China is a country full of mountains, and the mountain area includes about 65% of the total area. This paper selected Qian-Gui karst Mountain area, Hengduan Mountain area and Taihang Mountain area as the study areas (Fig. 1). The area of Qian-Gui karst Mountain area is about 21×10⁴ km², including Guizhou Plateau, the peak and depression areas in Guizhou and Guangxi, and the Guangxi hilly area. This area is located at the center of a karst landform, and its karst landform is well developed. Qian-Gui karst Mountain area is characterized by rugged topography, a dense population, less-plowable land, serious water and soil erosion, an expansive stony desertification area and an extremely vulnerable ecosystem (Xiong et al., 2012); it is also an important component of the ecological barrier for the upstream of the Yangtze River and the Pearl River. Hengduan Mountain area is located in south-western China and its area is about 45×10⁴ km². The topography fluctuates considerably (Ying and Fang, 2017) and is intricately varied. This area has clear vertical natural zones, vertical climate zones, stereoscopic agricultural zones and other natural landscapes. Hengduan Mountain area is endowed with abundant water resources, but has frequent debris flows, landslides and other natural disasters. Taihang Mountain area is located between Shanxi Province and the North China Plain, with a northeast - southwest trend, and an area of about 14×10⁴ km². It spans from Beijing West Mountain southward to the northern bank of the Yellow River between the border of Shanxi Province and Henan Province; in the western part it neighbors the Shanxi Plateau and in the eastern part, it is adjacent to the North China Plain. The topography of Taihang Mountain area is high in the western part and low in the eastern part. It has a warm temperate zone continental monsoon climate, the annual rain fall is 570 mm and the annual average temperature is 10 ℃. This area is characterized by high land cultivation and plantation rates and an intense conflict between land and population. This area also has a thin and fertile soil layer, as well as widespread water and soil erosion. Therefore, Taihang Mountain area is under high pressure for land ecology protection (Wang et al., 2017).

NPP and evapo-transpiration data of the three mountain areas used in this study were obtained from the MODIS MOD17 and MOD16 data source processed by NTSG, Montana University (http://www.ntsg.umt.edu/project) (Jiang et al., 2017). The rainfall data were obtained from the Resource and Environment Data Cloud Platform, Chinese Academy of Science (http://www.resdc.cn). Spatially interpolated data of annual rainfall in the three mountain areas were based on the daily observation data from meteorological stations. These data were then subjected to analysis, calculation and spatial interpolation treatment. The interpolation was carried out using an Australian ANUSPLIN interpolation software, a tool often used to analyze and interpolate multivariable data using smooth spine functions (Wang et al., 2006). Land utilization data of the three mountain areas in 1990, 2001, 2010 and 2015 were supplied by the space function optimization and regulation strategy research group of a “973 Project” of the National Key Basic Research Laboratory. These data were decoded by remotely sensed imaging, with a unified spatial resolution of 1 km and a total interpretation accuracy of more than 80%. The total production values of agricultural produce for the three mountain areas were from the Social-economic Yearbook of related regions. The change trends and correlations of ecosystem services were analyzed by the ArcGIS10.2 space analysis module raster calculator and a band set statistic tool. The F values of significance tests were analyzed by IDL (Interactive Data Language) programming.

3.1.1 Quantifying the value of net primary production

Net Primary Production (NPP) represents the total amount of dry organic matter produced by terrestrial green plants through photosynthesis per unit time and unit area minus respiratory consumption. NPP reflects the utilization capacity of plant vegetation for water, soil and other environmental resources (Tao et al., 2003; Sun et al., 2017).

The value of NPP is determined by the standard coal method, i.e., the amount of NPP is converted to its value by the formula below (Ren and Liu, 2013).

In the formula, V_npp represents the value of NPP (yuan); A represents the quantity of NPP (t C ha^‒1 yr^‒1); B represents standard coal and its value is 1; Q₁ is the calorific value for converting the amount of NPP (6.7 kJ g^‒1); Q₂ is the calorific value produced by standard coal (10 kJ g^‒1) and C represents the price of standard coal.

