N is the total number of patches of the landscape type; Ais the total area of the landscape type;\(Max\ (a_{1}\ldots a_{n})\ \)represents the area of the largest plaque;E represents the total length of the landscape edge;ai represents the area of the i-th plaque.\(g_{\text{ii}}\): Number of like adjacencies (joins) between pixels of patch type (class) i based on the single-count method.\(\max g_{\text{ii}}\): Maximum number of like adjacencies (joins) between pixels of patch type (class) i based on the single-count method. \(p_{i}\): Proportion of the landscape comprised of patch type (class) i .

3.4Metrics for analysis of S.alterniflora expansion

3.4.1 Standard deviational ellipse

The current study used the standard deviation ellipse to analyze the spatial variation characteristics of invasive species. This is a spatial statistical method that is used to quantitatively describe the spatial distribution characteristics of geographic elements, and is widely used in the fields of disease transmission, urban expansion, and pollution diffusion. The standard deviation ellipse parameters include the center of gravity coordinates, the deflection angle, and the length of the long and short half axes, which indicate the relative position of the spatial distribution pattern of geographic elements, the dominant trend direction of geographic element development, and the degree of dispersion in the primary and secondary directions, respectively. The calculation of key parameters can be found in previous studies (Wong 1999; Scott et al. 2010; Qiao et al. 2017).

3.4.2 Metric for analysis of the spatial expansion of S. alterniflora

The pattern of landscape expansion determines the spatial combination of landscape elements, and the spatial combination of landscape elements has an important impact on various ecological processes. Therefore, the landscape expansion mode is of great significance for understanding the process of landscape expansion. The landscape expansion index (LEI) was adopted to quantitatively realize the identification and analysis of landscape spatial expansion patterns (Liu et al. 2010; Wu et al. 2012). Its expression is as follows:
\(LEI=\frac{A_{p}-A_{0}}{A_{p}+A_{0}}\),
\(\text{where\ }\ A_{p}\ \)is the area of the expanded plaque, and\(\text{\ A}_{0}\) is the area of the plaque adjacent to the expanded plaque, which can be understood as the original plaque. The range of the LEI is from -1 to 1 (including 1). When the LEI value is in the interval (-1, 1), we can call it edge expansion. When LEI<0, it indicates that the expansion area is smaller than the original plaque area. When LEI≄0, it indicates that the expansion area is greater than or equal to the original plaque area. When LEI=1 (\(A_{0}\)=0), the original plaque does not exist, and the spatial expansion pattern of theS. alterniflora community is that of external expansion.