Study on the Trade-Off Synergy Relationship of “Production-Living-Ecological” Functions in Chinese Counties: A Case Study of Chongqing Municipality

: The trade-off and coordinated development of the “production-living-ecological” functions (PLEFs) of an area is an important basis for the optimization of the spatial pattern of the land, and helps to promote the harmonious symbiotic relationship between human beings and nature. This paper combines ecological niche theory, a coupling coordination model, and a trade-off synergy model to construct an evaluation index system for Chinese county PLEFs. Quantitative methods were used to measure spatiotemporal evolution characteristics, trade-off synergy of PLEFs in 38 counties in Chongqing, China, and the coupling coordination degree between PLEFs. The results showed that the ecological niche width of the “production-ecological” function revealed an overall growth trend. However, there was a mismatch in regional development of the “production-ecological” function, showing dislocation characteristics of “high in the west and low in the east” and “high in the east and low in the west.” The niche width of the life function is similar to the comprehensive niche width of PLEFs, showing the characteristics of ﬂuctuation and partition change. PLEFs and both the aforementioned functions showed distribution characteristics of “high in the west and low in the east,” with the whole moving towards the stage of coordinated coupling, of which the “production-living” function has the highest coupling level. The functional coupling coordination degree of “production-living-ecological” is generally manifested as “high in the west and low in the east,” and changing from the primary stage of imbalance to well-coordinated development. The “production-ecological” and “living-ecological” functions are in low-level imbalance in the primary and moderate coordination stages. Additionally, the evolution trend of the “production-ecological” and the “living-ecological” functions are similar, showing alternating and ﬂuctuating development characteristics. Overall, in the past 20 years, Chongqing’s “living-production” function has changed from a trade-off model to a collaborative development relationship, and the “living-ecological” function is generally based on a collaborative development relationship. The “ecological function” is manifested as a trade-off constraint relationship. Moreover, the coordinated development level of “living-production,” “living-ecological,” and “production-ecological” functions in the central urban area has been greatly improved, while counties have gradually shown different degrees of trade-offs


Introduction
Land space is the environmental place for national survival and the primary carrier of all economic and social activities. According to the use of land space, it can be divided Land 2023, 12, 1010 3 of 27 synergy theory, this paper discusses the functional coupling and coordination relationship between PLEFs and analyzes its pattern evolution characteristics. There is a basis for promoting the integrated and coordinated development of regional PLEFs and optimizing the spatial layout of the national territory. The research on the coupling and coordination of PLEFs is to diagnose the utilization status and efficiency between production functions, living functions, and ecological functions, evaluate the implementation effect of spatial planning in a particular area, and improve the deficiencies of spatial planning to promote the harmonious integration between economy, society and ecology and ensure the green and healthy development of the region [37,38]. Land use is explored by applying coupled coordination models [39][40][41][42][43]. The study area involves countries and urban agglomerations at the macro level [44], provinces and municipalities at the medium level [45,46], and counties and townships at the micro level. The typical research areas of the coupling and coordination analysis of the PLES mainly include the Yellow River Basin [47] and the Yangtze River Economic Belt [48]. From the research status of scholars at home and abroad, most scholars focus on the static pattern evaluation of PLEFs, and need to reveal more about the dynamic evolution rule. It is challenging to portray the continuity and dynamics of PLEFs and the state of a particular moment and predict the development trend [49,50].
Based on the above discussion and review, this paper selects 38 districts (counties) of Chongqing as the research targets and collects data for 2000, 2010, and 2020. Based on the socioeconomic data, ecological environment data, and land use data, the coupling and coordination degree between PLEFs and the two functions was measured to analyze the spatiotemporal pattern characteristics of PLEFs and the interaction relationship between PLEFs in Chongqing, and combined with ecological niche theory and spatial autocorrelation analysis, explore its pattern evolution characteristics, reveal its temporal and spatial evolution law, and discuss the "production-living-ecological" from the spatial and quantitative levels The functional synergy/balance relationship provides a new perspective for clarifying the functional interaction relationship of "production-living-ecological," to provide practical reference and reference for the optimization of land space layout.

Study Area
Chongqing (28 • 10 -32 • 13 N, 105 • 11 -110 • 11 E) is located in southwest China, the fourth city under central government jurisdiction, a comprehensive transportation hub in southwest China, and an economic center in the upper reaches of the Yangtze River. Chongqing's terrain is dominated by mountains and hills, with a total area of 82,400 square kilometers. There are 38 districts and counties under Chongqing's jurisdiction. These 38 counties can be geographically divided into "one district and two groups," namely, the main urban area of Chongqing (UC), the urban agglomeration of Wulingshan District in southeast Chongqing (SE), and the urban agglomeration of the Three Gorges Reservoir Area in northeast Chongqing (NE) (Figure 1). Chongqing is an important area for the implementation of the strategy of large-scale development of the western region, a necessary strategic node for the construction of the national "Belt and Road" initiative, and an important modern manufacturing base with unique location advantages and resource advantages, rapid industrial development and obvious industrial process [51]. However, due to problems such as single production mode, disorderly spatial expansion, extensive land use, industrial homogenization, and unreasonable resource allocation, the dual structure of urban and rural areas is prominent, the ecological environment is severely damaged, and the development of the region is unbalanced and uncoordinated, so the level of sustainable economic, social and ecological development needs to be improved [52,53]. In recent years, Chongqing has adopted rural measures of large cities and large rural areas, which has enabled the towns and villages under the jurisdiction of Chongqing to achieve sound development. As of 2020, in Chongqing municipal towns, the chemical rate reached 69.46%. However, land degradation is severe due to its location in the mountainous area of southwest China, high ecological fragility, unreasonable development, and excessive use of pesticides. In 2020, the area of soil erosion in the city reached 25,142.46 km 2 , which also caused a contradiction between production status, lifestyle, and ecological benefits in urban and rural development. Coordinating the interrelationship between the spatial PLEFs in urban and rural development is crucial, so Chongqing needs to use the PLES to clarify the spatial functions of the national territory. The spatiotemporal characteristics of development are replanned, the urban and rural ecological pattern is coordinated, and the relationship between the PLES in the county is reconstructed to enhance PLEFs effective synergy. the level of sustainable economic, social and ecological development needs to be improved [52,53]. In recent years, Chongqing has adopted rural measures of large cities and large rural areas, which has enabled the towns and villages under the jurisdiction of Chongqing to achieve sound development. As of 2020, in Chongqing municipal towns, the chemical rate reached 69.46%. However, land degradation is severe due to its location in the mountainous area of southwest China, high ecological fragility, unreasonable development, and excessive use of pesticides. In 2020, the area of soil erosion in the city reached 25,142.46 km 2 , which also caused a contradiction between production status, lifestyle, and ecological benefits in urban and rural development. Coordinating the interrelationship between the spatial PLEFs in urban and rural development is crucial, so Chongqing needs to use the PLES to clarify the spatial functions of the national territory. The spatiotemporal characteristics of development are replanned, the urban and rural ecological pattern is coordinated, and the relationship between the PLES in the county is reconstructed to enhance PLEFs effective synergy.

