2.1.1 Undesired output super-SBM model.

Since the traditional DEA model cannot address bias and impact due to radial and angular selection, The Super-SBM model is a powerful solution to this problem [34]. When the efficiency value of multiple decision units is 1, traditional DEA models cannot compare and rank these relatively efficient decision units; thus, further optimization obtains the Super-SBM model. The specific model is as follows: (1) Where ρ is the efficiency value, and m, q₁ and q₂ are the number of indicators for input, desired output and undesired output, respectively. x_k, y_k and b_k denote input variables, desired output variables and undesired output variables of the evaluated decision unit, respectively, and x_ik, y_rk and y_tk are elements of the input and output vectors. X, Y and b are input–output matrices; and denote the input, desired output and undesired output slack variables, respectively, and λ is the column vector.

2.1.2 Modified gravity model.

Interregional economic relations have a law similar to that of gravity; that is, the strength of interregional relations is directly proportional to the "quality" of the region and inversely proportional to the "distance" between regions [40]. This research explores the relation of tourism eco-efficiency among 30 provinces in China, so the "quality" of the region is regional tourism eco-efficiency. The research uses a modified gravity model to develop a tourism eco-efficiency correlation matrix among China’s provinces. The specific model is as follows: (2) where F_ij is the intensity of the tourism eco-efficiency linkage of each province in China, and K_ij is the gravitational coefficient. E_i and E_j indicate the tourism eco-efficiency of province i and province j, respectively. D_ij represents the "economic distance" between province i and province j. d_ij is the spherical distance between province i and province j. g_i and g_j denote the GDP of province i and province j, respectively. The spatial correlation matrix of China’s provincial tourism eco-efficiency is constructed from the gravity model, and the mean values of the data in each row of the matrix are binarized as threshold values and then converted into a binary matrix. If F is greater than the threshold, then the value is 1, indicating that there is a spatial correlation between the row and the tourism eco-efficiency of the column province; conversely, the value of 0 indicates that there is no spatial correlation between the row and the tourism eco-efficiency of the column province.

2.1.3 Social network analysis.

SNA is a sociological approach from a structural perspective, the core of which is to study structural issues from a "relational" perspective. In this research, network density, network connectedness, network hierarchy and network efficiency are selected to analyze the overall network structure of tourism eco-efficiency characteristics in China’s provinces. In the individual network, degree centrality, closeness centrality and betweenness centrality are selected to quantify the centrality of each province as a reflection of the province’s rights in the tourism eco-efficiency network. The "core-periphery" model reflects the position of a province in the network structure. Furthermore, QAP correlation analysis and regression analysis are used to identify the key factors affecting the spatial correlation strength of tourism eco-efficiency in China’s provinces. The analysis is based on the permutation of matrix data, and the estimation process is roughly divided into 3 steps. First, a conventional multiple regression analysis (correlation analysis) is performed on the corresponding long vector elements of the matrix to obtain the actual parameter estimates. Second, the rows and columns of the matrix are randomly permuted and re-estimated, keeping all estimated coefficients. Finally, the permutation step is repeated enough times to calculate the proportion of random permutations that are greater than or equal to the actual parameter estimates among the total number of random permutations. Thus, the standard error of the statistic is estimated, and the significance test is completed [38, 49]. The theoretical formula of this study is as follows: (3) where G is the tourism eco-efficiency spatial network matrix, EDL is the matrix of the economic development level, TIS is the tourism industry structure, TRE is the tourism resource endowment, IDL is the information development level, and TTL is the tourism technology level.

2.1.4 "Bottom-up" model of tourism carbon emissions and tourism energy consumption.

