Study on the Evaluation and Driving Factors of Interprovincial Virtual Cultivated Land Risk Transfer Under China’s Food Security Objective

Abstract

Driven by comparative returns, non-grain use of cultivated land (NGUCL) has intensified, posing risks to food security. This study approaches the problem by employing a risk transfer valuation framework, integrating a multi-regional input–output model with a synthetic risk index to establish China’s virtual cultivated land risk transfer network. Complex network analysis was utilized to explore its features while a temporal exponential random graph model was used to identify driving factors of its formation. Results indicate that fewer provinces took on additional pressures and risks. Despite differing motifs, transfer patterns showed little variation. Block analysis showed increasing net recipient relationships (from four to nine) and variable block divisions. Economic development and industrial structure are negatively associated with outgoing transfers, whereas population, production capacity and resource endowment are positively associated with them. The network exhibits time-dependent stability, with few new risk transfer paths forming. This study provides a theoretical basis and new ideas for optimizing land resource efficiency, re-shaping risk transfer patterns and maintaining food security.

1. Introduction

With the advancement of industrialization and urbanization, the economic returns from land resources have been increasingly substantial. Driven by comparative returns, many regions have prioritized short-term economic benefits from land [1,2]; the trends of “non-grain production” and “non-agricultural use” have intensified. Non-grain use of cultivated land (NGUCL) denotes the cultivation of non-grain crops on cultivated land. It has become increasingly prevalent in emerging economies’ grain-producing regions [3,4,5,6], posing new challenges to food security. Globally in 2022, an estimated 240 million people were faced with a food security crisis, with around 700 million suffering from acute shortages (The State of Food Security and Nutrition in the World 2023, FAO) [7]. As one of the most populous countries in the world with relatively scarce land resources, China has established a rigorous cultivated land protection system [8,9,10,11,12]. Nevertheless, low profitability continues to promote NGUCL conversion [13]. Comparative analysis of the second (2010) and third (2020) National Land Surveys reveals a 5.88% reduction in total cultivated land area, with substantial portions being converted for forestry and orchard uses [14]. Such a trend, if not handled properly, will result in a misjudgment impacting food security.

To ensure food security and protect cultivated land resources, regional economies and development are under pressure and facing risks. Against the backdrop of NGUCL, quantitative analysis of such pressure and risks is particularly crucial. One practical challenge is that cultivated land resources are fixed in location and cannot be moved, let alone traded. However, people’s demand for food keeps it in constant trade. Therefore, there is an urgent need for a method capable of resolving this contradiction. Virtual land trade has been proposed to reconcile the disparity between geographical distribution of land resources and demands of economic development and food security. It serves as a mediating tool that integrates various types of grain, enabling the quantification of the impact of grain trade [15,16,17]. It makes latent land resource flows explicit, providing a quantifiable scientific method for assessing actual food security risks in the process of NGUCL. Drawing on theories and the literature related to carbon emission pressure [18,19,20], virtual cultivated land flow has dual effects: on one hand, it alleviates pressure on cultivated land in receiving regions, while on the other hand, it increases pressure on exporting regions. Moreover, due to differences in economic, social and endowment aspects in different regions, the impact of this pressure transfer is spatially heterogeneous across different regions. Thus, such inequality in pressure transfers may compel some regions to reduce their economic growth rates to meet cultivated land preservation demands, resulting in potential risk of output losses, which can propagate through interprovincial trade, generating negative externalities for the entire economic system or failure to guarantee food security. From this perspective, virtual land transfer implies the transfer of pressure and risk. Therefore, it is essential to find an approach to measure such pressure and risk reliably so that it is then possible to coordinate risk transfer between regions, reducing overall risk.

This study proposed an approach from a risk transfer value perspective, combining a multi-regional input–output model with synthetic virtual cultivated land risk index to construct a virtual cultivated land risk transfer network. Complex network analysis and a temporal exponential random graph model were conducted to identify changes in features and patterns as well as crucial driving factors of the network, aiming to develop targeted solutions and policies for efficient land resource utilization and national food security. The major contributions of this study are as follows: First, it calculates the synthetic virtual land pressure index after taking the economic development levels of different regions into consideration. This approach optimizes the generally accepted calculation model for land pressure, making it more reflective of the actual situation. Second, by combining a multi-regional input–output model with the synthetic virtual cultivated land risk index, this study proposes an innovative method to evaluate the risk transferred between provinces. Third, given that existing research today mainly focuses on virtual water resources and carbon emissions, this study constructs a network for virtual cultivated land risk transfer, which provides a novel framework for research in this field. This study also offers new insights for exploring a horizontal compensation mechanism (HCM) for grain. Furthermore, by utilizing the temporal exponential random graph model (TERGM), this study takes time effects into consideration and constructs an innovative framework to better pinpoint the driving mechanisms of network formation.

2. Literature Review

In 1993, British scholar Tony Allen introduced “virtual water”, and the notion of “virtual land” was subsequently developed as an extension of this foundational idea [21,22]. It is used to represent the invisible land resource consumption embedded in agricultural trade [23], serving as a crucial tool for precisely quantifying regional virtual cultivated land risks and food external dependencies. In terms of quantification and measurement of virtual land trade, scholars have adopted many different methods [24,25,26]. Among them, the most commonly accepted and applied method is input–output analysis [27,28,29,30]. Input–output analysis (IOA) is a top-down approach that traces resource use or environmental emissions to final consumption via trade [31]. IOA models are classified as single-regional (SRIO) or multi-regional (MRIO) based on whether interregional economic linkages are incorporated in the input–output table [32,33]. A key limitation of SRIO models are their inability to differentiate between domestic and foreign production, whereas MRIO models provide more comprehensive data, making them more accurate for analyzing cross-regional trade [34]. Existing research has extended the MRIO method to the field of virtual land, but such studies remain relatively scarce, and those focusing exclusively on cultivated land are particularly rare [35,36,37,38], showing its promising prospect in this line of research. Therefore, this study builds upon the MRIO method and employs virtual cultivated land as the vehicle for its research.

Since virtual land reflects land resources embedded in inter-provincial trade, its inter-provincial flow will undoubtedly change the pattern of regional resource allocation, which would further affect resource pressure in different regions. The cultivated land pressure index is generally used to measure such pressure from the relationship between food production and consumption [29,39,40,41]. On the basis of this index, considering the heterogeneity of cultivated land quality, Xiang et al. proposed to revise the index by incorporating the correction coefficient for cultivated land quality [42,43]. This study followed this method but further incorporated economic factors into the existing cultivated land pressure index evaluation system, making it more responsive to research needs and reflective of the real situation, as it is the most critical factor affecting agricultural production choices [3]. Thus, this study arrived at a synthetic cultivated land pressure index, which serves as a cornerstone for subsequent research.

The discussion on the negative impacts of virtual resource trade has predominantly focused on risks related to water scarcity and carbon emissions, while largely overlooking the issue of virtual land transfer risk [44,45,46,47,48]. The risks studied in the field of land resources have different definitions, focusing on potential supply risks of virtual land [36]. This study applies the idea of resource scarcity risk transfer to land resource and introduces the Rasmussen coefficient to further construct a risk transfer model, attempting to measure such risks on the basis of virtual cultivated land pressure, clarify its network evolution mechanism and provide suggestions for regional coordinated development.