Construction of PLEFs Evaluation Index System
The county land space is a complex community involving multiple factors such as society, economy, and geographical environment. Based on the connotation and classification criteria of the PLEF function [54,55], it is crucial to consider the interaction of PLEFs. Furthermore, the study explores the combined relationship between dominant functions and multiple functions [56], drawing on synergy theory and niche situation theory [57][58][59], combined with Chongqing's unique geographical location, land use characteristics,

Construction of PLEFs Evaluation Index System
The county land space is a complex community involving multiple factors such as society, economy, and geographical environment. Based on the connotation and classification criteria of the PLEF function [54,55], it is crucial to consider the interaction of PLEFs. Furthermore, the study explores the combined relationship between dominant functions and multiple functions [56], drawing on synergy theory and niche situation theory [57][58][59], combined with Chongqing's unique geographical location, land use characteristics, and socioeconomic development status, based on the principles of comprehensiveness, regional, scientific, and innovative, from the aspects of material space for land use production, social space for living security, and natural space for ecological supply. Aiming at intensive and efficient production space, moderate livable living space, and beautiful ecological space, reference is made to the research experience of relevant scholars [60][61][62][63][64]. This article combined with the science, representativeness, comprehensiveness, and data availability of indicators covering agricultural production, economic development, living security, social services, ecological pressure, and ecological bearing, the land space functions of the county were identified as PLEFs, and we selected 17 PLEFs indicators. After standardizing by the extreme value method, the preliminary weight of each index is calculated by the entropy method. Then, the index weight is corrected by the analytic hierarchy method (AHP). The final weighted sum yields the combined weights of each indicator (Table 1). Note: "+" is a positive indicator, and "−" is a negative indicator.
(1) Production function refers to the ability of the county land space to provide products for human beings and increase social wealth. Therefore, this paper characterizes the production function from the two criteria of agricultural production and economic development and selects grain yield, land reclamation rate, per capita grain ownership, average industrial production value, financial contribution rate, economic density, and other indicators to characterize the production function, all of which are positive indicators, and the larger the value, the stronger the production function of the county land space. (2) Living function refers to the ability of the county land space to provide a living environment for human beings, which can reflect the income, consumption structure, and welfare of residents. Therefore, this paper characterizes the living function from the two standard layers of life security and social services and selects indicators such as the proportion of housing area, the density of transportation land, the population density, the number of hospitals per 10,000 people, the number of beds, the total retail sales of social consumer goods per capita, and the number of books in the per capita public library collection. Population density is a negative indicator, and the larger the value, the weaker the living function of the county. The rest are positive indicators, and the larger the value, the stronger the county living function. (3) Ecological function refers to the ability of the county land space to provide ecological products and services for residents, as well as to respond to external interference, realize self-repair, maintain ecosystem stability, conserve water sources, and maintain ecological security. Therefore, this paper characterizes the strength of county ecological functions from the aspects of ecological pressure and ecological supply. The two indicators of agricultural fertilizer input intensity and land degradation index were selected to characterize the ecological stress function of the county, both of which were negative indicators. The larger the value, the weaker the ecological function of the county. The three indicators of per capita water resources, forest coverage, and habitat abundance index were selected to characterize the capacity of county ecological supply, all of which were positive indicators. The larger the value, the stronger the rural ecological function.

Functional Niche Width Evaluation Model of PLEFs
Niche situation theory is one of the critical theories of ecology, in which the width of the ecological niche indicates the degree of resource utilization by a species. It has been widely used in urban geography, urban economy, and other fields, mainly including urban competition research [65][66][67] and sustainable use of arable land [68], and less used in the field of "sunshine" space research. Referring to the methods of [69], a functional [70] "production-living-ecological" model was constructed. In this way, the competitiveness of PLEFs in the research area was explored, and the larger the niche width, the higher the dominant position and the more assertive the competitiveness.
In the formula, i, j = 1, 2, · · · n; N i indicates the ecological niche of the evaluation unit indicator i; S i and P i represent the state and potential of the research unit i; S j and P j represent the state and potential of the research unit j; A i and A j are dimensional conversion coefficients; S j + A j P j is an absolute niche; W is a weight. The indicators of PLEFs measure the state in 2000, 2010, and 2020. The potential is measured by each indicator's average annual growth rate from 2000 to 2020, with a study period interval of 10 years and a dimensional conversion coefficient of 0.1.
In the formula, M i indicates the comprehensive ecological niche of the PLEFs of the region i, weighted by the three dimensions of production, living, and ecological function; j represents the dimension, N ij indicates the ecological niche of the region i in the dimension j, W j represents the weight of the dimension j. Considering the importance of the synergistic development of each function, the weight of these three dimensions is set to 1/3.