3.1.2 Quantifying the value of hydrological regulation

The hydrological regulation function of a mountain area is reflected by the water conservation and water retention services of its ecosystem. The quantity of water conservation is related to rainfall, evapo-transpiration, surface runoff, types of plant vegetation and other factors. Therefore, the hydrologic balance method is used to quantify water conservation and to characterize the strength of hydrological regulation in a region. In this method, the regional ecosystem is considered in its entirety; the input and output water volumes were calculated from the viewpoint of water balance. The quantification of hydrological regulation, i.e., the quantity of water conservation, is the difference between regional rainfall and surface runoff as well as evapo-respiration (Gong et al., 2017), which is calculated according to the formula below.

In the formula, TQ represents the total amount of water conservation in a region (m³); P_i represents rainfall (mm); R_i represents the amount of surface runoff (mm); ET_i represents evapo-transpiration (mm); M_i represents the area of class-i land utilization type or the ecosystem; i represents class-i land utilization type or the ecosystem; and j represents the number of land utilization types or ecosystems. The amount of surface runoff R_i, represents the cross product of the surface runoff coefficient and rainfall. Empirical data of surface runoff for every kind of land utilization type or ecosystem can be acquired from the coefficients of surface runoff of Qian-Gui karst Mountain area, Hengduan Mountain area and Taihang Mountain area based on published documents (Gu and Zhang, 2005; Zhang et al., 2007; Peng et al., 2008; Xiao et al., 2010; Chen et al., 2012; Wen, 2017).

The value of the water retention service can be calculated by the engineering substitution method (Li, 1999) as follows.

In the formula, V_tq represents the value of the water retention service; TQ represents the total amount of water conservation (m³); Q_g represents the amount of water storage of the water conservancy projects for alternative ecosystems; V_g is the construction price of the water conservancy projects for Q_g; and L is the coefficient of the developmental stage.

3.1.3 Quantifying the value of agricultural produce supply

Agricultural produce supply is an important type of ecosystem service, as well as a material basis that supports the sustainable development of human society (Liu et al., 2020). The value of agricultural produce of the cropland, grassland and any other land in the three mountain areas was calculated from the spatial land utilization data. The value of agricultural produce is calculated by the following formula.

In the formula, G_i represents the total production value of agricultural produce i supplied by a single raster in a region (yuan); M_i represents the land area that produces the agricultural produce i (km²); N_i represents the average production value of land i (yuan km^-2). N_i is calculated according to the following formula.

where, F_i represents the total production value of agricultural produce i produced in a region (yuan), and S_i represents the total land area in a region that produces agricultural produce i (km²), namely, the total area of all kinds of land utilization types that produce agricultural produce i.

The change trends of various ecosystem services during 1990‒2015 in the three mountain areas were calculated raster by raster using a linear regression method. The slope of the trend represents the changing orientation and speed of various ecosystem services (Wu et al., 2016; Li et al., 2017). The slope is calculated according to the following formula.

In the formula, $\theta$ represents the slope of the regression trend; x_i represents the values of various ecosystem services in year i; t_i is the year. In the change trend raster diagram, $\theta $>0 suggests an increasing trend of ecosystem services during the study period, and vice versa.

The F test was used to test the significance of the change trends of various ecosystem services. It is calculated by the following formula.

In the formula, $\bar{x}_{i}$ is the regression value of ecosystem services in year i; $\bar{x}$ is the mean value of ecosystem services in various years; x_i is the realized value of ecosystem services in year i. The F value was calculated using IDL programming and divided into three levels: F<0.01 represents extremely significant change; 0.01≤F≤0.05 represents significant change, and F >0.05 represents insignificant change.

The correlation analysis method was used to investigate the trade-offs and synergies of ecosystem services among the different typical mountain areas based on pixels. The correlation coefficient between NPP and the value of hydrological regulation, and that between NPP and the value of agricultural produce supply were both analyzed. The correlation coefficients were calculated as follows (Mu et al., 2013).