Following the acquisition of descriptive research findings, existing studies have also conducted extensive research on evolution mechanisms. When it comes to influencing factors, Structural Decomposition Analysis (SDA) has often been combined with the MRIO method [49,50,51,52]. However, the virtual cultivated land risk transfer network is complicated, shaped by a multidimensional variable system of endogenous structures and exogenous attributes. The TERGM proposed by Hanneke et al. is able to capture the temporal dependencies and dynamic features in the network by introducing time-dependent structural effects [53,54]. Existing research has already begun to combine the TERGM method with the MRIO method [46,55] in different fields, but such a combination is still rare in the field of virtual land transfer.

In summary, despite the growing body of research regarding virtual resource trade and risk, such studies are still very rare in the field of virtual cultivated land. Existing research on virtual resource risks primarily focuses on network structure and properties, with limited exploration of the underlying mechanisms driving risk transfer network formation. While MRIO and SDA methods are universally accepted in the study of virtual resource trade networks, few study have applied TERGM to analyze the factors influencing network formation and evolution, which can capture the time-dependent relationships and dynamic features in the network. Although the model of cultivated land pressure index has been continually revised and refined, it is still flawed in its consideration of economic factors. Therefore, using the above review as entry points, we constructed a model to measure virtual cultivated land transfer risk and apply the TERGM method to further examine the driving factors.

3. Methods

3.1. Multi-Regional Input–Output Model

In this study, interprovincial trade of virtual cultivated land is reflected through the multi-regional input–output model (MRIO), which provides a matrix framework for quantifying and tracking the flow of products and services across different regions and industries. Referring to the calculation of virtual water [31,56], this study calculates virtual cultivated land content as follows:

$${VL}_r={\displaystyle \frac{L_r}{Q_r}}$$

(1)

In the formula, ${VL}_r$ represents the direct land-use coefficient of region $r$. The agricultural output referred to in this study is defined as the first sector in the multi-regional input–output table, namely the sector encompassing agriculture, forestry, fisheries, and animal husbandry. $L_{r }$ represents the direct land area required in the production process of region $r$; $Q_r$ indicates total output of relevant sectors in region $r$. Assuming there are $i$ regions and $j$ sectors, the standard multi-regional input–output model can be written as follows:

$$Q_m^r=\sum _{s=1}^i\sum _{n=1}^j{z}_{mn}^{rs}+\sum _{s=1}^i{x}_{mn}^{rs}+e_m^r$$

(2)

where $Q_m^r$ represents the total output of sector $m$ in region $r$; $z_{mn}^{rs}$ represents the direct input of region $r$, sector $m$ to region $s$, sector $n$; $x_{mn}^{rs}$ represents the final demand for region $s$ provided by region $r$, sector $m$; $e^r$ is the export volume of region $r$, sector $m$ to other regions. The direct input coefficient $a$ refers to the amount of value of sector $m$ of region $r$ that is required for sector $n$ of region $s$ to produce one unit of output. The formula can be written as follows:

$$a_{mn}^{rs}={\displaystyle \frac{z_{mn}^{rs}}{Q_n^s}}$$

(3)

Formula (2) can therefore be modified to the following:

$$Q_m^r=\sum _{s=1}^i\sum _{n=1}^j{a}_{mn}^{rs}{Q}_n^s+\sum _{s=1}^i{x}_{mn}^{rs}+e_m^r$$

(4)

The formula can be expressed as the following matrix:

$$Q^{*}=A^{*}{Q}^{*}+X^{*}$$

(5)

In Formula (5), $Q^{*}=\left[Q\right]$ is the input matrix; $A^{*}=\left[{VL}_1,{VL}_2,{VL}_3,\cdots ,{VL}_r\right]$ is the direct input coefficient matrix; $X^{*}=\left[X^{sr},e^r\right]$ represents the final demand matrix. The next formula can be obtained through simplification and deformation of Equation (5):

$$Q^{*}={\left(I-A\right)}^{-1}{X}^{*}$$

(6)

In Formula (6), $I$ represents identity matrix; ${(I-A)}^{-1}$ is Leontief inverse matrix which can be used to calculate changes in output of region and sector induced by variations in final demand. Formula (6) is then further combined with a virtual cultivated land content matrix to obtain the following formula:

$$L=VL{\left(I-A\right)}^{-1}{X}^{*}$$

(7)

where $L$ represents the total area of virtual land embodied by all sectors of all provinces; $VL$ represents the land area directly used by a sector to produce one monetary unit. Due to the inherent limitations of input–output tables, considering data availability and quality, this study selected data from 2012 and 2017 as research data. Owing to data constraints, this research focuses exclusively on the 31 provincial-level administrative units of mainland China.

3.2. Synthetic Cultivated Land Pressure Index

3.2.1. Revised Cultivated Land Pressure Index

Building upon conventional cultivated land pressure index, considering the heterogeneity of land quality across different regions, Xiang et al. proposed a modified cultivated land pressure index, adjusting it by introducing correction coefficient for cultivated land quality [42].

$$K_s={\displaystyle \frac{K}{\sigma }}={\displaystyle \frac{\beta \frac{C}{pqk}}{S_a}}·{\displaystyle \frac{p_n{q}_n}{p_i{q}_i}}$$

(8)

$$K={\displaystyle \frac{S_{min}}{S_a}}, S_{min}=\beta {\displaystyle \frac{C}{pqk}}, \sigma ={\displaystyle \frac{p_n{q}_n}{p_i{q}_i}}$$

(9)

In Equations (8) and (9), $K$ is cultivated land pressure index, $S_{min}$ is minimum per capita cultivated land area, and $S_a$ is actual per capita cultivated land area; $\beta$ is food self-sufficiency rate. According to The National Medium-and Long-Term Plan for Food Security (2008–2020), which is referenced in the study of Gao et al. [43], the food self-sufficiency rate is set as 95%; $C$ is per capita food demand. Taking into account practices in the existing literature and the standards proposed by the National Advisory Council on Food and Nutrition, assuming an increasing trend, this study set the per capita food demand at 420 kg for 2012 and 437 kg for 2017. $p$ is grain output per unit area; $q$ is the proportion of sown area of grain to crops ($p_i$ and $q_i$ represent each province while $p_n$ and $q_n$ represent the whole country); $k$ is the multiple cropping index.

3.2.2. CRITIC Method

As this study attempts to measure the risk caused by NGUCL, the most important influencing factor is the economic level of different provinces. With economic development, people’s diverse needs have increased. As other crops offer greater economic returns, more and more cultivated land is being diverted to other uses to meet these demands [3,57]. Therefore, a synthetic cultivated land pressure index was constructed after considering economic factors. This study applies the CRITIC (Criteria Importance Through Intercriteria Correlation) method, which considers both indicator contrast intensity and inter-indicator correlation to measure regional cultivated land pressure.