PLEFs Functional Coupling Coordination model
With the PLEFs coupling coordination model, the coupling coordination degree of PLEFs was measured to reflect PLEFs in the study area and spatially the level of collaborative development.
where: C indicates the degree of coupling, C ∈ [−1, 1]. The higher the value of C, the stronger the correlation between functions; the lower the value of C, the weaker the correlation between functions. The coupling degree is divided into four stages [71] ( Table 2). P i , R i , and E i represent the total scores of PLEFs, respectively. T represents the coordination coefficient, and α, β, and γ represent the undetermined coefficients of PLEFs set to 1/3, respectively. D refers to coupled co-scheduling, reflecting the degree of coordination between various functions. The coupling coordination degree is divided into 7 levels ( Table 3). The higher the value of D, the better the coupling and coordination between various functions, and the higher the overall efficiency; The lower the value of D, the poorer the coordination between various functions, and the more obvious the conflict. Upon further analysis of the coupling coordination degree between the two pairs of PLEFs, the coupling coordination model of PLEFs is refined into C 1 , C 2 , and C 3 : Referring to existing research [72]. the "production-living" coupling coordination model T 1 : α = β = 0.5; In the "production-ecological" coupling coordination model T 2 : α =0.55, γ = 0.45; In the "living-ecological" coupling coordination model T 3 : β =0.55, γ = 0.45.

The PLEFs Weigh the Degree of Synergy
Estimating the synergy/trade-off relationship between production, living, and ecology further clarifies the spatial heterogeneity and correlation between PLEFs in Chongqing and the synergistic/trade-off development relationship between them from the quantitative and spatial perspectives. Ecosystem services trade-off degree (ESTD) is based on linear data fitting and is a method for reflecting the interrelationships between ecosystem services. The calculation method is: In the formula, ES ia and ES ib represent the values of the i type ES at moments a and b, respectively; ESCI i is the index of change for the i type ES; ESCI j is the index of change for the j type ES; ESTD ij represents the trade-off synergy between ES types i and j, ESTD negative value indicates that the ES between categories i and j is a trade-off relationship, ESTD positive value indicates that the ES between categories i and j is a synergistic relationship; The magnitude of the absolute value of ESTD reflects the level of trade-off and synergy.

Data Preprocessing
PLEFs index system involves 17 indicators, such as grain yield, land reclamation rate, and average industrial output value. Based on different efficacy, the extreme value method was used to eliminate the influence of dimensionality to normalize the positive and negative indicators and their average annual growth so that the processed value range was [−1,1]. The closer the value is to 1, the higher its power.
Formula: X ij indicates i the normalized value of j the regional indicator; X ij indicates the actual value of i the regional j indicator; and Max j indicates Min j the j maximum and minimum values of the first indicator.

Technical Route
This paper adheres to the problem-oriented and goal-oriented and adopts the technical route of "problem-raising-previous preparation-problem analysis-problem-solving" (Figure 2). The problem-raising stage mainly explains the research background, status, objectives, method, and value. The previous preparation stage mainly includes literature review, data collection and preprocessing, research framework, and constructing the index system of PLEFs. The problem analysis stage mainly analyzed the spatiotemporal evolution characteristics, evenness and coordination degree, and trade-off synergy of PLEFs in the study area. The contributions and shortcomings of the research are analyzed to optimize the spatial pattern of the county land effectively. The problem-solving stage mainly includes research contributions and research conclusions. The solution measures that effectively weigh the functional relationship of PLEFs in the coordinated county are proposed. The contributions and shortcomings of the research are analyzed to optimize the spatial pattern of the county land effectively.

Ecological Niche Evolution
The ecological niche width of PLEFs in 38 counties in Chongqing in 2000, 2010 and 2020 was measured by data visualization mapping analysis (Figure 3). To better present the mapping effect, the calculated values of a production function, living function, and total niche width of Yuzhong District are much higher than those of other counties, so the data of Yuzhong District are not added to the chart.

Production function niche width
From 2000 to 2020, the ecological niche width of production functions in Chongqing generally showed a growth trend, and the high-value areas were mainly located in the main urban areas, of which Yuzhong District (0.5437-0.4104) consistently ranked first, as the only area in Chongqing that did not have agricultural production and achieved complete urbanization, with the financial industry, commerce and trade as the leading industries, the financial contribution rate, The economic density advantage is obvious. Dadukou District (0.0703-0.0480) production function niche width downward trend is significant, as the former bearing place of Chongqing iron and steel industry, due to the overall relocation of heavy steel, the industrial output value and fiscal revenue have a lot of impact, is trying to explore a new path for the transformation and development of the old industrial base in the urban area, and the rest of the areas show stable growth with slight fluctuations. The low-value area is mainly located in the northeast, among which the welldeveloped and representative ones are Wanzhou (0.0060-0.0073), Matjiang (0.0062-0.0080), Liangping (0.0053-0.0073), as well as the southeast of Yu, of which Xiushan (0.0048-0.0059) is relatively prominent, but also limited by topography, traffic factors, alt-

1.
Production function niche width From 2000 to 2020, the ecological niche width of production functions in Chongqing generally showed a growth trend, and the high-value areas were mainly located in the main urban areas, of which Yuzhong District (0.5437-0.4104) consistently ranked first, as the only area in Chongqing that did not have agricultural production and achieved complete urbanization, with the financial industry, commerce and trade as the leading industries, the financial contribution rate, The economic density advantage is obvious. Dadukou District (0.0703-0.0480) production function niche width downward trend is significant, as the former bearing place of Chongqing iron and steel industry, due to the overall relocation of heavy steel, the industrial output value and fiscal revenue have a lot of impact, is trying to explore a new path for the transformation and development of the old industrial base in the urban area, and the rest of the areas show stable growth with slight fluctuations.
The low-value area is mainly located in the northeast, among which the well-developed and representative ones are Wanzhou (0.0060-0.0073), Matjiang (0.0062-0.0080), Liangping (0.0053-0.0073), as well as the southeast of Yu, of which Xiushan (0.0048-0.0059) is relatively prominent, but also limited by topography, traffic factors, although most of the production function ecological niche width continues to expand, in agricultural production is relatively good, and industrial development. In the future, the urban agglomeration of the Three Gorges Reservoir Area in the NE and the urban agglomeration in the Wuling Mountain Area in the SE and the main urban area will be further promoted, forming an industrial pattern of differentiated development and coordinated development.

