System theory posits complex systems comprise interrelated subsystems or elements characterised by intricate coupling relationships. The coupling coordination degree model is founded on system theory, which perceives the internal components of a system as an interconnected and interactive organic entity, facilitating quantitative analysis and evaluation. The coupling coordination model is extensively employed across various domains, including regional economics, industrial growth, social management, and ecological environments. Using the coupling coordination degree model, the interaction intensity among elements can be measured, allowing for a more comprehensive analysis of the system’s operational state. This establishes a foundation for system optimisation and facilitates the identification of issues within the system, enabling the implementation of specific enhancement strategies (Sun et al., 2024a). This paper utilises the coupling coordination degree model to examine the interplay between agricultural carbon emission efficiency and food security. The particular formulas employed are as follows (see Equations 10–12): C = C E E × F S / C E E + F S 2 2 1 / 2 (10) D = C × T 1 / 2 (11) T = α × C E E + β × F S (12) where C represents the coupling degree, and the value range is [0,1]; α and β represent coefficients to be determined. This paper believes that carbon emission efficiency and food security are equally important, so α and β are assigned the value of 0.5; D represents the coupling coordination degree. Based on previous research findings (Gu et al., 2023), the level of coupled coordination is classified into four categories: severe dysfunction, impending dysfunction, essential coordination, and extreme coordination. The coupling coordination degree is split into 12 subcategories based on the two primary characteristics of synchronous coordination and lagging dysfunction, together with the composite index of the two systems (CEE, FS) (Table 5).

The Gini coefficient is a conventional metric for assessing income or resource distribution inequality. In contrast, the Dagum Gini coefficient enhances and refines the Gini coefficient by employing the probability distribution function of the Dagum distribution. In comparison to the conventional Gini coefficient method, the Dagum Gini coefficient decomposition method adeptly addresses the issue of cross overlap among subsamples, allowing for the disaggregation of spatial disparities into intra-regional differences, inter-regional differences, and hypervariable density, thereby yielding more rigorous and precise measurement outcomes (Zhang L. et al., 2022). This method is primarily employed to analyse the distribution of resources across several countries, regions, or historical periods, thereby elucidating developmental disparities and imbalances among regions. This paper uses the Dagum Gini coefficient decomposition approach to examine the regional disparities and their origins in the interconnected coordination of agricultural carbon emission efficiency and food security. The specific formulas used are as follows (see Equation 13): G = ∑ j = 1 k ∑ h = 1 k ∑ i = 1 n j ∑ r = 1 n h y j i − y h r 2 n 2 μ (13) where n represents the number of provinces, k represents the number of total regions, n _j , n _h represent the number of provinces within regions j and h, y _ji , y _hr represent the degree of coupled coordination of the two systems in any province within regions j and h, μ represents the mean value of the degree of coupled coordination of the two systems. The method decomposes the Gini coefficient G into three components: intra-regional variations Gw, inter-regional variations Gb, and hypervariance density Gt. This decomposition fulfils the equation G = Gw + Gb + Gt.

Kernel density estimation is a non-parametric method that approximates the probability density function of a dataset by applying a kernel function to each data point and aggregating the results. In cases where the distribution form of the data is unknown or intricate, non-parametric kernel density estimation serves as an effective method for estimation that does not necessitate assumptions regarding the data distribution, instead deriving inferences directly from the data samples and is suitable for distributions of all shapes and types (Han X. et al., 2023). Consequently, it effectively represents the overall distribution of the coupled coordination degree of agricultural carbon emission efficiency and food security in the main food-producing areas. Furthermore, it can capture the dynamic characteristics of this distribution over time. The specific formulas used are as follows (see Equations 14, 15): f x = 1 n h ∑ j = 1 n k x j − x ¯ n (14) K x = 1 2 π e − x j 2 2 (15) where n represents the number of observations, x _j represents the independent and identically distributed observations, x ¯ denotes the mean value of the observations, and h represents the optimal bandwidth.

