What are the dominant factors and optimal driving threshold for the synergy and tradeoff between ecosystem services, from a nonlinear coupling perspective?

Exploring the dominant impact factors and optimal driving threshold of the synergic and trade-off relationship between ecosystem services (ESR) is conducive to the scientific management of the ecosystem. Previous studies seldom take ESR as dependent variables and are primarily based on linear regression models, which is difficult to reflect the real nonlinear ecological process. Based on the spatial mapping for 15 pairs of binary ESR between 6 typical ESs in Fujian Province, this study introduced "glass box" (interpretable and visual) machine learning models to construct a generalizable ESR driving mechanism exploration method system of "ESR spatialization - nonlinear correlation derivation". It visually expounds the nonlinear coupling process between ESR and " natural-socio-economic " variables, and based on this, the dominant factors affecting ESR and their optimal driving threshold interval for the maximized synergy between ESs were determined. The results show that (i) the climate and human traffic activities have the most significant effect on the ESR among the "natural-socio economic" factors. Annual total precipitation, annual sunshine radiation, average annual temperature, distance from railway, and GDP density are the dominant factors affecting the ESR in the sample area. (ii) The correlation between ESR and driving factors is nonlinear. By superimposing the nonlinear response curves of 15 pairs of ESR, the optimal threshold interval of the dominant factor under the guidance of comprehensive synergy maximization in the study area is obtained. (iii) In the comparison of three machine learning models and a linear regression model, the XGBoost model has the best fitting effect, and the machine learning models are all superior to the linear model. The methods and ideas of this study have strong generalization and application and can provide references for research in other regions and scales.