Spatial Correlation of Agricultural New Productive Forces and Strong Agricultural Province in Anhui Province of China

Abstract

Developing agricultural new productive forces (ANPF) according to local conditions is a key strategy for agricultural modernization. Using panel data from 16 prefecture-level cities in Anhui Province from 2010 to 2022, this study constructed indicator systems for ANPF and the construction of a strong agricultural province (CSAP). The entropy-weight TOPSIS method was used to calculate the levels of ANPF and the SAP index. This study employed a modified gravity model and social network analysis (SNA) to investigate the spatial correlation and evolutionary characteristics of these networks. Geographical detectors were also used to identify the driving factors behind agricultural transformation. The findings indicate that both ANPF and CSAP showed an upward trend during the study period, with significant regional heterogeneity, with Central Anhui being the most prominent. This study revealed spatial spillover effects and strong network correlations between ANPF and CSAP, with the spatial network structure exhibiting characteristics of multi-core, multi-association, and multidimensional connections. The entities within the network are tightly connected, with no “isolated island” phenomenon, and Hefei, as the central hub, showed the highest number of connections. Laborer quality, tangible means of production, and new-quality industries emerged as the core driving forces, working in synergy to propel CSAP. This study contributes new insights into the spatial network dynamics of agricultural development and offers actionable recommendations for policymakers to enhance agricultural modernization globally.

1. Introduction

Does the spatial spillover of ANPF drive CSAP? This question lies at the core of understanding how technological innovation, digital integration, and labor modernization—key components of ANPF—shape regional agricultural development. As highlighted by the 20th Central Committee of the Communist Party of China, cultivating locale-specific new productive forces is essential for achieving high-quality development [1,2]. Yet, the spatial dynamics through which ANPF enhances agricultural competitiveness and supports provincial-level agricultural strength remain underexplored.

Internationally, spatial spillovers from agricultural innovation—particularly green and digital technologies—have been shown to significantly enhance agricultural productivity across regions. For instance, spatial-Durbin econometric analysis across Chinese provinces demonstrated that agricultural science-and-technology innovation not only boosts green agriculture locally but also spills over into adjacent provinces [3,4]. Similarly, the spread of digital rural infrastructure exerts measurable spatial effects on agricultural circular-economy growth, with mechanisms such as peer imitation and technology diffusion driving regional development [5]. Moreover, broader analyses confirm that digital-economy development enhances high-quality agricultural development through spatial linkages, reinforcing the role of technology as a catalyst for provincial transformation [6].

This paper focuses on Anhui Province, a key agricultural region in China, which has made significant strides in its agricultural modernization. The province’s push for digital agriculture, including initiatives like “Digital Anhui Agriculture” and smart farming, aims to integrate new technologies into rural areas, thus increasing agricultural productivity and modernizing farming practices [7,8]. These trends resonate with ongoing global efforts to digitize agriculture. Internationally, Anhui’s experience offers valuable insights for other regions undergoing agricultural transformation. Countries in Southeast Asia, sub-Saharan Africa, and parts of Latin America—regions with transitioning agricultural economies—can draw lessons from China’s approach. However, these regions often face unique challenges, such as limited access to technological innovation and infrastructure, requiring tailored strategies similar to those implemented in Anhui. In Anhui, the transition from traditional agriculture to a modern, technology-driven model is essential for achieving both provincial and national agricultural goals. The key to this transformation lies in leveraging technological innovations to modernize labor forces, upgrade production methods, and promote digital agriculture [9,10,11,12,13].

Compared to traditional forms of production, ANPF represent a cutting-edge synergy of innovation and quality. The “new” involves the integration of modern technologies, new operational models, and enhanced equipment into agricultural systems, while “quality” refers to optimizing agricultural inputs—such as labor, materials, and machinery—to create more sustainable and efficient agricultural practices [14]. The shift from “old” to “new” productive forces, as demonstrated in Anhui, can serve as a valuable model for other agricultural regions aiming to modernize and improve productivity [15].

From the perspective of the basic elements of productivity, new laborers are the prerequisite, new labor objects are fundamental, and new labor materials are the core elements [16]. Therefore, the focus of ANPF is to achieve the digitalization and intelligence of agricultural production and operations to improve the productivity of all elements, such as labor, knowledge, technology, management, data, and capital [17,18]. In the construction of the evaluation indicator system, the focus is primarily on the three core elements: agricultural laborers, agricultural labor materials, and agricultural labor objects [2,13,19]. On this basis, indicators such as agricultural technological productivity, agricultural green productivity, and agricultural digital productivity are introduced [20,21,22].

To accelerate the development of new productive forces in agriculture, some scholars focus on rural infrastructure, rural industries, and rural talent [23], emphasizing the integration of digital technologies with traditional agricultural production elements [24]. This empowers agricultural supply security capabilities, agricultural science and technology equipment, agricultural operating systems, agricultural industry resilience, and agricultural competitiveness [25]. However, the development of ANPF requires the establishment of new production relations adapted to it, fully utilizing the intermediary power of new productive forces [1,26], ensuring that high-quality production elements are directed towards ANPF, effectively removing practical obstacles to CSAP. In rural areas where the market mechanism has not yet fully developed, it is crucial for the government to play a forward-looking guiding role, which is a highly characteristic solution for accelerating the formation of ANPF and driving the CSAP [27].

New-quality productivity serves as the core driver and strategic pathway for building a strong agricultural nation. Its spatial configuration is anchored in “innovation highlands”, which boost agricultural industry competitiveness through technological diffusion and optimized allocation of factor inputs. The formation, diffusion, and efficacy of this productivity exhibit distinct spatial dependency, differentiation, and networked characteristics. Scientific spatial planning and efficient spatial governance thereby advance CSAP [28].

While existing research has provided a foundation for understanding ANPF, gaps remain in the literature. Many studies primarily focus on theoretical aspects, exploring the connotations and pathways of these forces, with empirical studies being relatively sparse. Furthermore, few studies have examined the combined effects of ANPF and CSAP. Most analyses are conducted from a singular perspective, with insufficient attention paid to the interrelationships between these two areas. In addition, related studies are mostly conducted at the national level, with fewer studies focusing on individual provinces.

To address these gaps, this study adopted a multi-method empirical strategy. First, a TOPSIS-entropy weighting method was employed to construct composite indicators for both ANPF and SAP, ensuring objective evaluation of complex multidimensional data. Second, a revised gravity model and social network analysis were used to identify spatial correlation patterns among Anhui’s prefecture-level cities. Third, the geographic detector model was applied to investigate the spatial drivers and interactive influences of ANPF on SAP, quantifying both individual and synergistic effects.

In this context, the study pursued two primary objectives. First, using Anhui Province, China, as a representative case, we reconstructed the indicator systems for ANPF and SAP. The ANPF system encompasses six dimensions: labor quality, labor efficiency, tangible production inputs, intangible production inputs, emerging quality industries, and the production environment. The SAP system is similarly structured across six dimensions: agricultural supply capacity, industrial competitiveness, technological innovation, green development, rural modernization, and policy support intensity. Second, this study integrated both theoretical and empirical perspectives, employing modified gravity models, social network analysis, and geographical detector methods to build a spatial correlation network between ANPF and SAP. Through this framework, we examined the spatial interlinkages among prefecture-level cities in Anhui Province and assessed the driving influence of ANPF on SAP development.

Building on this foundation, this study aimed to identify breakthrough strategies and practical pathways for empowering the development of an SAP through new-quality productivity. It seeks to offer insights and reference points for advancing agricultural modernization in Anhui and across China, while providing policy guidance and theoretical support for the transformation of the ANPF in the new era and for the broader goal of constructing a strong agricultural nation. The research framework is illustrated in Figure 1.

The remainder of this paper is organized to reflect the logical progression of the research and to clearly delineate the application of methods and the presentation of results. Section 2 introduces the construction of the indicator systems used to measure both ANPF and SAP, including the application of the entropy-weighted TOPSIS method. Section 3 conducts the spatial correlation analysis based on the modified gravity model and social network analysis, presenting the corresponding results to reveal the spatial interaction patterns between regions. Section 4 investigates the driving factors of ANPF on CSAP using the geographical detector model, with results presented for both individual explanatory power and interaction effects. Section 5 provides an integrated discussion of the main findings, contextualizing them within existing literature and offering policy implications. Finally, Section 6 concludes the paper by summarizing the key insights and contributions of the study.

