2.3.1 Assessment of ecosystem health
Ecosystem health can be directly measured and fully assessed by its four main aspects: vigor, organization, resilience, services. By applying the VORS framework developed by Peng et al. (2015), we evaluated ecosystem health at the regional matrix. It should be noted that it is important to normalize each element to a value ranging from 0 to 1.The formula of calculating the ecosystem health index is conducted in the following way:
$$EHI=\sqrt[4]{{EV \times EO \times ER \times ES}}$$
1
In this case, the ecosystem health indicator (EHI) ranks 0-1depending on how healthy each ecosystem is. The ecosystem health index is divided into five categories using the equal-interval method: Highest Health(value from 0.8 to1),Suboptimal Health(value from 0.6 to 0.8),Average Health(value from 0.4 to 0.6),Unhealthy(value from 0.2 to 0.4),Degraded(value from 0 to 0.2).Ecosystem vigor represents net primary production as well as metabolism of ecosystem. This paper quantifies the ecosystem vigor by utilizing the NDVI (normalized difference vegetation index) which has been extensively utilized in ecosystem health assessments thanks to its ability to assess the character of eco-environments (Peng et al. 2017; Liao et al. 2018).
1) Ecosystem organization describes the ecosystem complexity as well as the structural stability. In this paper, The landscape pattern indicators was used to evaluate ecosystem organization, which include factors such as connectivity and heterogeneity of the landscape (He et al. 2019).Specifically, Our reflection of landscape heterogeneity was represented by mean patch fractal dimension (MPFD) and Shannon’s diversity index (SHDI).The landscape connectivity index includes two main components: the first was the connectivity of an overall landscape determined by the landscape contagion as well as fragmentation index, the second was the connectivity of important ecological patches (forests, streams, grasslands) determined by the cohesion and fragmentation index. Additionally, as far as previously documented studies and the advice of experts, the weight of overall landscape connectivity is 0.35, connectivity of ecological patches weight is 0.30 and landscape heterogeneity weight is 0.35 (Pan et al. 2020).
Specifically, the following is the calculation method:
$$\begin{gathered} EO=0.35LH+0.35LC+0.30IC=(0.25SHDI+0.10MPFD) \\ \;\;+\left( {0.25F{N_1}+0.10CONT} \right)+\left( {0.07F{N_2}+0.03COH{E_1}+0.07F{N_3}} \right. \\ \;\;\left. {+0.03COH{E_2}+0.07F{N_4}+0.03COH{E_3}} \right) \\ \end{gathered}$$
2
Where EO means ecosystem organization. FN1,FN2,FN3,FN4 represent landscape fragmentation indicator, forestland fragmentation index, grassland fragmentation index, and water fragmentation index, respectively; CONT ,COHE1, COHE2, COHE3 stands for landscape contagion index, forest cohesion index, grassland cohesion index and water cohesion index.
2) Ecosystem resilience refers to an ecosystem’s ability to remain structurally stable regardless of the interference of human beings or any external factors (Rapport et al. 1998).The area-weighted ecosystem resilience coefficients(ERC) is a measure of ecosystem resilience for all kind of land use. Specifically, based on specialist knowledge and relevant researches (Peng et al. 2017; Pan et al. 2020),Ecological resilience coefficient is determined. Below is the exact calculation formula:
$$ER=\sum\limits_{{i=1}}^{n} {{A_i}} \times ER{C_i}$$
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Where resilience of the ecosystem was abbreviated as ER, n stands for the number of different types of land use, Ai reflects the area proportion of land use type i.
3) Ecosystem services describe the capacity of ecosystem to generate products and benefits to mankind. An ecosystem service can be analyzed and measured by two different ways: The first is by evaluating the coefficients of ecosystem service provided by different land uses (Xie et al. 2017), which is obtained by comparing the ecosystem service value of a given land use type with that of all land uses. Secondly, Spatial neighboring coefficients differ among land uses, which was depending on Inner Mongolia’s actual situation and related literature. The specific calculation formula is as follows:
$$ES=\sum\limits_{{j=1}}^{n} E S{C_j} \times \left( {1+\frac{{SN{E_j}}}{{100}}} \right)/n$$
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Where ES refer to ecosystem services, The ESC j coefficients are the coefficients describing the ecosystem services provided by the pixel j, SNE j can be defined as the total of correlation coefficients between two spatial neighbors of the pixel j. n indicates the amount of pixel.