To eliminate the influence of different quantitative frameworks on the evaluation results, dimensionless processing of the indicators is required. In this study, both indicators are positive (the greater the indicator, the greater the pressure), so forward processing is chosen:

$$X_{ij}={\displaystyle \frac{X_j-X_{min}}{X_{max}-X_{min}}}$$

(10)

The standard deviation is used to reflect the degree of fluctuation of the internal value differences in an indicator. A higher value denotes greater dispersion, which enhances the indicator’s informational content and discriminatory power.

$$S_j=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(X_{ij}-{\overline{X}}_j\right)}^2}{n-1}}}$$

(11)

$S_j$ is the standard deviation of the indicator $j$. The conflicting relationship is expressed as correlation coefficients:

$$R_j=\sum _{i=1}^p\left(1-r_{ij}\right)$$

(12)

$r_{ij}$ denotes the correlation coefficient between indicators $i$ and $j$. A high correlation coefficient between indicators signifies redundant information. To avoid duplicative assessment, such indicators should be downweighed to maintain the overall balance of the evaluation framework.

$$C_j=S_j\sum _{i=1}^p\left(1-r_{ij}\right)=S_j\times R_j$$

(13)

A higher value of $C_j$ indicates a greater role of indicator j in the overall system, and thus it should receive a higher weight.

The weight is calculated as follows (results shown in

Table 1. Weights determined by CRITIC method.

Indicators	Indicator Variability	Indicator Conflict	Amount of Information	Weight (%)
modified cultivated land pressure index 2012	0.235	0.502	0.118	46.673
level of economic development 2012	0.269	0.502	0.135	53.327
modified cultivated land pressure index 2017	0.177	0.467	0.083	39.215
level of economic development 2017	0.274	0.467	0.128	60.785

):

$$W_j={\displaystyle \frac{C_j}{{\sum }_{j=1}^p{C}_j}}$$

(14)

Finally, China’s regional virtual cultivated land pressure index was constructed as follows:

$$LPI=\alpha K_S+\beta E$$

(15)

where $LPI$ is the synthetic cultivated land pressure index and $E$ is the economic factor measured by per capita GDP (Gross Domestic Production), as it assesses residents’ economic well-being to a certain extent [58]. $\alpha , \beta$ are the weights defined by the CRITIC method (results shown in

Table 2. LPI calculation result.

Indicators	LPI 2012	LPI 2017
Beijing	0.958638056	1
Tianjin	0.829907636	0.575840735
Hebei	0.158546132	0.106460503
Shanxi	0.230739536	0.098342087
Inner mongolia	0.347456678	0.215035207
Liaoning	0.317608912	0.157430259
Jilin	0.172075267	0.159321938
Heilongiiang	0.120865655	0.081283325
Shanghai	0.742628651	0.647498392
Jiangsu	0.368051095	0.47848008
Zhejiang	0.488567252	0.424476507
Anhui	0.08459185	0.092496032
Fujian	0.335084107	0.355914254
Jiangxi	0.078987055	0.092726108
Shandong	0.251449029	0.270606258
Henan	0.089496731	0.11084687
Hubei	0.160614742	0.195194236
Hunan	0.10534227	0.129470627
Tibet	0.379462971	0.341082291
Guangdong	0.1263666	0.069674881
Guangxi	0.23203989	0.154291944
Hainan	0.183161195	0.21864009
Chongqing	0.109231192	0.10294041
Sichuan	0.133879021	0.069311928
Guizhou	0.111019852	0.046034401
Yunnan	0.210180836	0.087600948
Shaanxi	0.252629845	0.192101563
Gansu	0.145947164	0.018582963
Qinghai	0.406716684	0.135911858
Ningxia	0.171183974	0.142737535
Xinjiang	0.132281933	0.102749751

).

3.3. Virtual Cultivated Land Risk Assessment Model

3.3.1. Virtual Cultivated Land Risk Index

When virtual resources are traded between provinces, they alleviate resource pressures on the receiving side while increasing them on the sending side. Due to disparities across regions, this shift in pressure is asymmetrical. Such an asymmetric shift in pressure creates risk. Therefore, trade is valuable when it alleviates pressure and reduces risk, but not valuable when it does the opposite.

In this study, we followed the ideas of related studies [20], expressing the index as the product of the possibility of risk occurring and its impact.

$$LRI=LPI·LC$$

(16)

In this formula, $LRI$ represents cultivated land risk while $LPI$ is cultivated land pressure and $LC$ is the impact coefficient.

3.3.2. Rasmussen Coefficient

The unconventional variation in regional production scale can influence the entire national economy through input–output linkages [59,60], necessitating an assessment of its potential systemic economic impact. Thus, Rasmussen’s impact coefficient ($LC$) is employed to quantify the ripple effects of a unit production decline in one region on the total output of the national economic system [61].

$$LC={\displaystyle \frac{\frac{{\sum }_{s=1}^n{L}^{sr}}{{\sum }_{r=1}^n{\sum }_{s=1}^n{L}^{sr}}}{n}}$$

(17)

3.3.3. The Transfer of Cultivated Land Risk

This study calculates the amount of risk transfer triggered by virtual land trade through the process of Equations (18) and (19):

$${LR}_s^{st}={\displaystyle \frac{{VLT}^{st}{ · LRI}^s}{L^s}}$$

(18)

$${LR}_t^{st}={\displaystyle \frac{{{VLT}^{st}·LRI}^t}{L^t}}$$

(19)

${LR}_s^{st}$ denotes the amount of risk increased in region s while ${LR}_t^{st}$ denotes the amount decreased in region t. $L^s$ and $L^t$ represent the total cultivated land area of $s$ and $t$. Drawing on relevant research [20,62], this study measures the risk transmission value through the ratio of “benefits” to “costs”. That is, increased risk would be considered as a “cost” while decreased risk would be considered a “benefit”. If the value is greater than 1, then “benefits” are greater than “costs” and thus have a high value. Conversely, risk transmission is not valuable.

3.4. Network Connectivity Feature Analysis

To depict the structural characteristics and evolution trend of the inter-provincial virtual cultivated land transfer network in China, this study introduces a complex network analysis method. Firstly, motif analysis was used to detect the key microstructures of inter-provincial virtual cultivated land trade. Secondly, social network analysis was conducted to examine the overall linkages and individual characteristics of the network. The details of indicators chosen can be found in Appendix A. Thirdly, block model analysis was utilized to distinguish the different roles of network nodes, revealing the network’s overall structure and inter-group relationships [37,47].

3.5. Temporal Exponential Random Graph Model

The exponential random graph model (ERGM) is a statistical approach for analyzing network data that identifies relational patterns and their formation mechanisms. Unlike conventional methods, ERGM enables integrated analysis of how multidimensional variables such as endogenous network structures, node attributes, and exogenous covariates collectively shape the network. As an extension of dynamic networks, the temporal exponential random graph model (TERGM) proposed by Hanneke et al. is able to capture time-dependent relationships and dynamic features in the network by introducing time-dependent structural effects to better analyze the process of network structure evolution and its driving mechanism over time [53].