2. Measurement of Variables

The preceding analysis reveals an endogenous relationship between the development of ANPF and CSAP. New quality productivity serves as a foundational driver, enhancing production efficiency, optimizing the agricultural industrial structure, improving product quality, and increasing value-added output—each of which contributes directly to the realization of an SAP. Conversely, efforts to build an SAP generate enabling conditions for the advancement of new quality productivity, including policy incentives, institutional support, and capital investment. This reciprocal dynamic reflects a bidirectional and synergistic relationship. Accordingly, the design of indicator systems for both domains must account for their mutual interdependence.

2.1. Construction of the Indicator System

2.1.1. Indicator System for ANPF

Compared with traditional productivity, the three elements of ANPF have undergone qualitative changes, emphasizing the coordinated efforts among production factors to drive the transformation of agricultural development models [29]. Drawing on the research of Qiao et al. (2024) and Ma and Zhou (2024) [2,19], this study constructed an evaluation system based on the new labor force, new means of production, and new objects of production. The system consists of six primary indicators and twenty secondary indicators, as detailed in

Table A1. Indicator System for Measuring the Level of ANPF.

	Primary Indicators	Secondary Indicators
Agricultural New Productive Forces	Laborer Quality (X1)	Number of Full-Time University Faculty Members (M1)
		Years of Education per Capita (M2)
		Agricultural Research and Development Personnel (M3)
	Laborer Efficiency (X2)	Per Capita Agricultural Output Value (M4)
		Rural Disposable Income per Capita (M5)
	Tangible Means of Production (X3)	Agricultural Mechanization Level per Unit Area (M6)
		Rural Delivery Route Length (M7)
		Mobile Phone Ownership among Rural Residents at Year-End (M8)
		Industrial Enterprises’ New Product Sales Revenue (M9)
		Total Postal and Telecommunications Volume (M10)
	Intangible Means of Production (X4)	Number of Rural Fixed Broadband Internet Users (M11)
		Degree of Development of Rural Digital Inclusive Finance (M12)
		Agricultural Science and Technology Paper Conversion Rate (M13)
		Number of Personnel in Digital Industries (M14)
	New-Quality Industry (X5)	Number of High-Tech Agricultural Enterprises (M15)
		Rural Retail Sales of Consumer Goods (M16)
		Number of Organic Agricultural Products in the Year (M17)
	Ecological Environment (X6)	Green Coverage Rate of Built-Up Areas (M18)
		Centralized Sewage Treatment Plant Rate (M19)
		Energy-Saving and Environmental Protection Fiscal Expenditures (M20)

.

Specifically, the dimensions are defined as follows. First, laborer quality forms the bedrock of advancing new quality productive forces. Highly skilled labor exhibits stronger learning capabilities, greater innovation potential, and elevated technological literacy, enabling rapid assimilation of emerging, disruptive technologies. This facilitates efficient and high-quality agricultural production. Full-time faculty at regular higher education institutions play a dual role: as key cultivators of talent and as highly qualified members of the workforce themselves—possessing robust disciplinary foundations, creative capacity, and applied competence. As a proxy for human capital quality, this study employed three indicators: the number of full-time faculty in higher education, the average years of education per capita, and the number of personnel engaged in agricultural research and experimental development. Together, these capture both the stock and refinement of human capital contributing to agricultural innovation.

Second, laborer efficiency reflects the productive output of agricultural workers, which is expected to rise alongside improvements in worker quality. Labor productivity gains not only enhance the overall efficiency and quality of agricultural output but also translate into tangible improvements in rural livelihoods. Farmers are both agents and beneficiaries in this transformation [30]. To capture this dimension, we used per capita agricultural output value and rural disposable income per capita—two metrics that indicate the scale of individual productive contribution and income derived from it.

Third, tangible means of production constitute the material and technological underpinnings of new quality productivity. Modern agricultural production has evolved beyond rudimentary tools to encompass smart machinery, precision equipment, and digitally integrated systems [19]. In this context, the traditional notions of land and basic equipment are supplanted by more sophisticated and modern production infrastructures. To capture this shift, we considered the mechanization level per unit of agricultural land, rural logistics capacity (measured by the length of delivery routes), the sales revenue of new industrial products, and the total volume of postal and telecommunications services.

Fourth, intangible means of production—while lacking physical form—play an increasingly vital role in data-driven, digital agriculture. As agricultural operations transition towards digitization and intelligent systems, intangible assets such as information, knowledge, and digital infrastructure become indispensable. This dimension is assessed using indicators including the number of rural broadband subscribers, the development level of rural digital inclusive finance, the conversion rate of agricultural scientific publications, and the number of personnel employed in digital industries.

Fifth, new quality industry represents an emergent material foundation for future agricultural productivity. This industry embodies high standards of specialization, standardization, and scale, and it is characterized by transformative approaches to agricultural production [31]. To reflect this sectoral evolution, this study included the number of high-tech agricultural enterprises, the retail sales of rural consumer goods, and the annual count of certified organic agricultural products.

Sixth, the ecological environment is a fundamental enabler and sustaining pillar of new quality productivity. Amid increasing environmental constraints and the urgent need for climate resilience, productivity must align with green, low-carbon, and sustainable principles. Regions with high environmental quality attract talent, investment, and innovation—reinforcing virtuous cycles of development. The state plays a crucial governance role in this domain, shaping regulations, coordinating stakeholders, and providing essential public services. To represent environmental quality, we employed three indicators: the green coverage rate of built-up areas, the centralized treatment rate of sewage treatment plants, and governmental expenditure on energy conservation and environmental protection.

2.1.2. Indicator System for CSAP

In line with the connotations and characteristics of constructing an agricultural strong province, and in accordance with the policy requirements of the No. 1 Document of the Anhui Provincial Party Committee, this study, drawing on the research of Yu et al. (2024), Gao (2023), and Jiang (2023) [32,33,34], constructed an indicator system with six primary dimensions: agricultural product supply capacity, agricultural industry competitiveness, agricultural technological innovation capacity, agricultural green development capacity, rural modernization level, and agricultural policy support intensity. This system encompasses 24 secondary indicators, as detailed in

Table A2. Index System for CSAP.

	Primary Indicators	Secondary Indicators
Strong Agricultural Province	Agricultural Product supply Capacity (A1)	Per Capita Total Grain Crop Yield (N1)
		Per Capita Total Meat Production (N2)
		Per Capita Total Oil Production (N3)
		Sowing Area of Grain Crops (N4)
	Agricultural Industry Competitiveness (A2)	Land Yield Rate (N5)
		Labor Productivity (N6)
		Capital Productivity (N7)
	Agricultural Technology Innovation Capability (A3)	Grain Yield Per Unit Area (N8)
		Total Power of Agricultural Machinery (N9)
		Number of Authorized Agricultural Patent Applications (N10)
		Full Number of Agricultural R&D Personnel (N11)
		Agricultural R&D Funding (N12)
	Agricultural Green Development Capability (A4)	Pesticide Usage Per Unit Area (N13)
		Unit Area Usage of Agricultural Plastic Film (N14)
		Fertilizer Input Intensity (N15)
		Artificial Afforestation Area (N16)
	Rural Modernization Level (A5)	Per Capita Disposable Income of Rural Households (N17)
		Average Penetration Rate of Tap Water in Rural Areas (N18)
		Area of Solar Water Heater (N19)
		Number of Village Clinics (N20)
	Agricultural Policy Support Intensity (A6)	Government Agricultural Expenditure Proportion (N21)
		Tax Exemptions for High-Tech Agricultural Enterprises (N22)
		Tax Deductions for Agricultural R&D Expenditures (N23)
		Government Rural Assistance Level (N24)

.

Specifically, the dimensions are as follows. First, agricultural product supply capacity. Food security is a national priority, and ensuring the stable and safe supply of grain and key agricultural products is a bottom-line task in building an agriculturally strong nation [35]. As a major agricultural region, Anhui has consistently prioritized food security in its provincial policy directives. Recent high-level policy documents—commonly referred to in China as “No. 1 Documents”—have underscored the need for farmland protection and emphasized that safeguarding food security is a shared responsibility between state and local authorities. However, alongside safeguarding food security, attention must also be paid to the stable supply of other agricultural products, particularly oilseed crops like soybeans and livestock such as sows and pigs. Ensuring the stable supply of grain, oil, and meat is an important embodiment of an agriculturally strong province. To reflect Anhui’s agricultural supply capacity, this study adopted four indicators: per capita grain output, per capita meat output, per capita oilseed output, and grain sowing area.