2.
Ecological niche width of living functions From 2000 to 2010, most areas generally showed an expansion trend, while the main urban areas showed a contraction or flat trend from 2010 to 2020, and the southeast and NE regions continued to expand as a whole. Specifically, areas with high ecological niche width of living functions were concentrated in the main urban areas, including Yuzhong District (0.2351-0.1722), Jiangbei District (0.0636-0.0.0611), and Shapingba District (0.0553-0.0878). and Banan District (0.0185-0.0257) showed improved living functions significantly. The living security and social service levels in housing, transportation, medical care, culture, and other aspects of high-value areas are generally better, and the quality of living index is high, so it is livable. The low-value areas were mainly located in the southeast and northeast of Chongqing, among which the living function of Zhongxian (0.0120-0.0164) and Xiushan (0.0124-0.0154) was significantly improved. The variation in the ecological niche width of living functions showed two states. The main urban areas with a high urbanization rate and more reasonable industrial structures tended to shrink or have stable development. The living space was relatively saturated and may be squeezed by production and ecological space. Compared with the backward urban agglomerations in the SE and NE, the urbanization rate needs to be improved. Various living guarantees such as medical care, housing, and transportation need to be improved and living space will be further expanded.

3.
Ecological function niche width Nanchuan District is also known as the "urban back garden," with rich ecological resources and good ecological functions.

4.
The comprehensive niche width of PLEFs From 2000 to 2020, the total niche width of PLEFs in Chongqing showed the characteristics of fluctuating changes. The high-value areas were mainly concentrated in the main urban area, with Yuzhong District (0.2628-0.1972), Shapingba District (0.0370-0.0547), Jiangbei District (0.0460-0.0535) and other areas as the representative areas, mainly due to industrial agglomeration, high level of economic development, with production and living functions to drive the overall efficiency of the region, or create production and lifetime value with higher ecological functions and improve the overall coordination level of PLEFs, such as Chengkou County (0.0333-0.0293) and Wuxi County (0.0269-0.0293) and other parts of the NE. The comprehensive ecological niche range of PLEFs in most areas is similar. A trend of fluctuation and alternating development within a specific range shows that PLEFs constantly compete and squeeze each other. It is necessary to optimize the industrial structure further and promote "production-living-ecological" spatial synergy, orderly integration, and balanced development.

Temporal and Spatial Correlation Analysis
Through Formula (6), the global spatial autocorrelation values of Chongqing's PLEFs can be calculated to test whether the study area has an overall spatial correlation. Table 4 shows that the test statistic Z score of the Global Moran's I Index of PLEFs from 2000 to 2020 was significantly more significant than the test threshold of 1.65, and the significance test of 10% was passed. The results show that the spatial distribution of production, living, and ecology in Chongqing from 2000 to 2020 shows significant spatial autocorrelation, showing a significant agglomeration distribution trend. Among them, the Z score of ecological function fluctuated slightly. From the time change trend perspective, the global Moran's I Index of PLEFs from 2000 to 2020 was more significant than 0 and gradually increased. It shows a spatial similarity in the adjacent counties, and the autocorrelation and spatial agglomeration distribution phenomena are also increasing, showing a positive spatial correlation. Among them, the global Moran's I of ecological function increased from 0.5872 to 0.6405, which is more spatial correlation than production and living functions; The living function is second, and the production function is lower.
Due to the differences in the spatial autocorrelation level between different spatial units and adjacent areas in the study area, the Local Moran's I Index was further used to analyze the spatial correlation between the spatial distribution of PLEFs in Chongqing and the neighboring areas with the help of the significance LISA map.

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Production function From 2000 to 2020, Chongqing's spatial distribution of production functions changed little. In 2000, the production function area had 5 hot and 12 cold spots. From 2010 to 2020, the number of cold spots increased to 14; the hot spot area remained unchanged. The proportion of the two increased, which showed that the agglomeration characteristics of production function space were strengthened. The low-value agglomeration areas of production functions are mainly located in the northeast and southeast of Chongqing. The high-value agglomeration areas are located in the main urban area. cold spots increased to 13 and then decreased to 11. The living function in SE showed the agglomeration characteristics of strengthening and weakening, and the hot spots remained unchanged. The agglomeration characteristics of living function space show a weakening trend. The high-value agglomeration area is located in the core area of the central city, and the proportion of the number of the two decreases.

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Ecological function From 2000 to 2020, Chongqing's spatial distribution of ecological function changed significantly (Figure 4). In 2000, there were, respectively, ecological functions of 5 hot spot and 15 cold spot areas, and from 2010 to 2020, the number of hot spots increased from 6 to 7, and the number of cold spots decreased from 14 to 13 and added 1 sub-cold spot area-Kaizhou District. In general, the characteristics of low-value accumulation in the main urban area were weakened, and the ecological function improved significantly. The clusters of high-value agglomeration areas were distributed in the NE and SE. The agglomeration characteristics in the NE were weakened, the agglomeration characteristics in SE were strengthened, and the proportion of quantity strengthened the spatial agglomeration characteristics of ecological function.
Land 2023, 12, x FOR PEER REVIEW 14 o From 2000 to 2020, Chongqing's spatial distribution of ecological function chang significantly (Figure 4). In 2000, there were, respectively, ecological functions of 5 hot s and 15 cold spot areas, and from 2010 to 2020, the number of hot spots increased from to 7, and the number of cold spots decreased from 14 to 13 and added 1 sub-cold s area-Kaizhou District. In general, the characteristics of low-value accumulation in main urban area were weakened, and the ecological function improved significantly. T clusters of high-value agglomeration areas were distributed in the NE and SE. The glomeration characteristics in the NE were weakened, the agglomeration characteris in SE were strengthened, and the proportion of quantity strengthened the spatial agglo eration characteristics of ecological function.

