## 2 Materials and Methods
### Quantification of Ecosystem Services  
Based on the characteristics of the SHMB, five types of ESs were selected: water yield (WY), carbon storage (CS), soil conservation (SC), habitat quality (HQ), and food production (FP). The specific calculation formulas and explanations of the indicators are as follows. (1) WY  
WY primarily includes the contributions from human activities and river runoff within the study area. The SHMB is an important river confluence region, characterized by abundant water resources. This study employed the water yield module of the Integrated Valuation of Ecosystem Services and Trade-Offs (InVEST 3.14.1) software model to assess water conservation in the SHMB. By utilizing the Budyko curve and meteorological parameters, the annual WY for each unit within the region was evaluated [28]. The formula is as follows:  
\[WY_{i}=\left(1-\frac{AET_{i}}{P_{i}}\right)\times P_{i}, \tag{1}\]  
where \(WY_{i}\) represents the annual \(WY\) for raster \(i\), \(P_{i}\) denotes the annual precipitation for raster \(i\), and \(AET_{i}\) refers to the annual actual evapotranspiration for raster \(i\). (2) CS  
CS reflects the carbon sequestration capacity of different ecosystems within the region. Terrestrial ecosystems typically include the aboveground biomass, belowground biomass, dead organic carbon, and soil organic carbon. The assessment used for the carbon storage and sequestration module in the InVEST model is primarily a combination of four carbon pools within the land use ecosystem [28], reflecting the carbon sequestration capacity under the influence of the complex forest ecosystems and anthropogenic patterns in the SHMB. The calculation is as follows:  
\[C_{t}=C_{a}+C_{b}+C_{s}+C_{d}, \tag{2}\]  
where \(C_{t}\) represents the total CS in the region, \(C_{a}\) denotes the amount of carbon stored in the aboveground biomass, \(C_{b}\) refers to the amount of carbon stored in the belowground biomass, \(C_{s}\) indicates the CS in the soil, and \(C_{d}\) is the amount of carbon stored in the dead organic matter. (3) SC  
The sediment delivery ratio component of the InVEST model quantifies the extent of soil erosion in a region [29]. Due to the complex topography and karst geomorphology of the mountainous areas in the SHMB, the diversity of ecosystems is vulnerable to degradation. Meanwhile, construction projects and urbanization have further compromised the vegetation cover. SC has led to the significant loss of soil and land resources. Understanding the soil erosion status in the SHMB is crucial for water and soil conservation, ecological restoration, and rational land use. The calculation is as follows:  
\[A=R\times K\times LS\times(1-CP), \tag{3}\]  
where \(A\) represents the soil retention capacity, \(R\) denotes the rainfall erosivity, \(K\) refers to the soil erodibility, \(LS\) represents the slope length and gradient, and \(C\) and \(P\) denote the vegetation cover factor and the conservation practice factor, respectively. (4) HQ  
The assessment of HQ reflects the habitat conservation processes and biodiversity within a region. The HQ of the SHMB, which is a significant gene pool for plant and animal genetic resources in China, plays a vital role in maintaining the biodiversity of the regional ecosystem. HQ was assessed using the InVEST model [28]. The model evaluates HQ byintegrating the impacts of different LUCC types and their vulnerabilities to various threat factors. The calculation is as follows:  
\[Q_{xj}=H_{j}\Bigg{(}1-\Bigg{(}\frac{D_{xj}^{z}}{D_{xj}^{z}+K^{z}}\Bigg{)}\Bigg{)}, \tag{4}\]  
where \(Q_{xj}\) represents the HQ of land use \(j\) on raster \(x\), \(H_{j}\) denotes the habitat suitability on land use type \(j\), \(D_{xj}\) indicates the degree of habitat degradation on raster \(x\) when land use is \(j\), and \(z\) and \(K\) are scale factors. (5) FP  
FP represents the ES of food yield, which is one of the basic ecosystem provisioning services that sustains human existence. There is a strong and clearly linear correlation between gross GPP and food yield.