Second, agricultural industry competitiveness. Strengthening the competitiveness of the agricultural sector is a fundamental objective for achieving national modernization and long-term economic resilience [36]. Improving factor productivity is a crucial aspect of enhancing industry competitiveness. Land output rate, labor productivity, and capital productivity reflect the efficiency of converting land, labor, and capital resources into wealth. Improvements in these productivity indicators contribute to the development of the agricultural industry and enhance its competitiveness. Therefore, agricultural industry competitiveness is measured using three indicators: land output rate, labor productivity, and capital productivity.

Third, agricultural technology innovation capability. Coordinating agricultural basic research, applied research, and technological innovation; strengthening the integration of science and technology with industry; and accelerating the formation of new agricultural productive forces are fundamental to ensuring the sustainable and stable development of agriculture and the long-term effective supply of agricultural products. These actions are crucial for supporting agricultural development [37]. This study selected five indicators to reflect agricultural technological innovation capacity: unit area yield of cereals, agricultural mechanization, patent application and approval rate, total R&D personnel, and R&D expenditure.

Fourth, agricultural green development capability. Building an agriculturally strong nation and province requires placing agricultural green development in a prominent position and effectively managing the relationship between resources and production [38]. The focus must shift from resource-intensive to sustainable development. Controlling carbon emissions is essential for advancing green agriculture; however, agricultural emissions primarily stem from inputs such as fertilizers, pesticides, and plastic films used in production. The 2024 No. 1 Document of the Anhui Provincial Party Committee advocates for the reduction and efficiency enhancement of fertilizers and pesticides; rational control of the use of agricultural films, pesticides, and fertilizers; and strengthening the recycling of waste agricultural films. It also encourages integrated pest management strategies, reduces dependency on pesticides and fertilizers, expands afforestation, and promotes agricultural green development. This study used four indicators to reflect agricultural green development capacity: pesticide use per unit area, agricultural plastic film use per unit area, fertilizer input intensity, and afforestation area.

Fifth, rural modernization level. Rural modernization is a distinctive feature of Chinese-style modernization and is an intrinsic requirement and necessary condition for building an agriculturally strong nation [39]. Rural residents’ income, as a major driving force for rural modernization, impacts their quality of life and is a key factor in improving living standards. It serves as a positive signal for the progress of rural agricultural modernization. This study selected four indicators to reflect rural modernization level: disposable income of rural residents, average rural tap water penetration rate, solar water heater area, and number of village health clinics.

Finally, agricultural policy support intensity. Agriculture, as the foundation of the nation and the strength of the country, requires the timely adjustment of agricultural support policies to promote the coupling and mutual development of agricultural modernization and national modernization. This can continually solidify the foundation of an agriculturally strong nation, as seen in Anhui, an agricultural powerhouse. The proportion of government agricultural expenditure is a direct reflection of agricultural policy support intensity, showing the degree of government focus and support for agricultural and rural development. Tax incentives for the agricultural sector guide resource allocation and shape societal expectations for agricultural development, clearly expressing government support for the agricultural industry. Rural assistance levels reflect the government’s efforts and effectiveness in providing aid, further demonstrating policy support intensity. This study used four indicators to measure agricultural policy support intensity: government agricultural expenditure proportion, tax exemptions for high-tech agricultural enterprises, tax deductions for agricultural R&D expenditures, and rural assistance levels.

A comparison of the indicators used to assess new agricultural productivity and the development of SAP reveals a partial overlap, stemming from shared objectives and similar measurement dimensions. This convergence does not represent redundancy but rather reflects different perspectives on agricultural development. Two indicators exemplify this overlap. First, both systems employ rural per capita disposable income as a measure—one as a reflection of labor efficiency and the other as an indicator of rural modernization. This dual use arises for two reasons. On one hand, per capita disposable income serves as a direct proxy for the benefits accruing to farmers from productivity gains. On the other, it encapsulates broader improvements in rural quality of life and economic development. Moreover, enhanced agricultural productivity underpins efforts to build SAP, with rising rural incomes serving as a common goal. Second, both indicator systems include metrics related to agricultural mechanization. The level of mechanization per unit area reflects the efficiency of equipment utilization, while total agricultural machinery power captures the capacity for technological innovation in production. The concept of new quality productivity emphasizes improved production efficiency through technological advancement and factor optimization. Modern agricultural machinery, often equipped with intelligent control systems, enables precision and data-driven farming. As such, both mechanization intensity and total machinery power illustrate how technological innovation drives the transition to intelligent, high-efficiency agriculture.

2.2. Research Methodology

The TOPSIS entropy weighting method was used to evaluate the new agricultural productive forces and the level of agricultural strengthening in Anhui. The reasons for selecting the TOPSIS entropy weighting method are as follows: First, the TOPSIS entropy weighting method can simultaneously process multiple evaluation indicators, providing a comprehensive assessment of the advantages and disadvantages of decision-making alternatives. In the measurement of new agricultural productive forces and agricultural strength, multiple indicators are incorporated into the same system for evaluation. Second, the TOPSIS method, in conjunction with objective weighting methods such as the entropy weighting method, avoids the subjectivity of data, thereby more objectively capturing the comprehensive impact of multiple influencing factors. This reduces the influence of subjective factors on the results, enhancing the scientific and objective nature of the calculations. Third, the TOPSIS method does not have strict limitations on data distribution, sample size, or the number of indicators, making it highly applicable and flexible in indicator measurement. The TOPSIS entropy weighting method is specifically divided into the following seven steps:

Step 1: Standardize the matrix to eliminate the influence of different units of measurement.

$$X_{ij}={\displaystyle \frac{x_{ij}-\mathit{min}\left(x_{ij}\right)}{\mathit{max}\left(x_{ij}\right)-\mathit{min}\left(x_{ij}\right)}}+0.0001$$

(1)

$$X_{ij}={\displaystyle \frac{\mathit{max}\left(x_{ij}\right)-x_{ij}}{\mathit{max}\left(x_{ij}\right)-\mathit{min}\left(x_{ij}\right)}}+0.0001$$

(2)

where $X_{ij}$ represents the value after standardization; $x_{ij}$ is the original value of the j-th element of the i-th indicator; and $\max \left(x_{ij}\right)$ and $\min \left(x_{ij}\right)$ represent the maximum and minimum values, respectively.

Step 2: Calculate the information entropy for each indicator.

$$e_i=-{\displaystyle \frac{1}{\ln n}}{\displaystyle {\sum }_{j=1}^n\left[\left(X_{ij}/{\displaystyle {\sum }_{j=1}^n{X}_{ij}}\right)\ln \left(X_{ij}/{\displaystyle {\sum }_{j=1}^n{X}_{ij}}\right)\right]}$$

(3)

where $e_i$ represents the information entropy of the i-th indicator, and $n$ is the total sample size.

Step 3: Calculate the weight of each indicator based on the information entropy.

$$w_i=\left(1-e_i\right)/{\displaystyle {\sum }_{i=1}^m\left(1-e_i\right)}$$

(4)

where $w_i$ represents the weight of each indicator.

Step 4: Construct the weighted matrix.

$$S={\left({\gamma }_{ij}\right)}_{m\times n},{\gamma }_{ij}=X_{ij}\times w_i$$

(5)

Step 5: Determine the optimal $A_j^{+}$ and worst alternatives $A_j^{-}$.

$$A_j^{+}=\max \left({\gamma }_{i1},{\gamma }_{i2},\dots ,{\gamma }_{in}\right),A_j^{-}=\min \left({\gamma }_{i1},{\gamma }_{i2},\dots ,{\gamma }_{in}\right)$$

(6)

Step 6: Measure the Euclidean distance $D$ between each evaluation indicator and the optimal and worst alternatives.

$$D_i^{+}=\sqrt{{\displaystyle {\sum }_{j=1}^m{\left(A_j^{+}-{\gamma }_{ij}\right)}^2}},D_i^{-}=\sqrt{{\displaystyle {\sum }_{j=1}^m{\left(A_j^{-}-{\gamma }_{ij}\right)}^2}}$$

(7)

Step 7: Calculate the new agricultural productive forces and the level of an SAP.

$$E_i=D_i^{-}/\left(D_i^{+}+D_i^{-}\right)$$

(8)

where $E_i$ is the new agricultural productive forces and the level of SAP. $0\le E_i\le 1$, the closer the value of $E_i$ is to 0, the lower the level; the closer it is to 1, the higher the level.