At present, no systematic approach has been developed globally for estimating energy consumption and CO₂ emissions from tourism [7]. In existing studies, "top-down" [50] or "bottom-up" [14] approaches are often used. The "top-down" approach, which directly estimates the share of tourism energy consumption (tourism carbon emissions) in a system, requires energy consumption statistics or carbon dioxide emission monitoring data at the national/regional level. However, China has not yet established a national and regional statistical monitoring system for greenhouse gas emissions, so they are difficult to estimate in this way. The "bottom-up" approach is based on estimating energy consumption (carbon emissions) in each sector of the tourism industry and then summing them. In this research, we use the "bottom-up" method to estimate the tourism energy consumption and tourism carbon emission intensity of 30 provinces (cities and districts) in China based on the estimation method of tourism energy consumption (tourism carbon emissions) [50–52]. It should be noted that tourism energy consumption (tourism carbon emissions) comes from numerous sectors (food, accommodation, travel, activities, shopping and entertainment), but its transportation, accommodation and principal activities constitute the leading sources of energy consumption, so this study will account for the energy consumption and carbon emissions of the above three modules and sum them [16]. The specific model is as follows: (4) where C_{transportation} is tourism traffic energy consumption (carbon emissions); Q_i is the passenger turnover of railroad, road and water transport; and w_i indicates the proportion of tourists among passengers. Referring to the research results [9, 51, 53], the proportions of tourists among railroad, road and water transport are taken as 31.6%, 13.8% and 10.6%, respectively. α_i is the energy consumption coefficient (carbon emission factor) of railroad, road and water transportation, taking the values of 1, 1.8 and 1.48 MJ/(person-km), respectively. C_{accommodation} is tourism accommodation-related energy consumption (carbon emissions), in which q is the number of beds, s is the room occupancy rate, T is the number of days in a year (365 d is selected for this research), and β indicates the accommodation energy consumption coefficient (carbon emission coefficient); the tourism accommodation energy consumption coefficient is 155 MJ/(person-night), and the carbon emission factor is 245.8 g/(person-night). C_activity is tourism activity energy consumption (carbon emission), P_k represents various types of tourism activity person-times, and γ_k represents the activity energy consumption coefficient (carbon emission coefficient). Referring to the research results [51, 53] the energy consumption coefficients of sightseeing, leisure and vacation activities, visiting family and friends, business meetings and other types of tourism activities are 8.5, 26.5, 12, 16 and 3.5 MJ/person, respectively, and the carbon emission factors are classified as 417, 1670, 591, 786 and 172 g/person, respectively.

2.2.1 Indicator system.

The core concept of eco-efficiency is the "minimum environmental impact, to produce the maximum economic output". The framework of the undesired output SBM model, in addition to concern for economic output, also includes undesired output indicators, such as environmental pollution. In terms of input indicators, current studies revolve mainly around the basic factors of capital, labor, and land. To this foundation, some scholars have added energy input and water consumption indicators. This study draws on the existing research results [14, 53] to consider the size of the tourism workforce as a labor input. It should be noted that, in view of the change in the caliber of statistics on the tourism workforce and the characteristics of the tourism industry, the population employed in the tertiary sector is treated as the tourism workforce. The number of travel agencies, the number of scenic spots classified as 3A level and above, and the number of 3-star and above accommodations are defined as capital investment. In addition, drawing on the research results [50, 51] tourism energy consumption is used in this study as an input indicator. The "bottom-up" energy accounting method is used to account for tourism energy consumption in tourism transportation, accommodation and activities. In the desired output, the study chooses total tourism revenue and total tourism visitors as the consensual output. In the case of undesired outputs, tourism carbon emissions are a core indicator of the environmental impact of tourism, accounted for using the "bottom-up" approach (Table 1).