Coupling and Coordination Analysis of PLEFs in Chongqing City
The coordinated development level of PLEFs in various districts and counties Chongqing is worthy of our in-depth understanding. This article calculates the PLEF

Coupling and Coordination Analysis of PLEFs in Chongqing City
The coordinated development level of PLEFs in various districts and counties in Chongqing is worthy of our in-depth understanding. This article calculates the PLEFs in 38 counties of Chongqing in 2000, 2010, and 2020, as well as the coupling degree and coordination scheduling between the two functions ( Figures 5 and 6). Referring to the existing research results of Chen et al. (2006) [73] and Wang and Tang (2018) [74], the frequency statistical analysis method is used to group statistics on the coupling and coordination degree of PLEFs and the two functions to draw the evolution curve of the coupling and coordination degree of PLEFs in Chongqing from 2000 to 2020 (Figures 7 and 8).  [74], the frequency statistical analysis method is used to group statistics on the coupling and coordination degree of PLEFs and the two functions to draw the evolution curve of the coupling and coordination degree of PLEFs in Chongqing from 2000 to 2020 (Figures 7 and 8).

Coupling and Coordination Analysis of PLEFs
From the spatial point of view, the functional coupling degree of "production-living ecological" functions in Chongqing presents a distribution trend of "high in the west and low in the east," and the regional differentiation is significant. The areas with high cou pling degrees are mainly concentrated in urban areas. The areas with low coupling de grees are concentrated in Chengkou County, Wuxi County, and Wushan County in the NE. From the time perspective, the overall functional coupling of "production-living-eco logical" in Chongqing has improved. The highly coupled areas with the main urban area as the core have continuously spread to the NE. From 2000 to 2020, Chongqing's average

Coupling and Coordination Analysis of PLEFs
From the spatial point of view, the functional coupling degree of "production-livingecological" functions in Chongqing presents a distribution trend of "high in the west and low in the east," and the regional differentiation is significant. The areas with high coupling degrees are mainly concentrated in urban areas. The areas with low coupling degrees are concentrated in Chengkou County, Wuxi County, and Wushan County in the NE. From the time perspective, the overall functional coupling of "production-living-ecological" in Chongqing has improved. The highly coupled areas with the main urban area as the core have continuously spread to the NE. From 2000 to 2020, Chongqing's average coupling degree of "production-living-ecological" increased from 0.73 to 0.82. It gradually

Coupling and Coordination Analysis of PLEFs
From the spatial point of view, the functional coupling degree of "production-livingecological" functions in Chongqing presents a distribution trend of "high in the west and low in the east," and the regional differentiation is significant. The areas with high coupling degrees are mainly concentrated in urban areas. The areas with low coupling degrees are concentrated in Chengkou County, Wuxi County, and Wushan County in the NE. From the time perspective, the overall functional coupling of "production-livingecological" in Chongqing has improved. The highly coupled areas with the main urban area as the core have continuously spread to the NE. From 2000 to 2020, Chongqing's average coupling degree of "production-living-ecological" increased from 0.73 to 0.82. It gradually entered the coordinated coupling from the running-in period, showing a solid benign promotion effect. However, some counties have fluctuated, such as Kaizhou County, which has undergone the "first increase and then decrease" of "running-in-coordinated coupling-running-in." Specifically, in 2000, the overall degree of medium and high coupling was the mainstay, the highly coupled areas were mainly concentrated in the main urban areas, and the degree of interaction between functions was substantial. Among them, the primary coupling area, the medium coupling area and the highly coupled area accounted for 13.16%, 44.74%, and 42.11%, respectively. At this stage, Chongqing focused on economic development and urban construction, which squeezed ecological functions into production and living functions. In most regions, the coupling degree of PLEFs is in the intermediate and advanced coupling stages. In 2010, the proportion of regions in the primary and medium coupling stages decreased to 5.26% and 28.92%, respectively. The proportion of highly coupled areas increased significantly to 65.79%. Dianjiang County, Liangping County, and Kaizhou County were the main increased areas. At this stage, Chongqing gradually realized the guaranteed role of ecological functions in production and living functions, further improved the intensity of ecological functions, and promoted the degree of coupling. In 2020, compared with 2010, although the coupling degree in local areas decreased, the highly coupled areas decreased to 63.16%. The moderately coupled areas increased to 31.58%, mainly dominated by the coordinated coupling period. Chongqing advocated sustainable development and combined economic development with ecological construction at this stage. It promoted the peaceful development of the coupling degree of PLEFs in Chongqing through ecological compensation policies such as "returning farmland to the forest." The coupling and coordination degree of PLEFs shows the spatial distribution trend of "high in the west and low in the east" as a whole. From the primary offset to the wellcoordinated evolution trend, the average level of coupling coordination increased from 0.45 to 0.48. High-value areas are mainly developed with the main urban area as the core and outer. Specifically, in 2000, the coupling coordination degree of Chongqing was between [0.31, 0.72]; the highest value was in Yuzhong District and the lowest was in Yunyang County. Yuzhong District mainly uses production and living functions to drive the overall efficiency of the area. Including three types: primary disorder, essential coordination, and good coordination, it accounts for 84.21%, 13.16%, and 2.63%, respectively. However, the coordination stage accounts for a small proportion, most of which are in the primary disorder stage. In 2010, the coupling coordination degree of Chongqing was between [0.35, 0.67], and the highest value was in Yuzhong District, but the degree of coordination decreased. It is mainly related to the fact that the ecological function is lower than that of production and ecological function, and the lowest value is in Tongnan District. It included four types: primary disorder, essential coordination, moderate coordination, and good coordination, accounting for 34.21%, 50.00%, 13.16%, and 2.63%, respectively. Compared with 2000, the proportion of primary dysregulation stages has decreased significantly, and moderate coordination phases have begun to appear. However, half of the regions are still in the primary coordination stage. In 2020, the coupling co-scheduling in Chongqing was between [0.35, 0.67], with the highest value being Yuzhong District and the lowest value being Dazu District. It included four types: primary disorder, essential coordination, moderate coordination, and good coordination, accounting for 31.58%, 60.53%, 5.26%, and 2.63%, respectively. Compared with 2010, the proportion of essential and moderate coordination has increased slightly, and the overall coordination is still in the primary coordination stage. Combined with the evolution curve of coupling coordination (Figures 3-6), the coupling coordination degree of PLEFs in Chongqing presents an inverted "U" shaped evolution trend. It shows that the gap in the degree of coupling and coordination of PLEFs will be further widened as a whole. When it reaches a certain extent, it will change into a shrinking trend, gradually coordinate the development, and finally, achieve spatial synergy.