2.3. Trend and Spatial Distribution Characteristics

2.3.1. Trend Analysis

The research object of this study is the 16 prefecture-level cities in Anhui Province, with a study period from 2010 to 2022. The data were sourced from the China Statistical Yearbook and Anhui Statistical Yearbook (2011–2023), statistical yearbooks of various cities in Anhui, and the EPS database (Economy Prediction System). Missing data were supplemented using linear interpolation. To address the limited instances of missing data—specifically, the year-end mobile phone ownership figures for rural residents in Suzhou (2016–2017), Tongling (2016–2017), and Xuancheng (2021–2022), as well as the 2010 digital inclusive finance index across cities in Anhui Province—we applied linear interpolation. Notably, the imputed values represent less than 1% of the full dataset. This minimal proportion, combined with the observation that adjacent data points exhibit a linear progression, supports the appropriateness of this approach. Nonetheless, we acknowledge the inherent limitation of linear interpolation, which assumes consistent trends over time and may not fully capture abrupt local deviations. The 16 prefecture-level cities in Anhui are divided into three regions: Northern Anhui, Central Anhui, and Southern Anhui. Specifically, Northern Anhui includes Bengbu, Fuyang, Suzhou, Huaibei, Huainan, and Bozhou; Central Anhui includes Hefei, Lu’an, Chuzhou, and Anqing; and Southern Anhui includes Wuhu, Xuancheng, Ma’anshan, Tongling, Chizhou, and Huangshan.

The ANPF and the level of building SAP in each region of Anhui Province from 2010 to 2022 are shown in Figure 2 and Figure 3. In terms of changes in the level of ANPF, Anhui’s ANPF increased from 0.083 in 2010 to 0.265 in 2022. Notably, the period from 2010 to 2017 saw relatively stable growth, while the period from 2018 to 2022 experienced rapid growth. This indicates that Anhui’s ANPF have demonstrated strong stability and sustainability during the transition to modernization, with significant progress in the innovation of agricultural elements, technology transfer, and other aspects. The support of relevant policies and the improvement of agricultural infrastructure have provided strong guarantees for this stability and sustainability.

In Northern Anhui, ANPF showed an overall upward trend from 2010 to 2022, increasing from 0.074 in 2010 to 0.194 in 2022, although with notable fluctuations. Significant growth occurred from 2011 to 2013 and 2015 to 2017, while a slight decline occurred from 2018 to 2019. This could be attributed to the complexity of agricultural industrial restructuring in the region, where traditional agricultural productivity still plays a significant role. The transition to new productive forces faces several challenges, such as relatively low technological levels and insufficient capital investment, resulting in a less stable growth process.

In Central Anhui, ANPF increased from 0.124 in 2010 to 0.342 in 2022, with the most significant growth among the three regions of Anhui. In most years, the growth rate was higher than the provincial average. This is attributed to Central Anhui’s strong agricultural industrial base, advantageous transportation location, and abundant technological resources, which enabled a rapid response to policy calls and the active introduction of new technologies and models, such as the development of smart agriculture and agricultural product processing industries. This has led to the extension of the agricultural industrial chain and an increase in added value.

In Southern Anhui, ANPF declined slightly from 2010 to 2011 but steadily increased since then, reaching 0.285 by 2022. The initial decline may have been due to the region’s agricultural industrial restructuring, where the traditional industries’ advantages weakened and emerging industries had not yet matured. However, over time, Southern Anhui, with its favorable ecological environment and tourism resources, developed an “Agriculture + Ecology + Tourism” model, promoting rapid growth in ANPF. This reflects the region’s emphasis on adapting to local conditions, leveraging its unique advantages, and promoting the steady growth of ANPF through the development of specialty agriculture and ecological agriculture, providing valuable insights for other ecologically rich regions.

In summary, the level of ANPF in Anhui Province showed a fluctuating upward trend from 2010 to 2022. Among the three regions, Central Anhui stands out with the highest level of ANPF, followed by Southern Anhui, with Northern Anhui being relatively lower.

During the study period, both the overall level of CSAP in Anhui and the levels in the three regions in Anhui Province showed an upward trend, with relatively steady development from 2010 to 2019. After 2019, the development speed accelerated. Among the three regions, Central Anhui consistently ranked first in terms of level of CSAP. This is largely due to the provincial capital, Hefei, being located in Central Anhui, which has attracted more policy support and resource allocation. Northern Anhui ranked second, while Southern Anhui had a relatively lower level. However, Southern Anhui’s growth rate surpassed that of Northern Anhui, and by 2022, its level had caught up with that of Northern Anhui.

Northern Anhui has traditionally focused on staple crop cultivation and the processing of agricultural by-products, with a high proportion of agricultural output derived from crop farming. As a result, its ANPF has been relatively low, limiting its economic benefits. In contrast, Southern Anhui, through industrial restructuring, has prioritized high-value-added industries, such as tea, highland vegetables, and edible fungi, along with the development of leisure agriculture by fully utilizing its tourism resources. This has extended the agricultural industrial chain and enhanced comprehensive benefits, with ANPF playing a significant role in this process.

2.3.2. Spatial Distribution Characteristics Analysis

To better analyze regional disparities among different prefecture-level cities in Anhui Province, from a spatial visualization perspective, ArcGIS Pro 3.0.0 software was used with the natural breaks method to categorize the ANPF and the level of CSAP into five categories: “low-value areas, relatively low-value areas, medium-value areas, relatively high-value areas, and high-value areas”. The spatial distribution characteristics of ANPF and the level of CSAP in the 16 prefecture-level cities of Anhui in 2010, 2014, 2018, and 2022 are shown in Figure 4 and Figure 5.

As shown in Figure 4, during the study period, the increase in ANPF in Northern Anhui was smaller compared to other regions of the province. Cities such as Suzhou, Bozhou, and Bengbu moved from medium-value areas to relatively low-value areas. In contrast, the ANPF in Southern Anhui grew relatively quickly, with cities like Tongling, Chizhou, and Ma’anshan showing varying degrees of improvement. Hefei consistently ranked first in the province for ANPF, followed by Wuhu, which also demonstrated strong technological innovation capabilities. Huangshan, Huainan, and Huaibei consistently ranked at the bottom in terms of ANPF throughout the study period, with minimal improvements. Hefei in Central Anhui and Wuhu in Southern Anhui are the two cities with the highest levels of economic development in the province. Their technological development also ranks among the top, and they have a significant positive radiation effect on the ANPF in other cities in Central and Southern Anhui.

As shown in Figure 5, during the study period, the level of CSAP in Anhui Province shifted from “central, northwest, and southeast in descending order” to a trend where “the central, northwest, and southeast regions are basically equal”. By 2022, Hefei City led the province in the level of CSAP, closely followed by prefecture-level cities such as Wuhu and Chuzhou, while Huangshan, Huainan, and Tongling lagged behind. Overall, the level of CSAP in Anhui Province was higher than that of ANPF, indicating that in recent years, agricultural development in the province has maintained a steady and positive trajectory. However, challenges remain, including insufficient agricultural technological innovation and underdeveloped new agricultural industries. The lack of driving forces for new productive forces has become a practical obstacle to CSAP.

3. Spatial Correlation Analysis

3.1. Research Methodology

To better analyze the spatial correlation between ANPF and CSAP, this study used a modified gravity model to determine the spatial correlation relationships among Anhui’s 16 prefecture-level cities and built a relationship matrix to explain the interactions between ANPF and CSAP. Furthermore, social network analysis was introduced to analyze the spatial network structure characteristics of ANPF and the CSAP in Anhui.

3.1.1. Modified Gravity Model

The traditional gravity model does not account for the directional relationships between indicators, yet there is bidirectionality and asymmetry in agricultural development between regions [40]. Therefore, this study modified the traditional gravity model based on the research of Sun and Luo (2016) and Peng et al. (2024) [41,42]. The modified gravity model offers two key advantages. First, it accommodates a range of agricultural scenarios, including spatial correlation analyses of diverse forms of supply capacity and technological innovation potential. Second, it incorporates advanced statistical techniques that improve parameter estimation, mitigating biases arising from unrealistic assumptions in traditional models and enhancing the model’s predictive accuracy for spatial correlations between ANPF and SAP.

