Spatial Analysis of Ecological Risk in a Coastal Dune Landscape Using High Resolution Aerial Photography

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Formulas to calculate the landscape disturbance_

Index	Equation	Assessment Unit
Landscape disturbance (Xie et al. 2013; X. Zhang et al. 2013; Liu et al. 2020)	Si = aCi + bNi + cDi a + b + c = 1 a = 0,5; b = 0,3; c = 0,2	landscape class or sub-class
Landscape fragmentation (X. Zhang et al. 2013; Liu et al. 2020)	Ci=niAi\[{{C}_{i}}=\frac{{{n}_{i}}}{{{A}_{i}}}\]	landscape class or sub-class
Landscape isolation, segmentation, or splitting (Xie et al. 2013; X. Zhang et al. 2013; Liu et al. 2020)	Ci=A2AiniA\[{{C}_{i}}=\frac{A}{2{{A}_{i}}}\sqrt{\frac{{{n}_{i}}}{A}}\]	landscape class or sub-class
Landscape dominance (Jin et al. 2019)	Di=(Qi+Mi+Li)3\[{{D}_{i}}=\frac{\left( {{Q}_{i}}+{{M}_{i}}+{{L}_{i}} \right)}{3}\]	landscape class or sub-class

Landscape ecological risk index calculation_

Index	Equation	Assessment Unit
Ecological risk	ERIi=∑i=1NAkiAk×Ri\[ER{{I}_{i}}=\sum\nolimits_{i=1}^{N}{\frac{{{A}_{ki}}}{{{A}_{k}}}\times {{R}_{i}}}\]	grid (if one grid contains > 1 classes or sub-classes, their indices are summed, adjusting the area proportion)
Landscape loss degree	Ri = Fi × Si	landscape class or sub-class

Calculation of global and local spatial autocorrelation_

Global spatial autocorrelation		Local spatial autocorrelation
I=∑in∑j≠1nWij(xi−x)2S2∑1n∑j≠1nWij\[I=\frac{\sum\nolimits_{i}^{n}{\sum\nolimits_{j\ne 1}^{n}{{{W}_{ij}}{{\left( {{x}_{i}}-x \right)}^{2}}}}}{{{S}^{2}}\sum\nolimits_{1}^{n}{\sum\nolimits_{j\ne 1}^{n}{{{W}_{ij}}}}}\]	S2=1n∑1n(xi−x¯)2\[{{S}^{2}}=\frac{1}{n}\sum\limits_{1}^{n}{{{\left( {{x}_{i}}-\bar{x} \right)}^{2}}}\] x¯=1n∑i(j)nxij\[\bar{x}=\frac{1}{n}\sum\limits_{i\left( j \right)}^{n}{{{x}_{ij}}}\] Zscore=I−E(I)Var(I)\[{{Z}_{score}}=\frac{I-E\left( I \right)}{\sqrt{Var\left( I \right)}}\]	Ii=zi∑j=1nwijzj(i≠j)\[{{I}_{i}}={{z}_{i}}\sum\limits_{j=1}^{n}{{{w}_{ij}}{{z}_{j}}\left( i\ne j \right)}\]

Global spatial autocorrelation of landscape ecological risk (LER) in the Parangtritis coastal dune_

Scenario	Moran’s I	Zscore
Sub-class 2011	0.4112	18.0872
Sub-class 2020	0.6342	27.0196
Class 2011	0.5775	24.6668
Class 2020	0.6177	26.3570

Landscape fragility index (Fi) of various landscape classes based on their genesis (natural processes or human interventions)_

Landscape class	Natural	Agrogenic	Tree agrogenic	Industrogenic	Info-telecommunication	Tourismsports	Traffic	Urbanogenic	Water management
Index	1.000	0.686	0.145	0.472	0.068	0.319	0.098	0.048	0.215