Coupling and Coordinated Analysis of Two Functions
• "Production-living" function From 2000 to 2020, the average coupling degree of the "production-living" function in Chongqing increased from 0.94 to 0.96, which has always shown a substantial mutual promotion effect. However, it showed a fluctuating development trend, and the proportion of moderately coupled areas changed from 18.42-5.26-13.16%, which was highly coupled. The regional proportion changed from 81.58% to 94.74% to 86.84%. It relates to relocating industries in Jiulongpo, Shapingba, and other areas or transforming the industrial center of gravity in Youyang and other places to tertiary industries such as tourism, reducing the production function, causing a decrease in the coupling degree. This decreases in coupling. "production-living" is the essential demand function of residents' living and economic development. The two promote each other and continue to develop in the direction of coordinated coupling.
The functional coupling coordination degree of "production-living" shows the development characteristics of "high in the west and low in the east" and from moderate imbalance to high coordination, showing a solid phenomenon of spatiotemporal differentiation. The average level of coupling coordination increased from 0.31 to 0.37, and the high-value areas mainly developed from the main urban area as the core to the outer layer. Specifically, in 2000, the coupling coordination degree was between [0.20, 0.96]; the highest value was Yuzhong District, and the lowest value was Wuxi County, among which there were mainly moderate imbalances, primary imbalance and essential coordination sum. There were four types of highly coordinated coordination, accounting for 71.05%, 13.16%, 13.16%, and 2.63%, respectively. The geographical differentiation is apparent, showing the development of fault-type and zonal stages of "essential coordination-high coordination," most of which are in the moderate imbalance stage. In 2010, the coupling coordination degree was between [0.25, 0.86]; the highest value was in Yuzhong District, but the coordination degree decreased. The lowest value was in Wuxi District, which mainly had moderate imbalance, primary imbalances, and essential coordination. There were five types, moderate coordination and high coordination, accounting for 23.68%, 52.63%, 7.89%, 13.16%, and 2.63%, respectively. Compared with 2000, the proportion of moderate dysregulation stage decreased significantly and began There is a moderate coordination phase, with most areas in the primary disorder stage; In 2020, the coupling coordination degree was between [0.26, 0.86]; the highest value was in Yuzhong District, and the lowest value was in Youyang County, among which there were mainly moderate imbalance, primary imbalance, essential coordination, moderate coordination, There are six types of good coordination and high coordination, accounting for 23.68%, 57.89%, 10.53%, 2.63%, 2.63%, and 2.63%, respectively. Compared with 2010, geographical differentiation was further intensified, and the scope of primary imbalance expanded. For example, the longevity zone regressed from the prior coordination stage to the primary disorder stage, and the proportion of good coordination increased. The evolution curve of coupling coordination also shows that the level of "production-living" function coordination has a downward trend. In general, the "production-living" function shows the difference between high coupling and low coordination; with the continuous improvement of urbanization and economic development levels, living conditions have been improved, and living standards have been further improved. The two complement each other and restrict each other. It is consistent with the conclusions obtained from the above production characteristics and ecological niche widths. The development speed between the two is not matched, and the living function needs to be stronger than the production function.
• "Production-ecological" function From 2000 to 2020, the average coupling degree of the "production-ecological" function in Chongqing increased from 0.81 to 0.83, which was in the period of coordinated coupling. High-value areas are mainly concentrated in the main urban area and the northeast Yu region, such as Dianjiang County, Liangping County, and Zhong County. The overall number included three types: primary coupling, moderate coupling, and coordinated coupling, and the regional proportions varied from 0% to 2.63%, respectively −2.63%, 44.74-36.84-36.84%, 55.26-60.53-60.53%. 2010-2020, through environmental remediation, pay attention to ecological function restoration, the transformation of production methods, strict management of production pollutants, and encourage the development of green production methods so that the production the coupling degree of "ecological" function has been significantly improved.
The coupling coordination degree of the "production-ecological" function shows the development characteristics of "high in the east and low in the west" and from primary imbalance to medium coordination. The average level of coupling coordination increased from 0.43 to 0.44, and the high-value areas were mainly distributed in SE and NE. Specifically, in 2000, the coupling coordination degree was between [0.38, 0.64]; the highest value was Yuzhong District, and the lowest value was Beibei District, among which there were mainly primary imbalance, essential coordination, and moderate. The three types, accounting for 18.42%, 78.95% and 2.63% respectively, are mainly in the primary coordination stage. In 2010, the coupling coordination degree was between [0.38, 0.61]; the highest value was in Yuzhong District, but the coordination degree decreased, and the lowest value was in Tongnan District, among which there were mainly primary imbalances, essential and moderate coordination and good coordination of four types, accounting for 7.89%, 84.21%, 5.26%, and 2.63%, respectively. Spatial synergy has been further enhanced compared to 2000. In 2020, the coupling coordination degree was between [0.35, 0.59]; the highest value was in Yuzhong District, and the lowest value was in Dazu Region, among which there were mainly primary imbalance, essential coordination and medium. There were three types of degree coordination, accounting for 13.16%, 78.95%, and 7.89%, respectively. The phenomenon of geographical differentiation intensified, and the synergy between SE and NE was enhanced. Some areas of the main urban area show low-value synergy and scattered distribution, and the overall "production-ecological" function shows the characteristics of alternating changes and small fluctuations.
• "Living-ecological" function From 2000 to 2020, the average functional coupling degree of the "living-ecological" in Chongqing increased from 0.69 to 0.84, gradually entering the period of coordinated coupling from the running-in period. Although there are fluctuations in local areas, such as Qianjiang, which has experienced the "running-in-coordinated coupling-running-in" process, it generally shows prominent growth characteristics. Among them are three types: primary coupling, moderate coupling, and coordinated coupling, and the regional proportion changes are 18.42-0-2.63%, 52.63-34.21-36.84%, 28.95-65.79-60.53%. With the development of the economy, people pay more and more attention to the impact of the ecological environment on the quality of living and then adopt measures such as comprehensive ecological improvement and the construction of a green and livable environment to promote harmonious coexistence between man and nature. However, in recent years, due to the construction of a livable environment, excessive emphasis on construction and neglect of management has weakened ecological functions and low-level development. Therefore, the coupling degree of the "living-ecological" function has a downward trend.
The functional coupling coordination degree of the "living-ecological" shows the overall development characteristics of "high in the east and low in the west" and from moderate imbalance to well-coordinated development. The average level of coupling coordination increased from 0.38 to 0.46. Compared with "production-living" and "production-Ecological" functions, the level of coupling coordination increased significantly, and the level of coordinated development of different regions in different years differed. In 2000, the coupling coordination degree was between [0.28, 0.66]. The highest value was in Yuzhong District, and the lowest was in Tongnan District, among which there were mainly moderate imbalances, primary imbalance, essential coordination, and sound. There were four types of coordination, accounting for 5.26%, 73.68%, 18.42%, and 2.63%, respectively. Mainly in the primary co-offset phase; In 2010, the coupling coordination degree was between [0.36, 0.61]; the highest value was Yuzhong District, but the coordination degree decreased, and the lowest value was Tongnan District, among which there were mainly primary imbalances, essential coordination and moderate coordination and good coordination of four types, accounting for 7.89%, 63.16%, 26.32%, and 2.63%, respectively. Compared with 2000, more than half of the regions have entered the primary coordination stage, and the spatial synergy relationship has been further enhanced; In 2020, the coupling coordination degree was between [0.34, 0.63]; the highest value was Yuzhong District, and the lowest value was Dazu Region, among which there were mainly primary imbalance, essential coordination and moderate There were four types of coordination and sound coordination, accounting for 15.79%, 63.16%, 18.42% and 2.63%, respectively, the phenomenon of geographical differentiation intensified, the synergy between the SE and NE increased. Some areas of the main urban area regressed to the primary disorder stage and showed the characteristics of agglomeration distribution; the evolution trend of the "living-ecological" and "production-ecological" functions are similar, showing the characteristics of alternating and fluctuating development.