Based on the ERGM, this study takes the time factor into consideration and constructs a K-order Markov correlation TERGM from the discrete-time Markov chain principle, expressed as Equation (20):

$$P\left(Y=y^t|y^{t-k},\cdots ,y^{t-1},\theta \right)={\displaystyle \frac{e^{\left({\theta }^{T}h\left(y^t,y^{t-1},\cdots ,y^{t-k}\right)\right)}}{c\left(\theta ,y^{t-k},\cdots ,y^{t-1}\right)}}$$

(20)

where $y^t$ represents the virtual cultivated land risk transfer network in year $t$; $h\left(y^t,y^{t-1},\cdots ,y^{t-k}\right)$ is the set of variables containing endogenous network structure variables, time-dependent effect variables, node attribute variables and exogenous network covariates. In this study, the MCMC MLE (Markov Chain Monte Carlo Maximum Likelihood Estimation) method is chosen for parameter estimation.

Figure 1 and Figure 2 show the theoretical framework and Technical framework of methodology of this study.

3.6. Variables Selection and Data Sources

In this study, the 2012 and 2017 Chinese multi-regional input–output tables were directly obtained from CEADs (China Emission Accounts and Datasets) [63], which are a reliable source that is widely used in academic research [20]. The other research data used in this study were obtained from the China Statistical Yearbook and China Rural Statistical Yearbook of the studied period. Specifically, Per Capita GDP is used to represent the economic factor (measured in CNY). The unit for cultivated land area was one thousand hectares. The crop planting area and grain planting area were measured in thousands of hectares while the total grain output was measured in ten thousand tons. The virtual cultivated land pressure index was calculated from the above data.

Moreover, to conduct the analysis of the driving factors of the network’s formation and evolution, relevant variables were incorporated. In terms of the economy, this study uses GDP and the proportion of tertiary industry to represent the economic development level of a region. The unit of GDP is CNY 100 million and the proportion of the tertiary sector is a percentage. As for cultivated land pressure, resource endowment and population were employed to measure the shortage of cultivated land resources. Resource endowment is represented by the total cultivated land area, measured in thousands of hectares. Population refers to the year-end population of each region, with the unit being ten thousand people. Per Capita grain availability, calculated by dividing grain yield by population, was applied to measure the grain production capacity. All raw data was sourced from the China Statistical Yearbook and China Rural Statistical Yearbook of the studied period.

4. Results

4.1. Analysis of Inter-Regional Virtual Cultivated Land Trade

4.1.1. Virtual Cultivated Land Trade Overview and Spatial Pattern

Figure 3 shows the change in inter-provincial virtual cultivated land (VCL) trades in China. In terms of total volume, there is a small decrease from 2012 to 2017, which is in consistent with the variation trends of actual cultivated land areas in China. As a major grain-producing province, Heilongjiang has always been the province with the highest virtual cultivated land outflow, which accounted for 11.79% of the national total in 2012 and 9.73% in 2017. As for virtual cultivated land inflow, Shandong had the highest in 2012 (9.82% of the national total) while Henan had the highest in 2017 (7.29% of the national total).

As illustrated in Figure 4, it can be concluded that more provinces became virtual cultivated land net inflow regions. Consequently, those virtual cultivated land net outflow provinces had to take on more responsibility and export more resources. Spatially, net inflow provinces are mostly distributed in the southeast coast. Typically characterized by high levels of economic development, these provinces, where agriculture accounts for only a small proportion of the GDP and which often have substantial population bases, require large amounts of food imports to sustain rapid economic growth. Specifically, Guangdong and Shandong are the provinces with the highest net inflow. The three provinces of Northeast China have always been virtual cultivated land net outflow provinces, but their net outflow amount decreased from 10.78 million hectares to 7.51 million hectares. From 2012 to 2017, some inland provinces have turned from net outflow provinces to net inflow provinces. To compensate for these changes in the direction of net flows, the outflows of other net outflow provinces increased significantly (including Inner Mongolia, Gansu, Xinjiang, Yunnan and Guizhou). This reflects the shrinking of major grain-producing regions and the deepening imbalance between regional grain supply and demand, which, if left unchecked, will constitute a long-term threat to national food security.

4.1.2. Motif Analysis

This section focuses on micro-level patterns within the virtual cultivated land transfer network. FANMOD software was used to generate three-node motif codes which are detailed in

Table 3. Basic motif structures in the virtual cultivated land risk transfer network (2012).

No.	Motif	Frequency	Z-Value	p-Value	No.	Motif	Frequency	Z-Value	p-Value
6		32.24%	−2.57	1.00	14		10.60%	2.62	0.00
38		5.02%	2.54	0.00	174		6.66%	2.25	0.02
36		0.18%	−1.58	0.86	46		32.90%	−2.88	1.00
12		0.37%	−3.44	1.00	78		0.37%	−1.54	0.88
238		11.28%	−0.51	0.66	102		0.37%	−1.71	0.93

and

Table 4. Basic motif structures in the virtual cultivated land risk transfer network (2017).

No.	Motif	Frequency	Z-Value	p-Value	No.	Motif	Frequency	Z-Value	p-Value
6		23.21%	−1.02	0.85	14		13.46%	0.91	0.19
38		10.13%	0.62	0.26	174		9.17%	0.27	0.39
140		0.27%	0.64	0.22	166		0.67%	2.78	0.01
36		1.10%	−1.53	0.94	46		26.16%	0.75	0.22
12		3.32%	1.48	0.07	78		0.88%	−2.56	1.00
238		9.43%	2.62	0.02	102		1.80%	−2.44	0.99
164		0.40%	0.49	0.26

. In 2012, three motifs (38, 14 and 174) were identified as key due to their high frequency (>5%) and statistical significance (Z-value > 2). Among them, motif number 14 had the highest frequency and Z-value. This motif indicates reciprocity and the existence of “broker” type of collaborative operation mechanism. Such characteristics enable the network to adopt a cross-regional coordinated transfer mechanism, as the “broker” can help allocate resources between different regions (e.g., Yellow River basin and Yangtze River basin). Motif number 174 showed strong characteristics of agglomeration and reciprocity. This means provinces tend to participate in virtual cultivated land transfer in a clustered manner. Such a “Regional integration” motif is of great importance for coordinated development between provinces.

As for the year 2017, three motifs were identified as key motifs (motifs number 12, 238 and 166). Although all key motifs were different for 2012 and 2017, the micro-interaction patterns did not necessarily have distinct features. For instance, motif number 238, with a Z-value of 2.62, was evidently the most significant, showing characteristics of agglomeration and reciprocity within the network (similar to motif 174 in 2012). In addition, motif number 166 also had the characteristic of agglomeration. However, even though it had a large impact on the network (Z-value 2.78), it was not extensive (frequency 0.67%). Motif number 12 is a “broker” type of collaborative operation mechanism with a similar function as motif number 14 in 2012.

Overall, although the micro-motifs were quite different, there were no significant variations in the transfer patterns within the five-year period of study. It is also worth mentioning that only 10 out of 13 motifs were identified in 2012 while all motifs were found five years later. Such a result indicates that the motif structure tended to be more simplified, leading to more stable but less innovative inter-provincial trade.