Download:

• PNG
  larger image
• TIFF
  original image

Table 1. Evaluation index system of provincial tourism ecological efficiency in China.

https://doi.org/10.1371/journal.pone.0272667.t001

2.2.2 Data source.

The tourism input and output panel data of China’s 30 provinces and regions (excluding Hong Kong, Macau, Taiwan and Tibet) from 2010 to 2019 are selected as the dataset for this research. Tourism workforce is from the China Statistical Yearbook. Total tourism revenue, the total number of tourists, the number of 3-star and above accommodations, the number of travel agencies and the number of 3A and above scenic spots are drawn mainly from the China Tourism Statistical Yearbook and the statistical yearbooks and statistical bulletins of each province (city and district). Both tourism energy consumption and tourism carbon emissions are calculated by the 2.1.4 "bottom-up" model of tourism carbon emissions and tourism energy consumption. To eliminate the effect of price fluctuations, all the above value indicators are deflated based on the Consumer Price Index (CPI) of the previous year, using 2010 as the base period. Some of the absent data are supplemented by linear interpolation for completeness. Referring to the existing research [54], the capital cities of the two provinces are taken as the centroids of the provinces, and the distance between the centroids is the distance between the two provinces. The center-of-mass distance is calculated by the "point distance" of ArcGIS 10.8 Proximity.

3.2.1 Overall network characteristics analysis.

1. Spatial linkage intensity: network density. As shown in Fig 5 (left), the trends of network density and correlations of provincial tourism eco-efficiency in China remained consistent from 2010 to 2019, essentially showing an N-shaped trend, that is, “increasing, then decreasing and then increasing”. Overall, network density increased from 0.155 in 2010 to 0.174 in 2019, and the number of network correlations increased from 135 in 2010 to 151 in 2019. This result indicates that the overall spatial correlations among provinces have been further strengthened, but the degree of correlation remains low. This relationship might be caused by the national tourism policy, which more closely links China’s tourism eco-efficiency among provinces. However, the new period of tourism industry development focuses on both speed and quality, and there is a downward trend as provinces and municipalities focus more on internal tourism collaboration and reorganization when restructuring their tourism industry.
   

   Download:

   • PNG
     larger image
   • TIFF
     original image

   Fig 5. The overall network characteristics of China’s provincial tourism eco-efficiency.

   https://doi.org/10.1371/journal.pone.0272667.g005

2. Spatial network relevance: connectedness, hierarchy and efficiency. As shown in Fig 5 (right), network connectedness remained at 1 during the research period, indicating that the overall network structure has good connectivity, accessibility and robustness. The network hierarchy was on the low side, fluctuating between 0.129–0.191. This result indicates that there is still a “hierarchical” spatial network structure in China’s provincial tourism eco-efficiency. Network efficiency decreased from 0.871 in 2010 to 0.842 in 2019, which indicates multiple overlapping spillover channels among network nodes, continuous strengthening of interprovincial spatial association, and gradual improvement of network stability.

3.2.2 Individual network characteristics analysis.

1. Core node roles: degree centrality. This result indicates the number of points connected to a province in the overall network and characterizes its "rights". The indegree variable indicates the aggregation and polarization effects of provinces on other elements in the overall network. The outdegree indicates the radiation and spillover effects of provinces on elements in other provinces in the overall network. During 2010–2019, the degree of centrality of the provinces changed considerably, and the regional tourism eco-efficiency strongly broke the “east high and west low” nonequilibrium pattern. In 2010, Chongqing city in western China and Guangdong Province in eastern China played important roles in China’s provincial tourism eco-efficiency spatial network, while in 2019, the eastern provinces of Jiangsu, Shandong and Guangdong were far ahead in terms of degree centrality. In terms of indegree and outdegree, Jiangsu, Shandong and Guangdong provinces were in the leading positions in 2010 and 2019. Their location in China’s coastal region offers obvious advantages in tourism resources, comprehensive tourism transportation facilities and high circulation of factors. A better tourism economy has a siphoning effect in these regions and will continue to be an important part of the country’s spatial network of provincial tourism eco-efficiency. Correspondingly, the outdegrees of all provinces were greater than 0 in 2010 and 2019, indicating a spatial radiation effect of tourism eco-efficiency in each province.
2. Network node function: closeness centrality. It characterizes the "distance" between a province and other provinces in the network. As shown in Table 3, the closeness centrality in 2010 and 2019 was mainly concentrated in [38, 39]. Their distribution was relatively balanced. In both 2010 and 2019, Jiangsu Province had the highest level of closeness centrality, standing out as the core of the overall network. Diversified tourism products and multiple tourism lines have vertically deepened the breadth and depth of tourism efficiency radiation, indicating that Jiangsu Province tourism resources are endowed with high tourism economic benefits. The interaction and complementarity of tourism development, coupled with its superior location advantage, makes this province an important "bridge" for interregional tourism exchanges and cooperation.
   