2.3.2.Spatial correlation test
The spatial autocorrelation analysis was applied to investigate the spatial dependencies of ecosystem health and its agglomeration pattern in Inner Mongolian. Spatial autocorrelation consist of both global autocorrelation as well as local autocorrelation, and can therefore indicate the degree to which the attribute of one area is dependent on the attribute of another. In order to identify the spatial agglomeration of the entire research area, Moran’s I index was utilized, as shown in Eq. (5) (Moran 1950).LISA (Anselin 1995) ( indicator of spatial association at a local level) is widely used to measure the spatial association between the value of one attribute and the value of the adjacent attribute (Eq. (6)).
\(Moran^{\prime}s\;I=\frac{{\sum\limits_{{i=1}}^{n} {\sum\limits_{{j=1}}^{n} {{W_{ij}}} } \left( {{x_i} - \bar {x}} \right)\left( {{x_j} - \bar {x}} \right)}}{{{S^2}\sum\limits_{{i=1}}^{n} {\sum\limits_{{j=1}}^{n} {{W_{ij}}} } }}\) (5)
\(Local\;Moran^{\prime}s\;I=\frac{{n\left( {{x_i} - \bar {x}} \right)\sum\limits_{{j=1}}^{m} {{w_{ij}}} \left( {{x_j} - \bar {x}} \right)}}{{\sum\limits_{{i=1}}^{n} {{{\left( {{x_i} - \bar {x}} \right)}^2}} }}\) (6)
Where n represents the overall number of grids in Inner Mongolia; m represents the amount of grids located geographically next to grid indicate the ecosystem health value of grid i and j ; and x stands for the mean value of ecosystem health. Parameter I value varies from − 1 to 1 and the absolute magnitude of I index is in accordance with the degree of spatial autocorrelation. When I > 0, correlation between spatial variables is positive, when I < 0, correlation between spatial variables is negative, and when I = 0, No spatial relation exists. There are four kinds of local autocorrelations that are considered in this study: including high-high (HH), high-low (HL), low-high (LH), low-low (LL), and units with a high level of ecosystem health are encircled by units with low ecosystem health level, which indicate the aggregate of units that exhibit a high level of ecosystem health, the aggregate of units that exhibit a low ecosystem health level, and units with a low level ecosystem health are surrounded by units with a high level ecosystem health, accordingly.
2.3.3.Modeling the determinants of ecosystem health
2.3.3.1 Variable selection
In this paper, the following factors have been selected as candidate variables for examining influential factors of ecosystem health. Based on previous research, seven factors in the field of meteorology, socio-economics, and natural resource endowments were considered (Bebianno et al. 2015; Cheng et al. 2018). Specifically, the average annual temperature(AMT), average annual precipitation (AMP) was used to define the meteorological condition. The socioeconomic development was measured by per area Gross Domestic Product (GDP), population density (PD), urbanization rate (UR), and land use intensity (LUI).Biodiversity index (BI) was used to reflect resource endowment.
As there is a high correlation between socioeconomic determinants, unsuitable choice of variables could lead to collinearity. Therefore, this study used ArcGIS exploratory regression to analyze ecosystem health figures and independent variables from in the year from 1995 to 2020 in all their possible combinations. Based on each regression model, the corresponding bias-adjusted Akaike information criterion (AICc) ,adjusted R2 and maximum variance inflation factor (Max-VIF) were respectively obtained. In fact, the three elements are actually tests for selecting the most appropriate regression model based on statistical principles. First step in selecting an suitable model involved pre-screening and identifying regression models whose maximum variance inflation factor (Max-VIF) was below 7.5.In second stage, the Adjusted R2 was ranked in descending order; the results are displayed in Table 1.According to Table 1 below, Variable combination models AMT + AMP + LUI + BI ranked first in 2000,2005,2010,2015 and second in the fittest degree in 2020, accordingly. Furthermore, its counterpart Max-VIF was comparatively smaller. Thus, AMT + AMP + LUI + BI were chosen as the independent variables in this study.