4.2. Analysis of Inter-Regional Virtual Cultivated Land Risk Transfer

Virtual land trade can significantly affect changes in related regional risk, but this bidirectional influence frequently fails to offset at the level of risk valuation. As shown in Figure 5 and Figure 6, horizontally, the elements represent the virtual cultivated land risk transfer value from one province to another. It can be inferred that as a whole, the risk value matrixes of the years 2012 and 2017 were stable, showing similar trends and patterns. However, a closer analysis reveals that the situation in the year 2017 was worse than that of 2012. Although the overall pattern had changed by a small margin, it was still evident that the value of more interprovincial trade had decreased. On the south-east coast, most of the provinces (such as Shanghai, Jiangsu and Zhejiang) exhibited high virtual cultivated land risk inflow values while low outflow values. Moreover, some developed provinces elsewhere, such as Beijing, Tianjin and Guangdong, shared such features. This proves the pattern of inter-provincial transfer of virtual cultivated land occurring between the majority of less developed provinces to a few economically developed provinces, which further highlights the unevenness of the change in the responsibility for food security.

Some of China’s major grain production bases, such as Jilin, Heilongjiang, Henan, Inner Mongolia and Anhui (they are now the only five provinces in China with net grain exports), generally have higher virtual cultivated land risk outflow values and low inflow values. From the perspective of efficiency, it is beneficial for the country as a whole if these provinces continue to maintain a net outflow, but it is important to recognize that these regions deserve to be compensated for the contributions and sacrifices made to ensure national food security.

4.3. Network Analysis of Virtual Cultivated Land Risk Transfer

4.3.1. Overall Structural Characteristics of the Network

To analyze the structural evolution of the interprovincial virtual cultivated land risk transfer network of China, this study compared key network metrics between the years 2012 and 2017, including degree centralization, in/out-degree centralization, network density and average distance. These indicators reflect the concentration, connectivity and efficiency of the overall network structure. The detailed result can be found in

Table A1. Microstructural features of virtual cultivated land risk transfer network.

	2012					2017
	Out-Deg	In-Deg	Out-Clos	In-Close	Between	Out-Deg	In-Deg	Out-Clos	In-Close	Between
Beijing	0	28	120	36	0	0	28	150	38	0
Tianjin	0	27	120	39	0	0	28	150	38	0
Hebei	21	0	57	120	0	21	0	66	150	0
Shanxi	19	25	61	43	6.723	20	18	70	52	10.248
Inner mongolia	19	23	61	45	3.507	20	12	70	67	0
Liaoning	17	26	63	42	3.943	19	22	71	47	4.099
Jilin	21	1	57	117	0	20	17	70	56	5.039
Heilongiiang	24	0	48	120	0	21	0	66	150	0
Shanghai	0	28	120	36	0	0	28	150	38	0
Jiangsu	17	26	63	42	3.943	17	27	74	42	7.035
Zhejiang	14	26	67	42	0.602	12	27	80	42	0.184
Anhui	23	0	51	120	0	21	0	66	150	0
Fujian	15	26	66	42	1.124	11	27	83	42	0
Jiangxi	21	5	57	105	0	19	21	71	48	2.692
Shandong	20	22	60	46	8.325	19	23	71	46	7.253
Henan	23	0	51	120	0	21	0	66	150	0
Hubei	20	20	60	48	4.333	19	22	71	47	4.099
Hunan	21	0	57	120	0	19	21	71	48	2.692
Tibet	16	26	64	42	2.187	17	27	74	42	7.035
Guangdong	20	14	60	58	0	21	0	66	150	0
Guangxi	14	26	67	42	0.602	12	27	80	42	0.184
Hainan	18	25	62	43	3.878	17	27	74	42	7.035
Chongqing	23	0	51	120	0	21	0	66	150	0
Sichuan	20	18	60	51	1.793	21	0	66	150	0
Guizhou	23	0	51	120	0	21	0	66	150	0
Yunnan	11	26	72	42	0	13	27	78	42	1.137
Shaanxi	19	25	61	43	6.723	18	26	72	43	13.408
Gansu	20	17	60	52	1.128	21	0	66	150	0
Qinghai	2	27	114	39	0	12	27	80	42	0.184
Ningxia	16	26	64	42	2.187	15	27	76	42	3.677
Xinjiang	21	5	57	105	0	21	0	66	150	0

of Appendix A.

The degree centralization slightly increased from 0.474 in 2012 to 0.484 in 2017, indicating a modest enhancement in overall concentration of network connections. This suggests that the network structure became marginally more centralized over time, with a few provinces playing increasingly dominant roles in virtual cultivated land risk transfer. In terms of directionality, in-degree centralization increased slightly from 0.389 to 0.399, while out-degree centralization significantly decreased from 0.251 to 0.158. This indicates that the inequality among risk value inflow provinces became slightly more pronounced, whereas the inequality among risk value outflow provinces declined considerably. The findings suggest a diffusion of virtual land risk among different provinces—more provinces began participating in risk value outflow activities, making the risk source more decentralized, while the risk value transferred became more concentrated in a smaller number of provinces.

The network density remained high and relatively stable, slightly declining from 0.557 in 2012 to 0.547 in 2017. This consistently high density reflects the extensive and complex interconnections among provinces in the virtual cultivated land risk transfer network. Despite the slight decrease, the overall connectivity of the system remained strong, indicating a mature and closely linked interregional transfer pattern.

The average distance of the network increased from 1.091 to 1.133, implying a slight decline in transfer efficiency. To elucidate, the average number of steps required for virtual land risk to travel from one province to another grew marginally, suggesting that some direct transfer paths may have been weakened or replaced by longer chains of intermediation. This could be linked to regional trade restructuring or adjustments in agricultural production layouts.

Collectively, the results reveal that while the virtual cultivated land risk transfer network in China maintained a highly connected structure between 2012 and 2017, there were notable shifts in the spatial organization of risk. The rise in in-degree centralization and average distance, along with the decline in out-degree centralization, indicate that the pressure and risks have become more evenly shared, while a smaller number of developed provinces continue to absorb disproportionate levels of risk value, exacerbating spatial inequality. These dynamics underscore the importance of differentiated policy interventions that promote equitable risk allocation and enhance overall network resilience.

4.3.2. Individual Node Characteristics Analysis

An analysis of node-level metrics reveals significant spatial and structural differentiation in the virtual cultivated land risk transfer network. In terms of out-degree centralization, which reflects a province’s capacity to export cultivated land pressure and risk value, provinces such as Henan, Anhui and Guizhou consistently ranked among the top in both 2012 and 2017. Notably, Sichuan and Gansu emerged as key value-output provinces in 2017, replacing Heilongjiang and Chongqing, suggesting a westward shift in the burden of cultivated land pressure. Conversely, in-degree rankings demonstrate that Beijing, Shanghai and Tianjin remained the dominant recipients of risk value across both years, indicating persistent structural dependence on external regions for cultivated land support. Interestingly, Qinghai and Xizang, which ranked highly in 2012, were replaced by Jiangsu and Hainan in 2017, signifying a growing reliance from more economically developed coastal regions.