In the formula, R_xy is the correlation coefficient between variables x and y; x_i and y_i are the values of the two variables in year i; $\bar{x}$and $\bar{y}$ are the mean values in various years of these two variables; and N represents the number of years.

Based on the formulas given above, the values were calculated for NPP, hydrological regulation and agricultural produce supply of the mountainous ecosystems in Qian-Gui karst Mountain area, Hengduan Mountain area and Taihang Mountain area at the four study time points of 1990, 2000, 2010 and 2015. Meanwhile, the distributions of change trends for the ecosystem services of the three mountain areas were calculated based on Formula (6) (Fig. 2). As seen from the change trends of the values of NPP in the three mountain areas during 1990‒2015 (Fig. 2a, 2b and 2c), the values tended to increase to a certain degree, but the spatial differences of the rates of increase differed considerably. In particular, the values of NPP in the peak and depression region of Qian-Gui karst Mountain area, the Yunnan Plateau in Hengduan Mountain area and the south-western area in Taihang Mountain area increased faster, while those in the middle city group in Qian-Gui karst Mountain area, the region in Guangxi hilly area with much cropland, as well as the northern part of Taihang Mountain area increased much slower. As seen from the value of hydrological regulation in these three mountain areas during 1990-2015 (Fig. 2d, 2e and 2f), the values also tended to increase. In particular, there were greater increases in the peak and depression region of Qian-Gui karst Mountain area as well as Guangxi hilly area; in the big and small Mountain Liang in Hengduan Mountain area and other middle regions; and in the low mountains and hills in the southeastern Taihang Mountain area. As seen from the value of agricultural produce supply in the three mountain areas during 1990-2015 (Fig. 2g, 2h and 2i), the values in Qian-Gui karst Mountain area and Hengduan Mountain area both tended to increase. In particular, the values in the karst mountain area of north Guangxi and the northern mountain area in Hengduan Mountain area increased faster, while that in Taihang Mountain area tended to decrease, especially in the low mountain and hill region of Taihang Mountain area with higher levels of urbanization and industrialization. However, the quantity of agricultural produce supply in the middle part, part of the area in the southern part and the Beijing Western Mountain area in the northern part of Taihang Mountain area tended to increase. Changes in the ecosystem services of the three mountain areas were analyzed with the F test (Fig. 3). The values of NPP, hydrological regulation and agricultural produce supply in most parts of these three mountain areas did not differ significantly, but those in small parts did vary significantly or extremely significantly. For example, the value of NPP in the northern part of Hengduan Mountain area increased significantly, while the value of hydrological regulation in part of the area of Guizhou Plateau in Qian-Gui karst Mountain area, western Guangxi, the peak and depression region at the border of Guizhou Province and Guangxi Province, Beijing and some of the counties in Hebei Province increased extremely significantly. The areas in the three mountain areas where the value of agricultural produce supply varied significantly were sparsely distributed, suggesting a relatively declining agricultural production service in the three mountain areas. In contrast, NPP, hydrological regulation and other support and regulation services increased very significantly.

In order to analyze the trade-offs and synergies of ecosystem services in the three mountain areas during 1990-2015, we first calculated the perennial means of the values of NPP, hydrological regulation and agricultural produce supply. Then, we calculated the correlation coefficients of the values of NPP, hydrological regulation and agricultural produce supply of the three mountain areas using the ARCGIS spatial analysis module (Table 1).

As shown in Table 1, the support service and regulation service of the values of NPP and the hydrological regulation in the three mountain areas were positively correlated, and both passed the significance test, suggesting that NPP is positively synergistic with the hydrological regulation service in the three mountain areas, while NPP and the hydrological regulation service were negatively correlated with the agricultural produce supply service. Therefore, there is trade-off among NPP, the hydrological regulation service and the agricultural produce supply service in the three mountain areas. As seen from the differences in the trade-offs and synergies of the ecosystem services in the three mountain areas, NPP was synergized the most with the hydrological regulation service in Hengduan Mountain area, while the synergy between NPP and the hydrological regulation service in Qian-Gui Mountain area was very weak, and the strongest trade-off was seen among NPP, the hydrological regulation service and the agricultural produce supply service in Hengduan Mountain area.