Geodetector is a statistical tool that relies on spatial autocorrelation in the distribution of geographic phenomena. It aims to identify the causal relationship between an independent and dependent variable by examining the degree of similarity in their spatial patterns. Geodetector is extensively employed in various disciplines, including ecology, environment, and economic development. The geodetector can identify the interaction between two elements affecting the dependent variable. By computing and contrasting the q-value of each factor with the q-value of the two factors combined, one may ascertain the presence of an interaction between the two factors, as well as the nature of that interaction—whether it is strong, weak, directional, linear, or non-linear, among other characteristics (Cai et al., 2023). This paper utilises factor detection and interaction detection in geodetector to identify the driving factors and their interactions that affect the coupled coordination degree of agro-ecological efficiency and food security in the main grain-producing areas. The formulated driving factors and their interactions are as follows (see Equation 16): q = 1 − ∑ h = 1 L N h σ h 2 / N σ 2 (16) where L represents the stratification of the coupling coordination degree driver X, N _h and N represent the number of samples in a specific stratum h and the entire study region, respectively; σ h 2 , σ 2 represent the variance of the specific stratum h and the entire study area. The variable q ranges from 0 to 1. Based on the significance test, a higher value of q indicates a more substantial explanatory power of driver X on the coupling coordination of agricultural carbon emission efficiency and food security degree. Conversely, a lower value of q indicates a weaker explanatory power.

On the basis of single-factor analysis, by comparing the q values q(X _i ) and q(X _j ) of the coupling and coordination degrees of pairs X _i and X _j and the q-value q X i ∩ X j after the superposition of the two factors, the strength and direction of the factor interaction are judged according to their mutual relations (Pan et al., 2024) (Table 6).

The GTWR model is a regression analysis technique that integrates the temporal dimension with the GWR model, which emphasises data variations in geospatial contexts and illustrates the relationships between variables across diverse geographic locations by incorporating geographic location weights. The GTWR model additionally incorporates the temporal dimension, allowing it to account for spatial and temporal variation (Zhao et al., 2023). This work presents the construction of the GTWR model utilising ArcGIS software to analyse the spatial heterogeneity of the factors influencing the linked coordination degree of agro-ecological efficiency and food security, represented by the following formula (see Equation 17): D i = φ 0 u i , v i , z i + ∑ j = 1 m φ j u i , v i , z i X i j + δ i (17) where D _i represents the degree of coupling coordination; X _ij represents the driving factors; u i , v i , z i represents the latitude and longitude coordinates of the study area and the time of observation, φ 0 u i , v i , z i represents the intercept, and δ i represents the random error.

Agricultural carbon emissions in the primary grain-producing regions from 1999 to 2022 exhibit two “increase and decrease phases,” as illustrated in Figure 2. Between 1999 and 2016, overall carbon emissions rose annually due to the contribution of numerous production factors, resulting in agricultural carbon emissions reaching 85.12 million tonnes in 2016, a 36.49% increase compared to 1999. From 2016 to 2022, influenced by national policy control and the international “Carbon Emission, Carbon Peak” initiative, agricultural carbon emissions have progressively decreased, reaching 76.16 million tonnes in 2022. Agricultural input carbon emissions constituted 82.09% of total carbon emissions, with contributions from fertiliser, irrigation, diesel, agricultural film, pesticides, and ploughing in descending order. Overall emissions exhibited a trend of initially increasing, followed by a decline, with fertiliser emissions representing 41.88% of the total. Carbon emissions from agricultural soils exhibit three phases: decrease, stabilisation, and resurgence. These emissions constitute 17.91% of the total, with maise and rice contributing significantly at 6.92% and 5.68%, respectively.

The agricultural carbon sink in primary food-producing regions from 1999 to 2022 exhibits a consistent annual increase, with a more rapid growth rate before 2016, averaging 2.39%, as illustrated in Figure 3. The overall agricultural carbon sink rose from 445.73 million tonnes in 1999 to 673.60 million tonnes in 2022, reflecting a 51.13% increase. This may pertain to the annual enhancement of soil carbon sequestration in primary grain-producing regions, the augmentation of plant growth efficiency, and the restoration and conservation of ecosystems. The composition of carbon sinks predominantly consists of rice, maise, and wheat, contributing 34.87%, 33.37%, and 27.44%, respectively, collectively exceeding 95% of the total carbon sinks, with maise exhibiting a superior average growth rate of 3.82%.

The primary grain-producing regions are categorised into the Yangtze River Basin, Songhua River Basin, and Yellow River Basin based on watershed delineations, as illustrated in Table 7. Agricultural carbon emissions in the Yangtze River Basin are moderate, exhibiting the lowest average growth rate of about 1.99%. Jiangsu Province accounts for the most agricultural carbon emissions, averaging 6.31 million tonnes. Agricultural carbon emissions in the Songhua River Basin are relatively modest, although the average growth rate is 12.09%. Notably, Heilongjiang Province exhibits the most rapid increase, with an average growth rate of 15.84%. Agricultural carbon emissions in the Yellow River Basin are elevated, demonstrating a substantial increase from 1999 to 2014, followed by a declining trend from 2014 to 2022, with an average growth rate of 3.84%. Henan Province and Shandong Province are the primary contributors, with average emissions of 10.16 million tonnes and 9.70 million tonnes, respectively. Agricultural carbon sinks in the Yangtze River basin are low, exhibiting the lowest average growth rate of merely 3.36%. In contrast, agricultural carbon sinks in the Songhua River basin are at a medium level but demonstrate a high average growth rate of 16.56%. Agricultural carbon sinks in the Yellow River basin consistently maintain a high level, with an average growth rate of 10.69%.