The modified model is as follows:

$$Q_{ij}=K{\displaystyle \frac{NQ{P}_i\times NQ{P}_j}{D_{ij}{}^2}}$$

(9)

$$A_{ij}=K{\displaystyle \frac{SA{P}_i\times SA{P}_j}{D_{ij}{}^2}}$$

(10)

In these equations, $Q_{ij}$ represents the strength of the correlation between the ANPF of city i and city j; $A_{ij}$ indicates the correlation strength of SAP between cities $i$ and $j$; $NQ{P}_{}$ denotes the levels of ANPF; $SAP$ represent the level of SAP; $D_{ij}$ is the geographic distance between cities $i$ and $j$; and $K$ is the gravity modification coefficient, which is set as a constant value of 1. The gravity correction coefficient is set to 1 to retain the mathematical simplicity of the traditional gravity model, thereby facilitating analytical tractability. This baseline setting also allows any subsequent adjustments to the coefficient to reveal their correctional impact with greater clarity. Sensitivity analyses are conducted using alternative values of K = 0.5 and K = 2. As the direction of the results remains consistent across all values—differing only in magnitude—these supplementary outcomes are as presented in

Table A3. Overall network structural characteristics (K = 0.5).

	ANPF			CSAP
	Network Density	Network Efficiency	Network Correlation	Network Density	Network Efficiency	Network Correlation
2010	0.3125	1	0.6952	0.3333	1	0.6762
2011	0.3000	1	0.6952	0.3292	1	0.6857
2012	0.2875	1	0.6952	0.3083	1	0.6667
2013	0.2833	1	0.7143	0.3167	1	0.6667
2014	0.2917	1	0.7048	0.3333	1	0.6762
2015	0.2875	1	0.7238	0.3292	1	0.6857
2016	0.2917	1	0.7143	0.3208	1	0.6952
2017	0.2875	1	0.7333	0.325	1	0.6952
2018	0.3	1	0.7143	0.3292	1	0.6952
2019	0.3083	1	0.7143	0.3125	1	0.7143
2020	0.3167	1	0.6952	0.3208	1	0.7048
2021	0.3125	1	0.6857	0.3375	1	0.6762
2022	0.315	1	0.6948	0.3292	1	0.6762

and

Table A4. Overall network structural characteristics (K = 2).

	Agricultural New Productive Forces			CSAP
	Network Density	Network Efficiency	Network Correlation	Network Density	Network Efficiency	Network Correlation
2010	0.3125	1	0.6952	0.3208	1	0.6952
2011	0.3000	1	0.6952	0.3125	1	0.7143
2012	0.2875	1	0.6952	0.3167	1	0.7048
2013	0.2833	1	0.7143	0.3292	1	0.6667
2014	0.2917	1	0.7048	0.325	1	0.6857
2015	0.2875	1	0.7238	0.3167	1	0.7143
2016	0.2917	1	0.7143	0.3167	1	0.7048
2017	0.2875	1	0.7333	0.3167	1	0.7143
2018	0.3	1	0.7143	0.3333	1	0.6857
2019	0.3083	1	0.7143	0.325	1	0.6952
2020	0.3167	1	0.6952	0.3083	1	0.7238
2021	0.3125	1	0.7048	0.3292	1	0.6952
2022	0.3125	1	0.7048	0.3208	1	0.7048

.

3.1.2. Social Network Analysis Method

The gravity model only reflects the degree of association between cities based on geographic distance. However, it inadequately captures the spatial network characteristics between cities. To address this, this study employed social network analysis grounded in empirical data. By capturing interaction data among individuals or organizations, constructing network models, and conducting quantitative assessments, the approach reveals structural characteristics objectively and minimizes subjective interpretation. The spatial correlation network elucidates the structural relationships between ANPF and the development of SAP in Anhui, both at the macro and micro network levels.

At the overall network level, the network’s degree of association is primarily calculated to reveal the degree of connectivity between nodes. The overall network characteristics are further broken down into three components: network density, network association, and network efficiency, as shown in

Table 1. Indicators for analyzing spatial correlation network structure features.

		Formula	Variable Explanation
Overall Network Structural Characteristics	Network Density	$D={\displaystyle \frac{L}{N\times \left(N-1\right)}}$	$N$ represents the total number of nodes in the network; $L$ represents the actual number of connections in the network; $V$ is the number of unreachable nodes in the network; $M$ and $\max M$ denote the number of redundant connections between nodes and the maximum possible number of redundant connections, respectively; $x_{i+}$ represents the connections initiated by node $i$, while $x_{+i}$ represents the connection absorbed by node $i$; $g-1$ denotes the maximum possible connection between node $i$ and node $j$; $g_{ik}$ represents the number of shortcut paths between node $i$ and node $j$; $g_{ik}\left(i\right)$ represents the number of nodes passed through in the shortest path between node $i$ and $j$; $b_{jk}\left(i\right)$ denotes the probability that node $i$ is on the shortest path between $j$ and $k$, with $j\ne k\ne i$ and $j<k$.
	Network Association	$C=1-V/\left[N\times {\displaystyle \frac{\left(N-1\right)}{2}}\right]$
	Network Efficiency	$NE=1-{\displaystyle \frac{M}{\max M}}$
Individual Network Structural Characteristics	Out-Degree	$Co\left(n_i\right)={\displaystyle \frac{x_{i+}}{g-1}}$
	In-Degree	$Cl\left(n_i\right)={\displaystyle \frac{x_{+i}}{g-1}}$
	Betweenness Centrality	$BC=2{\displaystyle \sum _j^N{\displaystyle \sum _k^N\frac{b_{jk}\left(i\right)}{N^2-3N+2}}}$$b_{jk}\left(i\right)=g_{ik}\left(i\right)/g_{ik}$

.

At the individual network level, the network centrality of each node in the spatial correlation network is measured to quantify its central position within the network, as shown in Table 1. Node centrality is further divided into in-degree and out-degree. A higher in-degree indicates that the province has a greater attraction within the network, and other provinces are more likely to establish spatial connections with it. On the other hand, a higher out-degree suggests that the province has stronger control within the network. Betweenness centrality measures the extent to which a node controls the interactions between other nodes. If a node has a high betweenness centrality, it plays a crucial intermediary role in the shortest paths between other nodes.

3.2. Spatial Correlation Analysis

3.2.1. Spatial Correlation Strength Analysis

Based on the modified gravity model, the gravity matrix for ANPF and CSAP in Anhui province was calculated. Using the visualization tool Netdraw in Ucinet 6 software, the spatial correlation network diagrams for ANPF and CSAP in 2010 and 2022 were created, as shown in Figure 6 and Figure 7.

The spatial network structure of ANPF and CSAP in Anhui’s prefecture-level cities exhibited characteristics of multiple associations, multiple cores, and multidimensional connections. The connections between entities in the network are tight, with no “isolated islands” present. Compared to 2010, by 2022, the network association degree of ANPF and CSAP in Anhui province increased.

Specifically, in 2010, the ANPF in Hefei, Wuhu, and Bengbu had a strong correlation. By 2022, a more distinct spatial pattern had formed, with Bengbu as the core in Northern Anhui, Hefei as the core in Central Anhui, and Wuhu as the core in Southern Anhui. Throughout the study period, Hefei consistently had the strongest correlation, while Huaibei had the weakest correlation.

In terms of CSAP, in 2010, Hefei had the strongest correlation and was in a core position, while Wuhu, Bengbu, and Xuancheng had weaker correlations, positioning them as secondary core cities. Huaibei had the weakest correlation. By 2022, the overall network became more tightly connected, with strengthened correlations. Hefei continued to have the strongest correlation, while Wuhu saw the fastest growth in correlation strength. Huaibei, Lu’an, and Ma’anshan saw slight increases in correlation strength, though Huaibei’s correlation remained the weakest.

