[Ecosystem Service Trade-off Synergy Strength and Spatial Pattern Optimization Based on Bayesian Network： A Case Study of the Fenhe River Basin].

Understanding the strength of trade-off and synergistic relationships among ecosystem services (ESs) is crucial for ecological management and restoration in the Fenhe River Basin. However, there is still a lack of sufficient research on the driving variables and spatial pattern optimization of the strength of ESs relationships in this area. Based on the quantitative assessment of six ESs in the Fenhe River Basin in 2000 and 2020, the ecosystem services trade-off synergy index (TSI) was introduced to quantitatively measure the strength of trade-off and synergistic relationships between each pair of ESs. A Bayesian network was constructed to identify the driving variables of trade-off and synergistic relationships, and sensitivity analysis was conducted to determine the degree of influence of key variables on the strength of these relationships. The optimization area of the strength of ESs trade-off and synergistic relationships was characterized in spatial patterns. The results showed that:① There were significant spatiotemporal differences in the six ESs in the Fenhe River Basin in 2000 and 2020. In terms of time scale, water yield, net primary productivity, crop productivity, soil conservation, and carbon storage all showed a trend of fluctuating increase. In terms of spatial scale, the spatial distribution changes in the six ESs were relatively small over the 20 years. ② The TSI of carbon storage was high in the surrounding area and low in the middle, showing a four-high and four-low pattern. The areas with the highest TSI between grain supply and other services were distributed from north to south. ③ Sensitivity analysis found that the strength of water yield, soil conservation, and habitat quality were significantly affected by precipitation, plant root depth restriction, and rainfall erosion. According to the conditional probability of different states of key variables, Wenshui County, Qingxu County, and Qi County in the central part of the Fenhe River Basin were identified as high-value areas for trade-off and synergistic relationships, which could be used as key areas for ecological restoration. These findings have important theoretical and practical significance for understanding the complex relationship between multiple ESs trade-off and synergistic relationships and their driving variables and for proposing sustainable ecological environment management policies.