In terms of closeness centrality, Beijing, Shanghai and Tianjin exhibited high out-closeness values, meaning they are structurally well-positioned to quickly transfer cultivated land value across the network. Provinces like Henan, Anhui and Guizhou maintained high in-closeness, highlighting their exposure and sensitivity to external risk inflows. Moreover, betweenness centrality, which captures a province’s role as a broker or intermediary, saw significant increases for Shaanxi, Shandong and Shanxi, which consistently held central bridging positions in both years. The rising centrality of Jiangsu and Xizang in 2017 also indicates growing heterogeneity in the paths of risk transfer, with more provinces taking on strategic intermediation roles.

These findings suggest a gradual but notable reconfiguration of the network: while economically developed eastern provinces remain the main risk value sinks, the network’s intermediaries and output sources have diversified westward. This implies a potential shift in national cultivated land risk governance, where resource-endowed but economically less-developed regions are increasingly embedded into national-level food security risk mediation, thereby reinforcing spatial inequalities in risk burden distribution.

4.3.3. Block Model Analysis

Block modeling refers to the chunking of spatially linked networks through spatial clustering methods, which in turn explores the composition of the network and the net sender relationships between the segments [64]. The CONCOR algorithm (convergence criterion 0.2, maximum cut-off depth 2) is used to analyze the capital flow network in China as a block model, dividing the 31 provincial-level administrative regions into four functional blocks.

Specifically, there are more receiving relationships than sending relationships in Block1, which establishes it as the net recipient block. There are much more sending relationships than receiving relationships in Block 2, which is recognized as the net sender block. Block 3 has more receiving relationships than sending relationships, and connections from other blocks account for a relatively large proportion of its relationships. These features characterize Block 3 as the major net recipient block. As for Block 4, it exhibits substantial bidirectional interactions with others; the number of receiving relationships is approximately equal to sending relationships. This pattern qualifies Block 4 as a broker block. It is worth noting that unlike in most existing studies, a bidirectional net sender block was not identified, suggesting the spatial correlation of virtual cultivated land risk transfer between blocks is more significant than that between provinces inside of one block, i.e., provinces tend to make value transfers between different blocks to alleviate pressure and risk. Such a result of block division also indicates that, in existing risk transfer patterns, net recipient regions far outnumber net sender regions (Figure 7 and Figure 8).

In comparison, the arc length of the bond at the receiving end of Block 1 (net recipient block) in 2017 is much longer than that of 2012, indicating an increase in net recipient relationships, which further reveals the deterioration of the situation of virtual cultivated land risk transfers. Block 1 of 2012 (net recipient block) was made up of mostly developed provinces and China’s major grain-consuming provinces (Beijing, Tianjin and Shanghai), which corroborates that economic development is a crucial factor for risk transfer and developed provinces are in a position of strength. This block continued to grow in size in 2017, with a total of nine members. These members included five out of seven major grain-consuming provinces, which further confirmed a deteriorating trend as more economically developed provinces turned into net recipient blocks, making other provinces less productive in grain production.

Despite the decrease in the number of members in Block 2 (major net recipient block), seven provinces stayed in the block throughout the studied period. It is worth mentioning that, in 2012, only 4 out of 13 provinces in Block 2 were major grain-producing provinces. The proportion increased significantly in 2017 (six out of nine provinces), showing a worrying trend in which major grain-producing provinces turned into net recipient regions in risk transfer valuations.

As the main source of risk value outflow, Block 3 (the net sender block) carried a lot of responsibility in maintaining national food security. While the block had 10 members in both years, it varied considerably—only half of its members stayed in the block during the studied period. Nevertheless, major grain-producing provinces were still in the majority.

Block 4 (the broker block) was the block of greatest change. But beyond all these changes, it was quite stable in total volume. Such drastic changes illustrate that the spatial linkages of virtual cultivated land risk transfer in China were not limited to geographical proximity or any fixed mode—they were more like a dynamic equilibrium.

4.4. Identification of Virtual Cultivated Land Risk Transfer Network Formation Mechanisms

After analyzing the characteristics and patterns of the virtual cultivated land risk value transfer network, this section will further employ the TERGM to explore the formation mechanisms of the spatial correlation network of virtual cultivated land risk transfer. The results are illustrated in

Table 5. TERGM estimation results for the virtual cultivated land risk transfer network.

Variable		Model 1	Model 2	Model 3	Model 4	Model 5
Network Endogenous Structure	edges	12.6152 *** (2.7133)	11.5538 *** (2.6689)	11.0675 *** (2.9659)	2.4311 (6.7627)	4.7519 (6.6310)
	mutual (reciprocity)		0.5805 * (0.2907)	0.5911 (0.3187)	1.7948 * (0.9087)	1.8316 * (0.9038)
	twopaths (connectivity)			−0.1093 * (0.0553)	−0.1722 (0.1060)	−0.1746 (0.1034)
	ctriple (circularity)			0.3154 *** (0.0742)	0.6072 *** (0.1517)	0.6115 *** (0.1502)
Outgoing Effects	gdp	−3.1557 *** (0.8173)	−4.3829 *** (1.0285)	−9.1874 *** (1.5144)	−19.2639 *** (3.3169)	−19.2774 *** (3.2671)
	structure	−12.2324 *** (2.1773)	−12.0801 *** (2.2245)	−10.1689 *** (2.1806)	−20.2953 *** (4.8515)	−20.2603 *** (4.9086)
	resource	5.9019 *** (0.8934)	5.7504 *** (0.9162)	4.5500 *** (0.9019)	13.5485 *** (2.5933)	13.6292 *** (2.5787)
	capacity	−1.2018 (0.6798)	−0.8932 (0.7125)	0.7683 (0.7498)	−3.3827 * (1.6910)	−3.4279 * (1.6843)
	population	2.3013 (1.2848)	4.0346 ** (1.5611)	10.7550 *** (2.1564)	17.2771 *** (3.8602)	17.2464 *** (3.7841)
Incoming Effects	gdp	16.1537 *** (1.0769)	16.3912 *** (1.1069)	17.7693 *** (1.1443)	29.9450 *** (3.8471)	29.9884 *** (3.7381)
	structure	0.2227 (2.1769)	0.8446 (2.2567)	4.7519 (2.4492)	0.3096 (5.3247)	0.1995 (5.3144)
	resource	0.2358 (0.8134)	−0.1006 (0.8244)	−1.7133 (0.8889)	−29.9292 *** (3.7125)	−29.8308 *** (3.7789)
	capacity	−4.0020 *** (0.6975)	−3.9724 *** (0.6930)	−3.8680 *** (0.7118)	16.0751 *** (2.5538)	15.9728 *** (2.6104)
	population	−21.7727 *** (1.5306)	−22.0004 *** (1.5551)	−23.2980 *** (1.5873)	−20.4396 *** (4.0372)	−20.5900 *** (4.0185)
Heterogeneity	gdp	2.6821 *** (0.6583)	2.5678 *** (0.6834)	2.0949 ** (0.6373)	3.3398 (1.7160)	3.3749 * (1.6975)
	structure	−3.1503 (2.6646)	−2.7498 (2.6102)	−2.5403 (2.5827)	−1.0136 (5.6924)	−1.0761 (5.6501)
	resource	1.8435 ** (0.5694)	1.9156 *** (0.5649)	1.1106 (0.5898)	−0.4342 (1.5422)	−0.4084 (1.5171)
	capacity	−1.1580 * (0.4801)	−1.0952 * (0.4720)	−0.7201 (0.4722)	−1.2227 (1.1092)	−1.1900 (1.1005)
	population	−2.4687 ** (0.8640)	−2.4007 ** (0.8868)	−2.0065 * (0.8325)	−2.3084 (2.0525)	−2.3811 (2.0213)
Time-Dependent effects	stability				2.010594 *** (0.363592)
	innovation					−3.995436 *** (0.731878)
Co-Network	geographic	−0.000500 *** (0.000130)	−0.000458 *** (0.000126)	−0.000372 ** (0.000123)	−0.000073 (0.000275)	−0.000066 (0.000279)
Num.obs		1860	1860	1860	930	930
AIC		1017.717503	2154.441794	2113.908187	256.325473	256.116727
BIC		1111.699143	2266.725942	2238.668352	357.864349	357.655603