In order to determine the dynamic change trends and spatial differences between the trade-offs and synergies of the ecosystem services in the three mountain areas, the correlation coefficients between NPP and the hydrological regulation service, as well as that between NPP and the agricultural produce supply service, at the four time points, i.e., years 1990, 2000, 2010 and 2015, were analyzed using the ARCGIS spatial analysis module, and both passed the significance tests. Therefore, the standard can reflect the degree of discreteness of a group of the dataset (Table 2) and the slope of the linear regression can reflect the change trend and its speed (Fig. 4).

As seen from the standard deviation (SD) of the correlation coefficient between NPP and the hydrological regulation service in the three mountain areas (Table 2), Qian-Gui Mountain area had the highest SD, followed by Taihang Mountain area, and Hengduan Mountain area had the lowest SD. This suggested that the correlation coefficient of NPP and the hydrological regulation service at the four time points in Qian-Gui Mountain area had the highest degree of discreteness and the synergistic relation was the most unstable. As seen from the slope of the linear regression of the correlation coefficients for NPP and the hydrological regulation service during 1990‒2015 (Fig. 4), the slopes for Qian-Gui Mountain area, Hengduan Mountain area and Taihang Mountain area were 0.0074, -0.0045 and -0.0039, respectively, suggesting that the fluctuation of the synergistic relation between NPP and the hydrological regulation service in Qian-Gui Mountain area was enhanced, while those in Hengduan Mountain area and Taihang Mountain area were weakened, and that in Hengduan Mountain area was weakened to a greater degree.

As seen from the SD of the correlation coefficients between NPP and the agricultural produce supply service in the three mountain areas during 1990‒2015 (Table 2), Qian-Gui Mountain area and Taihang Mountain area had the highest SD (SD = 0.03 for both areas), while Hengduan Mountain had the lowest SD. This suggested that the correlation coefficient between NPP and the agricultural produce supply service at the four time points in Qian-Gui Mountain area and Taihang Mountain area had the highest degree of discreteness and the spatial synergistic relation was the most unstable. As seen from the slope of the linear regression of the correlation coefficients for NPP and the agricultural produce supply service during 1990‒2015 (Fig.4), the slopes for Qian-Gui Mountain area, Hengduan Mountain area and Taihang Mountain area were 0.0032, -0.001 and -0.0029, respectively. This suggested that the fluctuation of the trade-offs between NPP and the agricultural produce supply service in Qian-Gui Mountain area was weakened, while those in Hengduan Mountain area and Taihang Mountain area were enhanced, and that in Hengduan Mountain area was weakened to a greater degree.

4.4.1 Spatial differentiation in the synergy between NPP and the hydrological regulation service

The spatial differentiation characteristics in the trade-off and synergistic relations between NPP and the hydrological regulation service and those between NPP and the agricultural produce supply service in the three mountain areas during 1990-2015 were calculated based on pixels using the ArcGIS space analysis module. The correlation coefficients between different pixels reflect the intensity of their trade-off and synergy.