   Download:

   • PNG
     larger image
   • TIFF
     original image

   Table 3. Centrality characteristics of spatial correlation network of tourism eco-efficiency of China in 2010 and 2019.

   https://doi.org/10.1371/journal.pone.0272667.t003

3. Bridging node function: Betweenness centrality. Most provinces showed a relatively balanced distribution of betweenness centrality, with some small differences. Nevertheless, a few provinces have experienced extreme situations. In 2010 and 2019, the betweenness centrality in the eastern provinces of Jiangsu, Shandong and Guangdong was significantly higher than that in other provinces, and the sum of these three provinces’ betweenness centrality accounted for 70.968% and 67.133% of China’s betweenness centrality, respectively. These three provinces play a powerful role as a bridge and intermediary in the process of the flow and transmission of tourism ecological elements and tourism resources, and the other provinces rely heavily on them. In 2010 and 2019, betweenness remained at 0 for Hainan Province, indicating that there is less communication between it and the other provinces and poor factor circulation.

3.2.3 Core and periphery structure evolution analysis.

The density matrix showed an overall convergence between the network density matrix within the core and periphery areas, with the network density within the core area decreasing from 0.442 to 0.367 and the network density within the periphery area decreasing from 0.063 to 0.033 (Table 4). The network density matrix of the core-to-periphery area and periphery area-to-core area generally showed a dispersion trend. The network density of the core-to-periphery area rose from 0.109 to 0.223, while the network density of the periphery-to-core area rose from 0.131 to 0.223. Furthermore, the core-periphery distribution and evolutionary trends showed that a clustering distribution of core-periphery areas of China’s provincial tourism eco-efficiency. As shown in Fig 6, in 2010, the core area was mainly located east of the Hu Line and included 13 provincial-level administrative units in Beijing city, Tianjin city, Hebei Province, Zhejiang Province, Guangdong Province, Jiangsu Province and Shandong Province in eastern China; Shanxi Province, Anhui Province, Jiangxi Province, Henan Province and Hubei Province provinces in central China; and Guizhou Province in western China. In 2019, the core area was displaced to some extent, and aggregation weakened. Based on the original data, Hubei Province and Tianjin City withdrew from the core camp, while Fujian Province, Gansu Province, Heilongjiang Province, Hunan Province and Sichuan Province joined it. In terms of the number of provincial administrative units occupied by the core fringe, in 2010, there were 13 provincial and urban areas in the core, while in 2019, this figure rose to 16, and overall spatial connectivity increased.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 6. The “core-periphery” structure of China’s provincial tourism eco-efficiency in 2010 and 2019.

(This map is based on the standard map with review number GS(2019)1697 downloaded from the Ministry of Natural Resources Standard Map Service website (http://bzdt.ch.mnr.gov.cn), and the base map has not been modified).

https://doi.org/10.1371/journal.pone.0272667.g006

Download:

• PNG
  larger image
• TIFF
  original image

Table 4. The core-periphery density matrix of China’s provincial tourism eco-efficiency in 2010 and 2019.