*** p < 0.001; ** p < 0.01; * p < 0.05.

. Model 1 is a baseline model that contains only edges, models 2 and 3 sequentially include three endogenous structural variables (reciprocity, connectivity and circularity) to test endogenous mechanisms of the model, and models 4 and 5 are comprehensive models that include stability and innovativeness as time-dependent effects, respectively.

4.4.1. Network Self-Organization Behavior

In Table 4, the coefficients of reciprocity (mutual) and circularity (ctriple) are positive, implying a significant impact on the formation of the network. The positively significant coefficients for reciprocity suggest that risk transfers between regions exhibit a relatively common two-way reciprocal tendency. Meanwhile, the coefficients for circularity indicate the interdependence and complexity of inter-provincial trade of virtual cultivated land risk, which may result in a dynamic regional cooperation relationship. The existence of such circular relationships may contribute to greater stability and coordination of inter-regional trade of risks.

The coefficients for connectivity (twopaths) are statistically insignificant, suggesting that there is no clear tendency towards connectivity in the network. In other words, it is more common to form a pattern of direct bilateral relationships between provinces rather than multi-level transmission between more than two provinces. Such results revealed that a relatively small number of core provinces dominate the sending and receiving of virtual cultivated land risk.

4.4.2. Time-Dependent Effects

In terms of time-dependent effects, the stability coefficient exhibits a positive and significant association, whereas the innovation coefficient is negative and statistically significant. The former indicates a high degree of persistence and continuity in interprovincial virtual cultivated land risk transfer relationships. The latter, on the other hand, suggests that the formation of new risk transfer paths is inhibited to some extent.

The persistence and continuity can be explained as resulting from multiple factors, such as industrial layout, established trade relations, market behavior and so on. Such characteristics make risk aversion and economies of scale possible while equally making optimization and improvement difficult. In addition to this, the negatively significant innovation coefficient also reflects the difficulty in exploring new risk trade paths, which is attributed to a variety of reasons such as trading barriers, trading expenses, risk estimation and so on. In conclusion, the inter-provincial trade pattern of virtual cultivated land risk is highly fixed. Effective measures ought to be taken to improve the situation, as there are obvious flaws, such as the lack of reciprocity mentioned in previous analyses, in the current pattern of virtual cultivated land risk transfer.

4.4.3. Social Selection Behavior

The factor of economic aggregation shows negative significant sending effects. A region with high economic aggregation faces higher virtual cultivated land risk, as it tends to invest resources into high value-added production, crowding out grain production. Thus, such a region will seek to cut down on its export of virtual cultivated land in order to reduce its own virtual cultivated land risk.

Conversely, economic factors show positive significant receiving effects. A large portion of China’s major grain-consuming areas are provinces with large amounts of economic aggregation, such as Beijing, Shanghai, Guangdong, Zhejiang, etc. The rapid development of the economy in these provinces led to a reduction in achievement of agricultural scale and development of agricultural production. Developed provinces have significantly higher marginal returns in secondary and tertiary industries (e.g., technology, finance and high-end manufacturing) or in the production of other cash crops than in grain production. Huge food consumption demands due to long-term net population inflow is another explanation for the growth in the propensity to import virtual cultivated land risk value in economically developed provinces. Some provinces, although abundant in grain production, may still face high virtual cultivated land risk due to overpopulation (e.g., Jiangsu, Shandong and so on).

As for sending effects, the coefficients of industrial structure are significantly negative, indicating that a higher percentage of the tertiary industry has negative impacts on risk-value-sending relationships between provinces. The current significant wage premium in the tertiary sector and the consequent continued outflow of young and able-bodied labor is causing difficulties in food production and thus a reduction in virtual cultivated land risk exports. In addition, commercial land yields far exceed those of agriculture, causing urban sprawl to eat up cultivated land. The growth of the tertiary industry may come at the expense of space for agricultural development. Therefore, regions that overly rely on the tertiary industry may experience agricultural shrinkage. To adapt to the rapid development of productivity, the export of virtual cultivated land shall decrease to keep the province’s own risk at a manageable level. Such a tendency is similar to that of the influence of economic factors analyzed above. It is worth mentioning that industrial structure factors have little impact in terms of outgoing effects, which suggests that a province’s change in industrial structure mainly influences its propensity to export rather than import.

The coefficients of grain production capacity are statistically insignificant, showing little effect on outgoing effects. This means that the ability to produce grain has no significant influence on the export of risk value. In contrast, the coefficients of grain production capacity showed significant negative effects on incoming effects, as higher capacity means higher efficiency in agricultural production. However, such a relationship was reversed in the long term, as the coefficients are significantly positive in model 4 and model 5. Such a phenomenon can be explained by the soaring value of highly productive cultivated land, which will in the long term induce non-grain use. Its release of labor and resources may continue to flow to high value-added industries, reversing agricultural production.

Resource endowment plays an important part in the export of virtual cultivated land risk value. Adequate resource endowment makes exports more robust and profitable. In this way, a province with sufficient resource endowment will have lower virtual cultivated land risks, which will then encourage it to develop a tendency to export virtual cultivated land.

A large population provides both labor and market demand and may also drive agricultural output well beyond local consumption through scale effects, which ultimately translates into export advantages. Thus, a region with a large population may not be reluctant to generate sending relationships with another region but instead will export its risk transfer value to make the most of its advantages.

Economic factors have the most significant impact on heterogeneous effects, suggesting that virtual cultivated land risk transfer valuation is more likely to happen between regions with large economic disparities. Such regions may also differ in the efficiency of agricultural production, which gives them a tendency to trade, optimizing the allocation of resources between regions at different levels of development.

Population factors also have a significant impact. Provinces with large demographic differences are more inclined to form trade relations due to multiple gaps in labor supply, food demand, etc., thereby alleviating this unfair distribution.

4.4.4. Network Embedding Effect

This study uses the spherical distance between provincial capitals (km) to represent the influence of geographical distance. As for exogenous network effects, geographic distance is significantly negatively correlated, reflecting the important role of geographic distance on the cost and convenience of inter-regional virtual cultivated land risk transfer. Shorter geographic distances typically imply lower transport and communication costs as well as higher investment controllability and therefore are more favorable to risk transfer. Also, provinces with shorter geographic distances are likely to have closer cultural relationships, which would make them more open to generating trade relations.