These evolving spatial configurations are not arbitrary. They reflect an underlying spatial linkage mechanism shaped by hierarchical urban development, infrastructure connectivity, and policy prioritization. Hefei, as the provincial capital and innovation hub, naturally exerts a gravitational pull on neighboring regions due to its stronger institutional support, resource aggregation, and technological diffusion capacity. Wuhu and Bengbu, benefiting from strategic geographical locations and integration into national agricultural modernization policies, emerge as sub-centers facilitating regional spillover effects. Conversely, the persistent peripheral status of Huaibei can be attributed to structural limitations such as weaker agricultural innovation capacity, less integration into regional logistics networks, and fewer incentives under major provincial programs. These patterns illustrate that spatial association strength is a function of both physical proximity and systemic alignment within broader regional development frameworks.

Thus, the increasing spatial correlation from 2010 to 2022 not only reflects denser linkages but also signals the maturing coordination mechanisms among cities. This offers theoretical insight into how institutional hierarchy and functional specialization contribute to the spatial restructuring of agricultural productivity forces and CSAP.

3.2.2. Spatial Correlation Structural Characteristics Analysis

(1)

Overall Network Structural Characteristics Analysis

Using the Density and Krackhardt GTD tools in Ucinet 6 software, the network density, network efficiency, and network correlation degree were measured. Network density refers to the degree of connectivity between the nodes of ANPF and CSAP in the prefecture-level cities of Anhui Province. A higher value indicates more correlations. The results are shown in

Table 2. Overall network structural characteristics.

	ANPF			CSAP
	Network Density	Network Efficiency	Network Correlation	Network Density	Network Efficiency	Network Correlation
2010	0.321	0.695	1	0.329	0.695	1
2011	0.304	0.695	1	0.317	0.714	1
2012	0.300	0.695	1	0.308	0.724	1
2013	0.296	0.705	1	0.321	0.695	1
2014	0.296	0.714	1	0.317	0.714	1
2015	0.296	0.714	1	0.325	0.705	1
2016	0.300	0.705	1	0.325	0.705	1
2017	0.296	0.714	1	0.329	0.695	1
2018	0.300	0.724	1	0.329	0.695	1
2019	0.300	0.724	1	0.329	0.695	1
2020	0.317	0.695	1	0.317	0.714	1
2021	0.325	0.686	1	0.333	0.695	1
2022	0.325	0.686	1	0.325	0.705	1

.

The overall network density of ANPF in Anhui Province showed a fluctuating upward trend, reaching 0.325 in 2022, indicating that the degree of connectivity in ANPF became increasingly tighter during the study period. The accelerated flow of technological elements led to more intense flows of elements between regions. This enhanced connectivity enabled more efficient coordination in resource management, streamlined the interregional transport of agricultural inputs and products, and facilitated the diffusion of innovation across prefecture-level cities.

The construction of Hefei as a comprehensive national science center drove the integration of agricultural scientific resources across the province. The application of digital agricultural technology further promoted technological transfer between regions, fostering cross-regional collaboration between industry, academia, and research. Such social network linkages played a pivotal role in aligning agricultural production with local strengths, optimizing labor and capital deployment, and extending industrial chains through synergistic partnerships. The adjustment of agricultural industrial structure has led to diversified expansion of agricultural production towards agricultural product processing industry, rural tourism, etc. With the continuous extension of the agricultural industry chain, information exchange and resource sharing have become more frequent, accelerating the formation of a spatially coordinated system of new productive forces. This has further promoted the development of new quality agricultural productivity and increased network density.

The network density of SAP reached its highest value of 0.333 in 2021, and its lowest value of 0.308 in 2012. The instability in the network density of SAP was largely due to the impact of economic structural transformation. The economic structural transformation and unequal distribution of agricultural resources in certain prefecture-level cities, especially resource-based cities such as Huainan and Huaibei, restricted agricultural investment due to ecological restoration pressures. Furthermore, labor outflow further hindered the modernization of agriculture, reflecting a decreasing trend in redundant connections of agricultural elements.

The network efficiency of ANPF initially increased and then decreased, rising from 0.695 in 2010 to 0.724 in 2019, before slightly declining to 0.686 by 2022. This reflects the varying operational efficiency of the ANPF network in different years, with the speed and effectiveness of information, resources, and influence in the network declining over time. The network efficiency of agricultural strengthening exhibited an unstable trend, fluctuating between 0.695 and 0.724 during the study period. This variability could be linked to factors such as the speed of agricultural technological innovation, the implementation of ANPF policies, and changes in the supply and demand of the agricultural market.

In both 2010 and 2022, the network correlation degree of ANPF and agricultural strengthening in Anhui Province was 1. This indicates that the strength of the correlations between the nodes of ANPF and CSAP in the network remained stable, meaning that the network structure was relatively stable, and the interactive relationships between nodes did not change significantly. It also implies that ANPF and CSAP in the prefecture-level cities of Anhui are interconnected, with evident spatial spillover effects and network association relationships. There were no isolated regions in the development process, and the network had strong connectivity and correlation.

These changes fundamentally reflect the fact that Anhui Province, while advancing agricultural modernization, has benefited from the development strategy of the Yangtze River Delta integration. However, it also faces deep contradictions in regional development imbalances. A number of technological innovation hubs and emerging industrial sectors are gradually rising, but key core technologies are still constrained by external sources. This has led to homogenous competition within the limited industrial value chains, with minimal division of labor, collaboration, and functional complementarity, affecting cooperation and exchange of new productive forces between cities. The dual radiation effect of the Hefei metropolitan area and the Nanjing metropolitan area has promoted the development of the Wanjiang City Belt as a demonstration zone for industrial transfer, resulting in the reallocation of elements and the formation of a networked cooperation system in industrial development. Through institutional innovation and technological empowerment, the efficiency of element allocation can be improved while maintaining network connectivity, thus achieving high-quality agricultural development.

(2)

Internal Network Individual Characteristics Analysis

To better analyze the spatial correlation characteristics, based on the analysis of overall network structural characteristics, this study used Ucinet 6 software’s Centrality tool to calculate the out-degree, in-degree, and betweenness centrality for ANPF and the CSAP in the prefecture-level cities of Anhui Province in 2022. This analysis explores the centrality characteristics of the network nodes in the spatial correlation network, as shown in

Table 3. Internal individual characteristics in 2022.

City	ANPF			CSAP
	Out-Degree	In-Degree	Betweenness Centrality	Out-Degree	In-Degree	Betweenness Centrality
Hefei	6	14	83.309	6	11	72.365
Huaibei	3	3	0.000	3	4	0.704
Bozhou	5	4	7.675	4	5	8.293
Suzhou	4	3	2.458	3	3	0.000
Bengbu	6	6	36.483	6	6	39.607
Fuyang	5	3	9.917	6	3	15.139
Huainan	5	4	19.133	6	5	26.748
Chuzhou	4	4	21.025	5	4	19.711
Luan	5	4	21.283	4	4	19.581
Maanshan	4	5	10.483	4	4	9.086
Wuhu	4	9	10.674	4	8	10.925
Xuancheng	6	5	12.952	6	5	13.983
Tongling	5	6	13.235	5	6	16.198
Chizhou	6	4	8.214	6	4	6.140
Anqing	5	2	4.158	5	4	12.021
Huangshan	5	2	0.000	5	2	0.500
Mean	4.875	4.875	16.312	4.875	4.875	16.938

.

From the internal characteristics of the ANPF network, cities such as Bengbu and Hefei have relatively higher out-degrees, while Huaibei has a relatively lower out-degree. Hefei and Wuhu have higher in-degrees, indicating that Hefei and Wuhu are highly dependent on other cities in Anhui Province in the spatial correlation network of ANPF. These cities serve as core input nodes for resources, information, and industrial collaboration. Cities such as Tongling and Bengbu are also among the cities with high mean values. A multi-core, multi-layer spatial distribution characteristic is observed around these central cities, which can quickly and conveniently establish spatial connections with other cities in the network. The betweenness centrality of ANPF in Hefei, Bengbu, Chuzhou, Lu’an, and Huainan is higher than the average, accounting for 69.44% of the total betweenness centrality. This indicates that these cities significantly influence and control the flow of labor, digital technologies, and other resources in the spatial network, playing an important “bridge” role in connecting the exchange of new productive forces. Hefei has the highest betweenness centrality, suggesting that it plays a key “intermediary” role in the ANPF network and controls cross-regional resource flow. The remaining cities in Anhui Province account for only 30.56% of the total betweenness centrality, making it difficult for them to influence the development of new productive forces in other cities, thereby placing them at the periphery of the network. Therefore, there is an urgent need to break the significant imbalance in the control of resource elements between cities.