In general, there was a synergistically positive relationship between NPP and the hydrological relation service in the three mountain areas during 1990‒2015, but the synergy within a mountain area had considerable spatial differences (Fig. 5). In particular, the synergistic relation between NPP and the hydrological regulation service in the middle-south Guizhou Plateau and the southeastern part of Guangxi hilly area in Qian-Gui karst Mountain area was very strong, while that in the western Guizhou Plateau and the northwestern part of Guangxi province was very weak. The latter area is characterized by widespread rocky desertification. It is also an area with concentrated successive poverty in mountain Wumeng, Yunnan province, Guangxi province and Guizhou province. Influenced by fertile soil in the karst mountain area, the NPP of plant vegetation grows slowly and insignificantly, as does the water conservation role. Therefore, the synergistic relation between NPP and the hydrological regulation service in this area is very weak (Fig. 5a). The synergistic relationship between NPP and the hydrological regulation service in the northwestern part of Hengduan Mountain area and the middle-eastern part of Yungui plateau was very strong, while that in the big and small mountain Liang area was very weak. The latter is an area with concentrated poverty, and there is a prominent contradiction between humans and land, great topographic relief, warm and cool climates, more sloped cropland and low soil productivity. Reclamation and plantation activities affect the recovery of plantations, while the poor water conservation capacity of the sloped cropland leads to a low synergistic degree between NPP and the hydrological regulation service (Fig. 5b). The positive synergistic relationship between NPP and the hydrological regulation service in the southern part of Taihang Mountain, northern Beijing and part of Hebei province in Taihang Mountain area was very strong, while that in the middle part of Taihang Mountain area was very weak. This area is facing dual pressures from regional economic development and ecological service demands in Beijing, Tianjing and Hebei province. The contradiction between humans and land is still very prominent. Coal mining and exploitation of mineral resources destroyed the regional vegetation and reduced its water conservation capacity, leading to a weak synergistic relation between NPP and the hydrological regulation service (Fig. 5c).

4.4.2 Spatial differentiation in trade-offs between NPP and the agricultural produce supply service

In general, there was a synergistic trade-off between NPP and the agricultural produce supply service in the three mountain areas during 1990-2015, but the trade-off within a given mountain area also had considerable spatial differences (Fig. 6). In particular, the trade-off between NPP and the agricultural produce supply service in Qian-Gui karst Mountain area was stronger in the peak and depression area of southern Guizhou province and the karst mountain area in northwestern Guangxi province, while the synergistic relationship between NPP and the agricultural produce supply service in the middle-western Guizhou plateau and Southeastern Guangxi province and other smooth areas was very weak. The former area is characterized by widespread rocky desertification, a rugged earth surface, more sloped cropland and a high degree of poverty. There are also frequent land exploitation activities in that area and an extremely vulnerable eco-environment. As a result, the trade-off between NPP and the agricultural produce supply service was significant (Fig. 6a). The trade-off between NPP and agricultural produce supply service in the northeast and the big as well as the small Mountain Liang in Hengduan Mountain area was very strong. This is a concentrated region with successive poverty and high rates of reclamation and plantation. The natural ecology in this area is also influenced by land exploitation activities, and there is a marked trade-off between NPP and agricultural production activity in this area (Fig. 6b). In Taihang Mountain area, the trade-off between NPP and the agricultural produce supply service in northern Shanxi province and part of Hebei province was very strong. This area is facing dual pressures from regional agricultural development and ecological protection. Environmental problems during the agricultural production process are still very strong and there is an intense trade-off between NPP and the agricultural supply service in the context of collaborative development in Beijing, Tian and Hebei province (Fig. 6c).

Taking three representative mountain areas as examples, the spatial variation of the trade-offs and synergies of ecosystem services in the mountain areas of China was investigated. The trade-offs and spatial differentiation characteristics of ecosystem services among the three mountain areas were clarified. Our findings provide a scientific basis for the sustainable utilization and management of the ecosystem services in the three mountain areas. Due to the poor availability of data, the timeliness of research data needs to be improved. The driving factors and mechanisms governing the trade-offs and synergies of ecosystem services in the three mountain areas should be addressed in future studies. Based on the spatial and temporal differentiation characteristics and developmental laws of trade-off and coordination of the three mountainous areas, the planning and construction of ecological restoration projects in the typical mountain areas should be carried out according to local conditions. At the same time, it is necessary to strengthen the comparative study of the trade-offs and coordination of ecosystem services in different types of small watersheds within a given mountain area. In addition, experimental studies, scenario analysis and mechanism studies including field surveillance, multipurpose planning, investments and their applications should be highlighted in the future. Such efforts may quantify the connections among different ecosystem services and realize prospective simulation and prediction. They could also guarantee the scientific nature, validity and operability of ecosystem service management in the future. In addition, mountain areas are usually the origin or upstream of rivers. Therefore, studies concerning the trade-offs and synergies of ecosystem services in mountain areas should consider the functional localization of mountain areas as well as the differential demands of mountain areas and their neighboring regional socio-economic development with respect to ecosystem services. To realize the sustainability of mountain areas and related regions and to maintain humankind’s benefits and welfare, social ecological methods should be used to evaluate the ecosystem services in different mountain areas and their relations. The mountain area is a settlement of multiple nations and houses the upstream of rivers. Their various ecosystem services, such as cultural services, soil conservation, carbon fixation and oxygen release, are all of equal importance. Therefore, an assessment of such ecosystem services and their relations should be enhanced in the future.

