}$$

where wij is the spatial weight matrix between observation unit i and its neighboring units j: i and j are established by diving the study area into uniform grids based on its appropriate scale; x<sup>i</sup> and x<sup>j</sup> are the observed values of adjacent research area i and j, respectively; n is the number of spatial units of the research area, and x is the average value of all observed values in the sample. Index I ranges from −1 to 1, and as the absolute value of I increases, the spatial correlation gets stronger. I = 0 indicates a random spatial distribution.

Further, bivariate Moran's Ixy [66] (Equation (4)), which is based on the principle of univariate spatial correlation, has been adopted on the specific scale of 1000 × 1000 m. On this spatial scale, the analysis scale between each landscape metric and each influencing factor can be unified. The spatial autocorrelation analysis of each landscape metric at this scale was extremely significant. Through the spatial autocorrelation analysis, the relationship between the landscape metric and spatial influencing factors was captured and the strength of the association between the two variables was measured over the study area.

$$\mathbf{I}\_{\mathbf{x}\mathbf{y}} = \frac{\mathbf{n}}{\sum\_{\mathbf{i}} \sum\_{\mathbf{j}} \mathbf{w}\_{\overline{\mathbf{i}}\mathbf{j}}} \times \frac{\sum\_{\mathbf{i}} \sum\_{\mathbf{j}} \mathbf{w}\_{\overline{\mathbf{i}}\mathbf{j}} (\mathbf{x}\_{\mathbf{i}} - \mathbf{x}) (\mathbf{y}\_{\mathbf{j}} - \mathbf{y})}{\sqrt{\sum\_{\mathbf{i}} \left(\mathbf{x}\_{\mathbf{i}} - \overline{\mathbf{x}}\right)^{2}} \sqrt{\sum\_{\mathbf{j}} \left(\mathbf{y}\_{\mathbf{j}} - \overline{\mathbf{y}}\right)^{2}}} \tag{4}$$

where Ixy also ranges from −1 to 1, x<sup>i</sup> is the attribute values of adjacent research areas i and x, while x<sup>j</sup> is the attribute values of adjacent research areas j and y; x and y are the average attribute values of x and y in the sample, respectively; and n is the number of the spatial units of the research area.