Synergy Trade-Off Analysis of PLEFs in Chongqing City and County
To deeply explore the trade-off synergy between production, living, and ecological functions in Chongqing, 38 counties were used as the essential units to study the PLEFs of counties in 2000, 2010, and 2020. The matrix distribution of PS, LS, and ES values can better express the spatial interaction relationship between the two functions adjacent to the region and the spatiotemporal evolution characteristics (Figure 9).

The Degree of Trade-Off Synergy of PLEFs of the County
As shown in Figure 9, from 2000 to 2010, 20 counties in Chongqing weighed off the synergy between "living and production," accounting for 52.63%. Among them, Jiangbei District has the strongest trade-off (−17.71). 18 counties showed synergistic relationships, accounting for 47.36%. The Dadukou District has the highest degree of synergy (6.96). For the "living-ecological" functional trade-off synergy, 18 counties showed a trade-off relationship, accounting for 47.36%. Among them, Jiangbei District still has the most robust trade-off relationship (−17.71); 20 counties showed synergistic relationships, accounting for 52.63%. Among them, Yubei District has the highest synergy (54.11). For the "productionecological" functional trade-off synergy, 24 counties showed the trade-off relationship, accounting for 63.15%. Among them, Yuzhong District had the strongest trade-off (−14.01); 14 counties showed synergistic relationships, accounting for 36.84%. Among them, Yubei District still has the highest synergy (48.91).
Between 2010 and 2020, 18 counties in Chongqing were regarded as the "livingproduction" functional trade-off synergy. The proportion was 47 In the first ten years, among the 38 counties in Chongqing, the trade-off between "living-production" and "living-ecological" functions in Jiangbei District was the strongest, and the coordination level of "living-ecological" and "production-ecological" functions in Yubei District was the highest. The "living-production" function in Dadukou District has the highest degree of synergy, and the trade-off relationship between the "productionecological" function in Yuzhong District is the strongest. In the following decade, the counties with the strongest trade-off between the "living-production" function, "livingecological" function, and "production-ecological" function were Qijiang District, Zhongxian County, and Wanzhou District. Wulong District has the highest degree of "livingproduction" function and "production-ecological" function synergy, and Jiangjin District has the highest degree of "living-ecological" function. On the whole, in the past 20 years, the "living-production" function in Chongqing has changed from a trade-off to a collaborative development relationship, the "living-ecological" function is generally based on the collaborative development relationship, and the trade-off constraint relationship dominates the "production-ecological" function. Moreover, the coordinated development level of "living-production," "living-ecological," and "production-ecological" functions in the central urban area has been dramatically improved. In contrast, the counties in SE and NE have gradually shown different degrees of trade-offs.