From the perspective of CSAP, Bengbu and Hefei have relatively higher out-degrees, while Huaibei and Suzhou have relatively lower out-degrees. Hefei and Wuhu have higher in-degrees. In 2022, the betweenness centrality of Hefei, Bengbu, Huainan, Chuzhou, and Lu’an is above the average, accounting for 65.69% of the total betweenness centrality, while the remaining cities account for only 34.31%. Hefei, Wuhu, and other cities have favorable geographical conditions, a strong economic base, and a complete talent cultivation environment. These cities continue to attract funds and talent from other cities, accelerating breakthroughs in key and frontier technology areas. As regional central cities, they use their advantages in information, technology, and experience to radiate and drive other cities. In contrast, cities like Huaibei have relatively underdeveloped infrastructure, have slow internal flow of elements, and are positioned at the periphery of the network.

4. Driving Factors of ANPF on CSAP

4.1. Research Methodology

Spatial network correlation explains the attraction of central points to surrounding regions, but it does not reflect the impact of different factors on one another. Therefore, this study employed the Geographical Detector Model. The geographical detector is a statistical method designed to detect driving factors and their interactions based on spatial heterogeneity issues in geographical elements [43]. It determines whether there is interaction between two factors, as well as the strength and direction of the interaction, by calculating and comparing the q-values of each single factor and the q-value of the sum of two factors. It does not require linear assumptions about the relationship between variables, overcoming the limitations of traditional statistical methods in dealing with nonlinear relationships. This model has immunity to multivariate collinearity, and its calculation process and results are not affected by multivariate collinearity, thus ensuring the reliability of the analysis results.

This study used factor detection and interaction detection to quantitatively analyze the degree of influence and the interaction relationship of driving factors of ANPF on CSAP in Anhui Province. The calculation formula for factor detection is as follows:

$$q=1-{\displaystyle \frac{{\displaystyle {\sum }_h^L{N}_h{\sigma }_h^2}}{N{\sigma }^2}}=1-{\displaystyle \frac{SSW}{SST}}$$

(11)

where $N$ represents the total number of units in the study area; $N_h$ represents the number of units in the sub-region; ${\sigma }^2$ represents the variance of efficiency in the entire study area; and ${\sigma }_h^2$ is the variance of efficiency in the sub-region. $SST$ represents the total variance for the entire region; $SSW$ represents the sum of the variances of the sub-regions; and $q$ represents the degree of influence.

Interaction factor detection involves comparing the $q$ values of a single factor and the $q$ values of a two-factor spatial superposition. This method assesses whether the interaction between multiple variables on CSAP is enhancing, weakening, or independent. The higher the value, the stronger its explanatory power for the spatiotemporal differentiation of the level of CSAP. The specific criteria for this judgment are presented in

Table 4. Criteria for judging the interaction types of two factors.

Judgment Criteria	Interaction Type
$q\left(X_1\cap X_2\right)<Min\left[q\left(X_1\right),q\left(X_2\right)\right]$	Non-Linear Weakening
$Min\left[q\left(X_1\right),q\left(X_2\right)\right]<q\left(X_1\cap X_2\right)<Max\left[q\left(X_1\right),q\left(X_2\right)\right]$	Single Factor Non-Linear Weakening
$q\left(X_1\cap X_2\right)>Max\left[q\left(X_1\right),q\left(X_2\right)\right]$	Dual Factor Enhancement
$q\left(X_1\cap X_2\right)=q\left(X_1\right)+q\left(X_2\right)$	Independence
$q\left(X_1\cap X_2\right)>q\left(X_1\right)+q\left(X_2\right)$	Non-Linear Enhancement

.

4.2. Driving Factors Analysis

4.2.1. Driving Factor Detection

To further analyze the extent to which ANPF drive CSAP, this study considered the six primary indicators of the ANPF evaluation system as driving factors. Using ArcGIS software, these indicators were discretized. Taking 2022 as an example, the q-values for each driving factor’s impact on the spatiotemporal differentiation of CSAP in Anhui Province were detected, as shown in

Table 5. Driving factor detection results.

	Laborer Quality	Laborer Efficiency	Tangible Means of Production	Intangible Means of Production	New-Quality Industries	Ecological Environment
q-value	0.6276 **	0.2277	0.7919 ***	0.2020	0.5865 **	0.1515
Ranking	2	4	1	5	3	6

Note: ** and *** indicate significance at the 5% and 1% levels, respectively.

.

Among the examined factors, tangible means of production exhibited the highest explanatory power in CSAP, with a q-value of 0.7919 and statistical significance at the 1% level. This underscores their critical role as a primary driver of SAP development. The quality of the labor force ranks second (q = 0.6276), followed by the new quality industry (q = 0.5865); both pass the 5% significance threshold, indicating that these factors also substantially contribute to the advancement of SAP. In contrast, labor efficiency, intangible means of production, and ecological environment exert comparatively weaker influence and do not pass significance tests, suggesting their current impact on CSAP is limited.

These ‘enhancement effects’ can be theoretically interpreted through the lens of production factor complementarity and systemic capacity upgrading. Tangible means of production, such as infrastructure and machinery, serve as foundational enablers, directly enhancing agricultural output and resilience. When coupled with high labor quality and advanced industrial inputs (i.e., new quality industries), a synergistic interaction emerges—human capital is better equipped to utilize improved tools and systems, while technological innovation amplifies the productivity of physical and human resources. In contrast, the weak effects of labor efficiency, intangible production inputs, and ecological environment may indicate a lack of integration or maturity in these systems, which limits their current ability to exert significant influence. This theoretical framing suggests that interactive effects stem from aligned improvements across material, human, and institutional dimensions of agricultural productivity.

From this, it can be seen that tangible means of production, labor quality, and new quality industry are the core driving forces for promoting CSAP through new quality productivity. Their role is far higher than other indicators, and they are the direction that needs to be prioritized at the current stage. In the future, attention should be paid to the improvement of agricultural labor skills, the modernization support of tangible means of production, and the leading effect of new quality industry. At the same time, attention should be paid to the potential impacts of intangible means of production, labor efficiency, and ecological environment, and their impact mechanisms and conditions should be explored in order to comprehensively understand the driving system for CSAP.

4.2.2. Driving Factor Interaction Detection

The spatiotemporal differentiation characteristics of CSAP are not solely driven by a single factor but are the result of interactions among multiple driving factors. To further explore the interaction relationships between driving factors, this study used interaction detection from the geographical detector model to analyze the degree of impact of the interactions between ANPF driving factors on the spatiotemporal differentiation of CSAP. The results of the driving factor interaction detection were visualized in a heatmap using Origin 2024 software, as shown in Figure 8.

The interaction detection results show that tangible production materials, labor quality, and new quality industry have the strongest interaction with other factors, indicating that these three factors are system hubs and can significantly amplify their impact on CSAP when combined with other factors. Specifically, the combination factor interaction between tangible means of production (X3) and new quality industry (X5) has the strongest driving force for CSAP, reaching 0.9732. This strong synergistic effect can be theoretically attributed to the complementary roles of industrial upgrading and infrastructure development. New quality industry inherently demands advanced and efficient production inputs, thereby stimulating investment and innovation in tangible means of production. Conversely, the modernization of production infrastructure creates favorable conditions for the expansion and scaling of emerging industries, reinforcing a positive feedback loop.

In addition, the combination factor interaction between new quality industry (X5) and laborer quality (X1), tangible means of production (X3) and intangible means of production (X4), laborer efficiency (X2), and laborer quality (X1) also has a strong interaction effect of 0.9 or above. Such patterns suggest that human capital, in both its qualitative and efficiency aspects, acts as a catalyst in maximizing the productivity gains from sectoral and technological transformation.

The combined factors of tangible means of production (X3) and ecological environment (X6), new quality industry (X5) and intangible means of production (X4), laborer quality (X1) and labor efficiency (X2), intangible means of production (X4), and ecological environment (X6) have interactive effects ranging from 0.8 to 0.9, while the other combinations of interactive factors are all below 0.8. These moderate but notable enhancements reflect systemic co-dependencies where environmental and intangible assets—such as technology, policy, and institutional support—reinforce physical and labor inputs, further amplifying their collective influence. From this, it can be seen that the interactions between the driving factors are all of an enhancing nature, including both dual factor enhancement and non-linear enhancement, indicating that the interaction between pairs of driving factors has a greater impact on the spatiotemporal differentiation of CSAP in Anhui Province than the influence of individual factors.

