## 1 Introduction  
Ecosystem services (ESs) refer to the benefits that humans derive from ecosystems, integrating society and ecosystems to support the continued survival and development of human populations [1]. There are several types of ESs, each with drastically variable spatial distributions [2]. Large-scale ecological restoration projects are one of the key drivers of change in the relationships among various ESs [3]. These projects serve as good indicators for evaluating the ecological benefits of developmental projects by effectively linking human well-being to their surrounding environment [4]. In general, ES trade-offs involve an increase in one ES accompanied by a decrease in another ES [5]; synergy, on the other hand, refers to the simultaneous increase or decrease in ESs [6]. Consequently, understanding the factors that influence ES trade-offs is essential to maintaining a diverse and sustainable supply [7]. Trade-offs/synergies happen in ecosystems at different temporal and spatial scales,and analyzing ESs dynamics is critical to understanding their trade-offs and synergies; ESs impact one another and can have some nonlinear responses [8]. Improving the current understanding of these linear or nonlinear relationships between ESs and quantitative expressions is a prerequisite for a thorough scientific assessment of ESs. Although remote sensing techniques are currently the most popular methods used to evaluate ESs, the quantitative and spatial response relationships between ESs trade-offs/synergies and ES changes need further clarification [9]. Previous research in this area focused on simple trade-offs and synergistic relationships among ecosystem services but neglected the exploration of the drivers and mechanisms of these relationships [10]. Although both external and internal factors influence relationships between ESs, trade-offs and synergistic relationships are of greater interest in response to ever-changing ESs. The generalized additive model [11] (GAM) is a semiparametric extension of the generalized linear model, which is a free and flexible statistical model that can handle nonlinear relationships between response variables and multiple explanatory variables using nonparametric smoothing functions [12]. It is not limited by the linear combination of explanatory variables and allows for the summation of various functions of explanatory variables. In addition, GAM is suitable for a variety of distribution types (e.g., Gaussian, binomial, gamma, and Poisson). Due to their various advantages, GAMs have been widely used in ecological and environmental health assessments in recent years. For example, [PERSON] et al. [13] used a GAM to analyze the nonlinear relationship between socioeconomic circumstances and air pollution, and its effect on human life expectancy. [PERSON] et al. [14] used a GAM and machine learning to model the effect of tropical cyclone activity on the northern Indian Ocean with the Boreal summer intra seasonal oscillation (BSISO) of the northern summer intra-seasonal oscillation. GAMs have been used in relatively few investigations into ES trade-offs/synergies relationships, and our research used this model to analyze ES response relationships in Southwest China. This area is dominated by mountainous landscapes and is one of the most important regions for the function of ESs in China. The vegetation in Southwest China has improved in recent years [15]; changes in land-use types through ecological restoration projects have been considered to be the driving force behind this vegetation improvement phenomenon in Southwest China [16]. Coupled with accelerated urbanization and rapid climate change, there is immense pressure for urgent ecological conservation. Therefore, evaluating ESs and investigating the trade-offs/synergies relationship (and their drivers) between ESs has become an important theme in ecological management. The state of ESs and their trade-off patterns are very complex due to the large internal variation and high substratum heterogeneity.