https://doi.org/10.1371/journal.pone.0272667.t004

3.3.1 Factors influencing the provincial tourism eco-efficiency network structure.

The sustained optimization of the spatial pattern of tourism eco-efficiency is a combination of multiple factors. The level of economic development directly affects interprovincial cooperation in tourism project investment and tourism infrastructure cobuilding concerning the growth of the tourism eco-efficient network structure, using GDP per capita to represent the regional economic development level [56]. The tourism industry structure objectively reflects the attention of local governments to tourism, and a reasonable tourism industry structure is the key to the ecological tourism economy [57]. The research selected the ratio of total regional tourism revenue to regional GDP to characterize the tourism industry structure [57]. Tourism resources drive the flow of tourism factors, affecting the flow and allocation of tourism input factors between provinces; thus, the choice of different levels of scenic spots was based on weighted representation. The level of information development is the bridge between tourism economic spatial agglomeration and radiation, expressed in terms of total postal and telecommunications services [38, 58]. The application of regional technology innovation and progress in the tourism industry improves the utilization efficiency of tourism energy resources and strengthens the energy-saving and emission-reduction abilities of tourism enterprises [38]. The flow and disposition of technology and personnel promotes regional tourism ecological efficiency, and the energy consumption per unit of tourism income is used to express the level of tourism technology [56].

In this study, we chose 2019 as a representative year in the study period, the intensity of the spatial association of tourism eco-efficiency of provinces as the explanatory variable, and the matrix of economic development level (EDL), tourism industry structure (TIS), tourism resource endowment (TRE), information development level (IDL), and tourism technology level (TTL) as explanatory variables. To avoid the interference of magnitude differences on the data fit, individual data were normalized before the formal data analysis.

3.3.2 Results of QAP correlation analysis and regression analysis of provincial tourism eco-efficiency network structure.

The constructed model was used to perform QAP regression analysis on the spatial network of tourism eco-efficiency and the matrix of influencing variables in China’s provincial areas, with the number of permutations set to 2000. As shown in Table 5, the results showed that the adjusted R² = 0.229 and passed the 1% significance level test, indicating that the variation in the selected indicators could explain 22.9% of the spatial correlation of tourism eco-efficiency in China’s provinces. Previous research has shown that QAP models based on the same data generally had lower coefficients of certainty than ordinary least square(OLS) models, and the values of R² in studies based on QAP methods ranged mostly between 12.5% to 40.3%. The R² data of the research were moderate, and the fit of the indicators was good, so it has good explanatory power [59, 60].

Download:

• PNG
  larger image
• TIFF
  original image

Table 5. QAP correlation analysis and regression analysis results.

https://doi.org/10.1371/journal.pone.0272667.t005

The results of the QAP regression analysis were essentially consistent with the correlation analysis, but some of the variables failed the significance test, which is also similar to existing studies [50]. Among all variables that passed the significance level, EDL, IDL and TTL proved to be significant contributors to the development of the spatial network structure of tourism eco-efficiency in China’s provinces. The provincial areas with higher levels of economic development are both destinations and sources of tourists. Tourism flows connect the two regions, allowing tourism components to flow into each other. This flow, coupled with the investment and construction of tourism infrastructure facilities, leads to the spillover of economic resources, thereby strengthening the link between the two regions. The tourism technology level is directly related to its provincial tourism eco-efficient spatial structure development. Technology determines the ecological civilization era of the track; enhances tourists’ sense of participation, experience and access; reduces the pressure of tourism on the environment; and enhances communication and exchange between tourist places. In the era of intelligent tourism, the tourism information level is conducive to the diversion of different tourist destinations, promoting the spatial replacement of passenger flows among provincial and urban areas and thus improving the level of tourism efficiency and spatial network correlation.

It should be noted that TIS and TRE did not pass the 5% significance test. The tourism industry structure laterally reflects the importance that local governments attach to the tourism industry, whereas the disparate tourism industry status does not facilitate cooperation between developed and backward tourism regions, preventing the development of a spatial network structure of tourism eco-efficiency in China’s provinces. Tourism resources, as the native attraction of tourists, largely determine the level of development of tourist destinations, yet the lack of scientific planning and long-term calculation of tourism resources has led to a low level of attractiveness for tourism resources. Furthermore, tourism resource development project planning ideas and planning principles are common, and development ideas and concepts are similar, resulting in excessive homogenization of tourism, which is not conducive to interregional tourism cooperation and exchange.