5. Discussion

5.1. Research Findings

This study, based on panel data from 16 prefecture-level cities in Anhui Province from 2010 to 2022, presents a novel analysis of ANPF and CSAP. This study applied a comprehensive methodology that includes the entropy weight TOPSIS method, a modified gravity model, social network analysis (SNA), and geographical detectors to measure, analyze, and interpret the spatial relationships and driving factors of agricultural development. The major findings of the study are as follows:

First, from 2010 to 2022, both ANPF and CSAP showed consistent upward trends in Anhui, with significant achievements in agricultural development and technological innovation. Central Anhui led in both ANPF and CSAP throughout the study period, while Southern Anhui had higher levels of ANPF compared to Northern Anhui. Interestingly, Northern Anhui outperformed Southern Anhui in CSAP, with Hefei maintaining the highest overall level. These findings resonate with the broader literature, which often emphasizes the importance of technological innovation and infrastructural development in agricultural progress [44]. However, this study’s distinction lies in its spatially nuanced analysis, revealing how regional disparities persist even amidst overarching progress.

Second, the analysis of network structures reveals an increase in the overall network density of ANPF, indicating greater city-level connectivity. However, this study found a decline in network efficiency, with the speed and effectiveness of ANPF—such as information flow and resource distribution—becoming less efficient over time. This contrasts with CSAP, where network density decreased, but network efficiency increased. This observation is significant as it introduces a dynamic understanding of how different agricultural networks evolve over time, which has not been widely addressed in existing literature. This study suggests that while increased connectivity might lead to tighter collaboration, it can also result in inefficiencies that require careful management of agricultural resources [7].

Third, one of the unique contributions of this study is the application of social network analysis (SNA) to ANPF. The spatial network structure of ANPF and CSAP in Anhui’s prefecture-level cities exhibited characteristics of multi-association, multi-core, and multidimensional connections, with no “isolated islands”. Hefei stood out with the most connections, exhibiting the highest in-degree and betweenness centrality, which reflects its role as a hub in Anhui’s agricultural science and technology innovation network. This finding aligns with existing research on the role of central cities in driving regional innovation [45] but adds new insights into how spatially distributed agricultural networks influence agricultural policy and resource allocation. By emphasizing Hefei’s central role, this study introduces a new perspective on how urban hubs can facilitate the diffusion of agricultural innovations across regions.

Fourth, this study identifies laborer quality, tangible means of production, and new-quality industries as the primary drivers of ANPF. These elements collaborate synergistically to drive the spatiotemporal differentiation in CSAP. Among these, tangible means of production, laborer efficiency, and new-quality industries exhibited the strongest interactions with other factors. This finding is consistent with recent literature highlighting the importance of technological, labor, and industrial transformations in agricultural productivity [46]. However, the novelty of this study lies in its emphasis on the interactivity between these core driving forces and its exploration of how they dynamically influence agricultural strengthening at the regional level.

The findings of this study contrast and complement existing research on agricultural modernization. While studies such as those by Li et al. (2025) and Wu et al. (2022) have emphasized the role of technological innovation and regional cooperation [47,48], the novelty of this study lies in its spatial network approach, which provides a more granular understanding of how ANPF interact across regions. This study’s identification of network inefficiencies, despite increased connectivity, adds a layer of complexity not typically addressed in existing work, highlighting the need for strategic interventions to improve resource flow and effectiveness.

Additionally, this study’s focus on multi-dimensional regional development, as seen in the differing trends across Central, Southern, and Northern Anhui, presents a more dynamic view of agricultural transformation, which extends beyond a simple linear analysis of growth. This contributes to the existing body of literature by showing that regional disparities in agricultural modernization are not only influenced by technological advancement but also by the interplay of local policies, resource allocation, and infrastructure development.

In conclusion, the findings of this study offer new insights into the complex interplay of ANPF and CSAP. By integrating spatial network analysis and highlighting the interactions between key driving forces, this study provides contributions to the field of agricultural development, particularly in the context of regional disparities and their implications for policy and practice.

5.2. Implications of Finding

Although grounded in the specific context of Anhui Province, our findings provide a transferable framework for understanding agricultural modernization across diverse socio-economic and geographic landscapes. The upward trajectories observed in ANPF and in CSAP suggest a replicable model for regions undergoing agrarian transition. In particular, the coordinated rise of laborer quality and technological innovation, as well as the emergence of new-quality industries, underpins a developmental strategy applicable to similarly positioned economies.

Our spatial analysis revealed a polycentric network structure—characterized by multiple hubs and interconnected pathways—which facilitates interregional resource flows and technological dissemination. This structure underscores the value of fostering multi-core agricultural networks that integrate urban innovation centers with rural production bases. For countries or regions with fragmented agricultural sectors, the development of such spatially optimized systems can enhance both productivity and resilience.

Crucially, this study emphasizes the importance of tailoring policies to regional conditions. Central Anhui’s leadership in ANPF contrasts with Northern Anhui’s infrastructural constraints and Southern Anhui’s ecological strengths—illustrating how differentiated, region-specific strategies are necessary for balanced development. This principle holds globally: regions with heterogeneous economic or ecological profiles should adopt targeted interventions that build on local advantages while mitigating systemic weaknesses.

The implications extend beyond agriculture to broader industrial and governance contexts. Technological convergence—particularly the integration of biotechnology, digital agriculture, and smart farming—emerges as a central engine of growth. Policymakers should not only incentivize research and development but also remove barriers to technology transfer, strengthen public–private collaboration, and improve the commercialization pipeline. Simultaneously, workforce development must accompany these innovations to ensure that productivity gains are inclusive and sustainable.

Governance structures also play a decisive role. The case of Hefei exemplifies how regional hubs can serve as anchors for policy coordination, innovation diffusion, and resource mobilization. For countries with multi-level governance systems, fostering such nodes can bridge administrative fragmentation and align national priorities with local execution.

Informed by these insights, we propose a set of policy directions with global relevance. First, establish integrated agricultural innovation systems that include funding mechanisms; streamlined commercialization pathways; and partnerships across academia, industry, and government. Second, design spatial strategies that strengthen central nodes while empowering peripheral areas, improving resource allocation and network efficiency. Third, institutionalize performance monitoring frameworks that track the evolution of ANPF and enable adaptive policymaking. Finally, embed agricultural modernization within broader development agendas to ensure coherence across sectors and governance levels.

Taken together, our findings argue for a nuanced, systems-level approach to agricultural transformation—one that balances technological innovation with human capital development, spatial planning with policy integration, and local specificity with global applicability.

5.3. Limitations and Future Research

This study has several limitations that could be addressed in future research. First, its focus on Anhui Province and the period from 2010 to 2022 may limit the generalizability of the findings to other regions or longer timeframes, suggesting the need for cross-regional and longitudinal comparisons. Second, the reliance on aggregated data at the prefecture level may overlook important micro-level variations, and future research could benefit from more granular data, such as household-level surveys or detailed agricultural sector data. Lastly, while this study focuses on economic and technological factors, it does not fully account for environmental and social factors, such as climate change and inequality, which can significantly influence agricultural development. Future research should explore the interaction between these factors to gain a more comprehensive understanding of agricultural modernization.

6. Conclusions

This study provides valuable insights into the dynamics of ANPF and CSAP, using Anhui Province as a case study. The findings show significant upward trends in both ANPF and CSAP from 2010 to 2022, accompanied by regional disparities. The application of spatial network analysis revealed how increased connectivity between cities led to tighter collaboration but also highlighted inefficiencies in resource flow, which suggests the need for targeted management strategies. Moreover, Hefei’s central role as a hub in agricultural science and technology innovation underscores the importance of key urban centers in facilitating regional development. This study also identified key driving factors—laborer quality, tangible means of production, and new-quality industries—that work synergistically to propel agricultural modernization. These findings contribute to the literature by offering a more nuanced understanding of how spatial network structures and interrelated driving forces interact across regions. By integrating technological, labor, and industrial factors, this study enhances our understanding of agricultural transformation, especially in contexts where regional disparities persist. Ultimately, this research lays the groundwork for the development of region-specific policies that can guide agricultural modernization globally, offering actionable recommendations for policymakers and stakeholders in both developed and developing agricultural economies.