A graphic representation of influencing factors and network effects are shown in Figure 9

4.5. Model Validation

A goodness-of-fit (GOF) test was conducted to diagnose MCMC convergence and verify the robustness of the model estimates (Figure 10). The convergence test confirms the efficacy of the identified drivers in explaining network formation. The goodness of fit of the model was assessed by comparing the original network (solid black line) against a distribution of simulated networks. The dashed lines and box plots form a 95% confidence envelope for the simulated network statistics. The fact that the observed statistics largely fall within this envelope indicates that the model captures the salient structural features of the original network. The ROC (Receiver Operating Characteristic) curves are also plotted to observe the fitting effect of the model. It is found that the ROC curves enclose a very large area around the diagonal, which indicates that the model is fitted well.

5. Conclusions and Discussion

5.1. Conclusions

This study performs a comprehensive analysis of virtual cultivated land risk transfer through a combination of the MRIO method, complex network analysis and the virtual cultivated land risk assessment model. Then, by applying the TERGM method, this study conducted an in-depth investigation of driving factors of the formation and evolution of virtual cultivated land risk transfer network as well as its characteristics. The conclusions are summarized as follows:

• In terms of virtual cultivated land trade, China’s total amount in 2017 was slightly lower than in 2012. The number of China’s net virtual cultivated land inflow provinces increased significantly, which reflects the shrinking of major grain-producing regions and the deepening imbalance of supply and demand. On a micro-level, characteristics of connectivity, agglomeration and reciprocity were recognized within the network. Although key motifs were found to be different, no significant variations were detected in the transfer patterns from 2012 to 2017, and inter-provincial virtual cultivated land trade tended to be more simplified but less innovative.
• Although the overall pattern of the risk value matrix has only minor changes, it is evident that the value of more inter-provincial trade has decreased. The pattern of inter-provincial risk transfer occurs from the majority of less developed provinces to the minority of economically developed provinces, which further underscores the inequality of the responsibility of food security. While the virtual cultivated land risk transfer network maintained a strongly connected structure, notable changes were identified in its spatial organization. The rise in in-degree centralization and average distance, along with the decline in out-degree centralization, indicate that pressures and risks have become more evenly shared; a smaller group of developed provinces continue to absorb disproportionate levels of risk value, intensifying spatial inequality. Block model analysis divided 31 provinces into a net recipient block, net sender block, broker block and major net recipient block. From 2012 to 2017, the proportion of net recipient blocks increased significantly, indicating a worrying trend. The members of different blocks varied during the studied period, but overall, major grain-production regions bear more risks and economically developed provinces are the net recipients.
• It was found that a small number of economically developed provinces are in a favorable position while less developed provinces bear more cultivated land pressures and risks, with their evolution tending towards deterioration. As for spatial-temporal dimension, the virtual cultivated land risk transfer network exhibits significant time-dependent effects, manifesting itself in strong path-dependent characteristics and limited path-innovation capabilities. In terms of influencing factors, the impact of economic development is similar to that of industrial structure. Resource endowment solely showed a positive outgoing effect while grain production capacity was only significant in incoming effects. Contrary to common belief, population was actually beneficial for the generation of sending relationships and negatively associated with the generation of receiving effects.

Based on these conclusions, under the objective of maintaining food security, we propose paying more attention to the major grain-producing regions who bear growing pressures and risks and increasing policy support for their economic development and agricultural production, as the pattern of risk transfer valuation occurs from a majority of less developed provinces to a minority of developed provinces. Also, it is crucial to continue strengthening the protection of cultivated land resources, ensuring the balance between land reclamation and occupation. Regarding the issue of the reduced value of inter-provincial risk trade, land-use efficiency needs to be improved, so more meticulous regulations on cultivated land use are required. We should promote more cutting-edge agricultural technologies and comprehensively reduce virtual cultivated land risks.

5.2. Discussion

The pressure and risk calculation system used in this study is consistent with the prevailing consensus in the field [20,46,65]. Building upon this foundation, certain expansions and innovations have been implemented, such as the adoption of the TERGM, and the construction of the synthetic virtual cultivated land pressure index. Compared to other studies in the same field [25,30,31], which focus on global scales or multiple land types, this paper adopts a smaller research scale and focuses on a more concentrated subject (cultivated land), thereby contributing to the enrichment of current research in this domain. Regarding the research conclusions, our findings are in line with the work of Song et al, Wang et al. [66,67], who also reported an increase in virtual land flow and intensified pressures in inland provinces, as well as the impact of regional disparities.

In order to ensure food security, more targeted and powerful measures need to be adopted. As a start, it is essential to establish a Horizontal Compensation Mechanism (HCM) among provinces. The Chinese government is already actively promoting the construction of such government-mediated interregional bargaining mechanisms, aiming to balance regional interests through fiscal transfers from grain-consuming to grain-producing regions [68]. Likewise, virtual cultivated land risk can also be balanced through such mechanisms, as the root cause of NGUCL are economic factors. When established, it will function as a regional equalization instrument, reducing the risks of all provinces to an acceptable level.

To optimize an HCM, a standardized accounting system for grain ecosystem services should be developed to calculate the transfer amount reliably. Based on research data, it is recommended to establish and improve the HCM according to the transfer of virtual cultivated land risk. Provinces that bear more pressure and risks deserve more compensation. Such compensation shall be determined comprehensively based on multiple factors such as the economic development level of a region. Also, a provincial-level trading platform for the balance of virtual cultivated land and a unified calculation scheme can be established to better record transactions and determine the amount of compensation. Governments can also strengthen macro-controls, set up special funds to monitor the development of HCM and provide targeted support for specific provinces. The existing literature has not yet explored such methods in-depth, leaving a promising direction for future research. Many possible solutions, including opportunity cost pricing, the aggregate weighting method and performance appraisal systems may all be considered before a final solution is obtained.

In addition to improve the situation of regional balance, consideration should also be given to reducing the total volume of virtual cultivated land risk. To do so, land-use efficiency must be improved. Thus, more research can be conducted relating to the driving factors of the virtual cultivated land risk transfer network. In this study, five driving factors were identified and analyzed. However, the formation and evolution of the network are complicated, affected by many factors. In future studies, more driving factors can be discussed and examined.

A profound comprehension of regional disparities in land-use patterns and their evolving trends is essential for enhancing land-use efficiency and maintaining food security. One of the limitations of this study is the inability to consider all factors in a holistic manner, such as provincial policy factors. Since the focus of this study is the NGUCL and the economic element is the primary element of such practice, incorporating other factors would not be the primary consideration. In the future, more factors and perspectives could be considered, including price signals, climate factors and topographic factors [69], making the research of cultivated land pressure and risk more comprehensive and in-depth. Additionally, in terms of model optimization, a two-wave TERGM may also be considered, which better addresses data scarcity issues. Also, the scope of this study was set to be a 5-year period due to data availability. Regarding this, future studies can be conducted over a longer time span so that more features and patterns can be discovered, making the conclusions more responsive to long-term trends. Since most data were obtained directly from statistical yearbooks, measurement errors remain in this study despite accounting for crop rotation factors.