Considering three kinds of ecosystem services (NPP, hydrological regulation and agricultural produce supply) as representatives and three mountain areas (Qian-Gui Mountain area, Hengduan Mountain area and Taihang Mountain area) as examples, the spatial-temporal characteristics of the trade-offs and synergies of ecosystem services during 1990-2015 were analyzed using linear regression analysis and correlation analysis based on the values of reproductive NPPV, hydrological regulation and agricultural produce supply. The main conclusions are as follows.

(1) In the three mountain areas, the agricultural produce supply service was relatively reduced, but NPP, hydrological regulation and other support and regulation services were increased dramatically. In most regions of the three mountain areas, the values of NPP, hydrological regulation and the agricultural produce supply service did not change significantly. The values of NPP, hydrological regulation and agricultural produce supply were changed extremely significantly or significantly in only relatively small areas. For example, the value of NPP in the northern part of Hengduan Mountain area increased significantly; the value of the hydrological regulation service in Guizhou Plateau, the northern part of Guangxi Province, the peak and depression area at the border between Guizhou Province and Yunnan Province of Qian-Gui karst Mountain area, Beijing area of Taihang Mountain area, and some counties in Hebei Province were also increased extremely significantly. The areas where the value of agricultural produce supply changed significantly were sparsely distributed in the three mountain areas.

(2) NPP showed positive synergy with the hydrological regulation service in the three mountain areas. The spatial synergistic relationship between NPP and the hydrological regulation service in the three mountain areas was enhanced, while those in Hengduan Mountain area and Taihang Mountain area were weakened, and the spatial synergistic relation in Hengduan Mountain area was weakened to a greater degree. There was a synergistic relationship among NPP, the hydrological regulation service and the agricultural produce supply service in the three mountain areas. In particular, the spatial trade-off between NPP and the agricultural produce supply service in Qian-Gui Mountain area became weaker, while those in Hengduan Mountain area and Taihang Mountain area became stronger, and that in Taihang Mountain area was enhanced to a greater degree.

(3) There were significant spatial differences between trade-offs and synergies of ecosystem services in the three mountain areas. As seen from the synergistic spatial differences between NPP and the hydrological regulation service, it was stronger in the middle-southern part of Guizhou plateau and the southeastern part of Guangxi hilly area in Qian-Gui Mountain area, while in the western part of Guizhou plateau and the northwestern part of Guangxi province it was very weak. The synergistic spatial difference between NPP and the hydrological spatial difference was strong in the northwestern part of Hengduan Mountain area and the middle-eastern part of Yungui Plateau, while in the big and small mountain Liang and the other middle area it was very weak. The synergistic spatial difference between NPP and the hydrological spatial difference was strong in the southern part of Taihang Mountain area, the northern part of Beijing, and part of the area in Hebei Province, while in the middle part of Taihang Mountain area it was very weak. As seen from the spatial difference in the trade-off of ecosystem services between NPP and the agricultural produce supply service, it was strong in the peak and depression area of Qian-Gui Mountain area, the Karst mountain area in the northwestern part of Guangxi province, the northeastern part of Hengduan Mountain area, the big and small mountain Liang area, the northern part of Shanxi province in Taihang Mountain area and part of the area of Hebei Province, while in the middle-western part of Guizhou plateau, the southeastern part of Guangxin Province and the other smooth area it was very weak.