Table 1
Selection of independent variables.
|
Variable Combination
|
Adjusted R2
|
AICc
|
Max-VIF
|
1995
|
AMT + LUI + BI
|
0.831
|
-267.190
|
2.375
|
LUI + BI
|
0.816
|
-259.638
|
1.035
|
2000
|
AMT + AMP + LUI + BI
|
0.851
|
-281.053
|
1.975
|
AMP + LUI + BI
|
0.842
|
-276.541
|
2.742
|
2005
|
AMT + AMP + LUI + BI
|
0.865
|
-273.130
|
1.430
|
AMP + LUI + BI
|
0.852
|
-264.941
|
2.702
|
2010
|
AMT + AMP + LUI + BI
|
0.838
|
-262.537
|
1.588
|
AMP + LUI + BI
|
0.820
|
-253.373
|
2.769
|
2015
|
AMT + AMP + LUI + BI
|
0.866
|
-271.667
|
2.057
|
PD + AMP + AMT + LUI + BI
|
0.835
|
-267.095
|
2.214
|
GDP + AMP + AMT + LUI + BI
|
0.813
|
-245.598
|
2.501
|
2020
|
AMP + UR + LUI + BI
|
0.893
|
-296.267
|
2.579
|
AMT + AMP + LUI + BI
|
0.886
|
-289.108
|
1.706
|
2.3.3.2 Geographically weighted regression model
Firstly, the factors of the health ecosystem were examined using Ordinary Least Square (OLS).In OLS regression model, dependent and independent variables are assumed to behave the same in all locations within the given geographical area. Hence, it is unable to measure the non-stationarity of spatial distributions of ecosystem health. In this regard, the estimation of parameters via OLS model tends to be biased and inefficient. After that, we used model with variable parameters(GWR) (Fotheringham et al. 2003), which tests whether variables are spatially interconnected across locations.
The OLS regression model is described by the Eq. (7):
$${y_i}={\beta _0}+\sum {{\beta _j}} {x_i}+{e_i}$$
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Where yi represent the ecosystem health value for the ith county, and xi is its determinants .Similarly,β0 represents the constant and βj represents the coefficient that should be estimated for the dependent variable, while ei represents the stochastic error term. As shown in Eq. (8), The GWR model can be described as a modification of Eq. (7):
$${y_i}\left( {{u_i},{v_i}} \right)={\beta _0}\left( {{u_i},{v_i}} \right)+\sum {{\beta _j}} \left( {{u_i},{v_i}} \right){x_i}+{e_i}\left( {{u_i},{v_i}} \right)$$
8
Where (ui,vi) indicates the geographic location or the geographical site coordinate (i.e.,counties). In this study, ui and vi here are the longitudes and latitudes of the ith county’s center point, respectively. The GWR is a model that fits datasets of observations nearby a specific county, resulting in a set of parameters that can be estimated separately for each county. GWR not only estimates parameters for each observation individually, but also gives greater observed data(i.e.,counties) near the center as opposed to those at a greater distance.
Using the GWR model, the estimated coefficients can be written as follows, Eq. (9):
$$\hat {\beta }\left( {{u_i},{v_i}} \right)={\left( {X^{\prime}w\left( {{u_i},{v_i}} \right)X} \right)^{ - 1}}X^{\prime}w\left( {{u_i},{v_i}} \right)Y$$
9
Where w(ui,vi) is a diagonal spatial weight matrix per observation (i.e., county).A weight matrix for spatial patterns represent the central idea of the model; The parameter value is determined by the bandwidth and geographic location which is used to describe the non-stationarity characteristics for a location (Poudyal et al. 2012; Yang and Wong 2013).In our case, we utilized ArcGIS 10.5 to assess GWR and OLS models. In GWR models, Gaussian functions were used to assign Weight in space matrices, and across verification processes, the appropriate bandwidth was determined to reduce the Akaike Information Criteria (AICc).