Contributions and Deficiencies
Based on the connotation and characteristics of PLEFs, this paper constructs the index system of PLEFs from various aspects, such as agricultural production, economic development, livelihood security, social services, ecological pressure, and ecological carrying capacity. Our research enriches the theoretical framework for optimal county land development and spatial patterns in China. Based on the connotation and characteristics of PLEFs, this paper constructs the index system of PLEFs from various aspects, such as agricultural production, economic development, livelihood security, social services, ecological pressure, and ecological carrying capacity. Previous studies have only emphasized the relationship between PLEFs, focusing on the impact of space function on land space utilization. However, the degree of synergy and balance between PLEFs needs to be discussed in depth [75]. Therefore, this paper focuses more on the discussion of the impact between functions, provides a new method for coordinating the relationship between human activity intensity in counties from the perspective of PLEFs [45,76,77], and provides a scientific basis for optimizing and adjusting the relationship between PLEFs according to local conditions.
(1) By introducing the ecological niche situation theory [78], the interrelationship between PLEFs was explored based on the microscale of the county [79]. Previous studies have explored PELFs from a single perspective, such as rural, regional, or urban ecological functions [80,81]. However, the territorial space of a given region involves both urban and rural areas. Therefore, this paper reveals the temporal and spatial evolution law from the entire county and combines GIS spatial analysis and correlation analysis to help explore the functional synergy/balance relationship of "production-living-ecological" from the spatial and quantitative levels, clarify the interaction of PLEFs, and provide a new perspective.
(2) As with many research results, the correlation between PLEFs in typical regions is measured. The dynamic changes and spatial differentiation patterns of the relationship between PLEFs in the study area are systematically studied. However, in this paper, the moderating effect model is further used to identify the driving role of several basic urbanization factors on the evolution of the relationship between PLEFs [82]. Adopting the composition of the interaction technology between different functions in PLEFs can help identify environmental factors that impact the spatial pattern of land development.
(3) In this paper, an evaluation model suitable for the functional niche width of "production-living-ecological" in the county was constructed; when measuring the width of a single ecological niche, each subsystem in the PLEFs is regarded as an independent unit, which effectively avoids interference and reveals the trade-off synergy between PLEFs in the county. The paper highlights the trade-offs and synergies between the PLEFs and supports assessing the spatial pattern of land development. Once again, the trade-offs and synergies between PLEFs are demonstrated, and the results are consistent with the current study [83]. This new technical framework can help provide theoretical guidance for regional sustainable development.
However, it should be pointed out that the research methods and research ideas of this paper still need to be improved: (1) Due to the inconsistency of the statistical caliber of each county in the study area, coupled with the dilemma of data acquisition and limited technology, the data sources of some indicators have been replaced. Although explained in the text, there may also be the problem that the evaluation of PLEFs is not accurate enough, the research scale needs to be further refined, and measures and precise measures are implemented according to local conditions to make a systematic and overall evaluation of the coordinated development level of PLEFs. (2) Dynamic changes with time accompany the functional relationship of "productionliving-ecological" in the county. The selected indicators in this paper mainly focus on the current and past periods and the future-oriented indicators. The complex relationship between them also needs to be further explored, so the continuity and dynamic transformation characteristics of the trade-off synergy of long-time series analysis must be further studied. (3) Many biological processes and physical and chemical mechanisms in the PLES in the county. In the future, it is necessary to strengthen the exploration and analysis of biological, physical, and chemical processes and pay more attention to the interpretation of biological, physical, and chemical processes to clarify the driving mechanism of PLEFs better to improve the resilience and stability of the ecosystem and promote sustainable development under the effective synergy of PLEFs.

Policies and Recommendations
Based on the above analysis and demonstration, combined with the spatiotemporal pattern and evolution characteristics of PLEFs in Chongqing and the degree of coordination between functions, corresponding optimization strategies are proposed according to the economic level, human settlement environment, ecological pattern, and other conditions.
(1) For the main urban metropolitan areas with "production living" functional advantages, each district should take economic development as the premise, ecological protection as the foundation, and improving the quality of life as the goal, strengthen economic ties, coordinate the development, avoid low-level, repetitive construction of homogeneous and disorderly competition, and radiate and drive the economic development of the NE and SE. For the NE and SE, which has the functional advantages of "production ecology" and "living ecology," the NE and SE regions should utilize the advantages of the natural environment and landscape resources, encourage the development of a "low-carbon economy," complement and compete with the advantages of the main urban areas, and form a sizeable industrial pattern of differentiated and coordinated development, and explore the integrated development path of PLEFs. (2) Overall, the development trend of PLEFs coupling coordination in Chongqing presents a benign trend. The "production-living" function is mainly low-level imbalance, so it is more feasible to improve the coordination of PLEFs. When formulating policy measures, we should focus on improving the people's living standards and strengthening infrastructure construction to improve the green living index. The main urban area should improve the livability of living space, promote the progress of new energy technology, upgrade and transform industrial industries, and promote supply-side structural reform. Use benign and green industrial development to meet people's growing needs for a better living. In terms of "production-ecological" and "livingecological" functions, it is necessary to strengthen further the concept of "green water and green mountains are golden mountains and silver mountains," change the traditional industrial development model, adjust and optimize the economic structure, vigorously develop the ecological economy and circular economy, and continuously promote the normalization and institutionalization of ecological governance, to promote Chongqing's road of "ecological priority and green development."

Conclusions
Exploring the trade-off synergy between the three leading functions of production, living, and ecology in the county is the critical link to realizing the optimization and integration of PLES, rationalizing the order of spatial development, coordinating urbanrural relations, improving regional competitiveness, and promoting rural revitalization. This article combines the research methods of ecological niche situation theory, PLEF spatial theory, coupling coordination model, and trade-off synergy to quantitatively measure PLEFs and the coupling coordination degree between the three eight counties in Chongqing, and analyze the evolution characteristics of their spatiotemporal patterns. The following conclusions were reached: (1) Significant diversity exists in Chongqing's spatiotemporal differentiation characteristics of PLEFs. During the study period, the overall growth trend of production niche width, the high-value area was mainly located in the UC, and the downward trend in