From 1999 to 2022, the agricultural carbon emission efficiency in major grain-producing regions improved annually, with the average efficiency rising from 0.589 in 1999 to 0.990 in 2022, reflecting an increase of 0.401. This substantial enhancement indicates significant potential for further carbon emission reductions through technological advancements and the optimisation of input factors.

The regional and temporal distribution of agricultural carbon emission efficiency in the primary grain-producing regions is illustrated in Figure 4, revealing a pattern of elevated efficiency in the north and south, with diminished efficiency in the central area. In 1999, four provinces—Jilin, Sichuan, Hunan, and Jiangxi—exhibited no redundancy in agricultural production carbon emissions, whereas the other provinces’ agricultural carbon emission efficiencies were below 0.8. From 1999 to 2004, the agricultural carbon emission efficiencies of five provinces—Heilongjiang, Henan, Shandong, Hubei, and Liaoning—increased. From 2004 to 2014, the majority of provinces exhibited an upward trend. From 2014 to 2022, all provinces in the primary grain-producing regions showed a notable efficiency enhancement. Hubei and Inner Mongolia saw substantial improvements in agricultural carbon emission efficiency, increasing by 0.455 and 0.520, respectively. The grain cultivation structure has undergone substantial alterations, evidenced by a notable increase in the area dedicated to rice and beans, alongside a significant reduction in the area allocated for potatoes, which decreased by 58.11%. In Hubei Province, the grain farming pattern remained unchanged; nevertheless, agricultural inputs experienced a significant decline, with pesticide application decreasing by 32.59%.

From 1999 to 2022, the food security level in primary grain-producing regions exhibited a gradual upward trajectory, with the average food security index increasing from 0.397 to 0.527, reflecting a 32.71% rise. This improvement was propelled by the medium- and long-term national food security planning initiatives, indicating further potential for enhancement in food security levels.

The regional and temporal distribution of food security levels in primary food-producing areas is illustrated in Figure 5, indicating a gradual increase in food security from the south to the north of the region. In 1999, the food security levels in most provinces were inadequate, with Heilongjiang being the sole exception exhibiting considerable safety. From 1999 to 2009, the food security levels in most provinces exhibited a fluctuating rising trend. From 2009 to 2022, food security levels in primary food-producing regions experienced substantial enhancement, with Heilongjiang, Hubei, Shandong, and Liaoning provinces exhibiting the highest average growth rates of 20.55%, 19.25%, 17.55%, and 14.86%, respectively. However, Liaoning’s food security level remains low at 0.335, significantly inferior to the other provinces. Heilongjiang Province consistently maintains high food security, achieving a score of 0.857 in 2022 because of its advantageous flat terrain, fertile black soil, and low population density.

To elucidate the characteristics of the relationship between agricultural carbon emissions efficiency and food security levels in primary food-producing regions, the coupling coordination degree model was employed to classify and analyse the coupling coordination degree. This approach identified 10 distinct coupling coordination types by integrating agricultural carbon emissions data with food security development in these areas. From 1999 to 2022, the temporal conflict between agricultural carbon emissions and food security diminishes in the provinces of primary food-producing regions, as severe dislocation virtually vanishes, imminent dislocation persists in declining, and areas of fundamental and extreme coordination consistently expand. From 1999 to 2022, the food security lagging coupling type constituted 67.95% of the total, signifying that the degree of food security is the primary factor impeding their synergistic development.

The regional and temporal patterns of the interrelationship between agricultural carbon emission efficiency and food security levels in principal grain-producing regions are illustrated in Figure 6. From 1999 to 2009, the average value of the linked coordination degree decreased from 0.530 to 0.502. Nine provinces were in a dysfunctional state in 1999, of which three provinces—Liaoning, Shandong, and Henan—were in a severe dysfunctional stage, exhibiting a significantly low level of coordination. In 2009, most provinces were categorised as near-dislocation co-loss type and near-dislocation food security lagging type, with only Heilongjiang and Sichuan advancing to the bare coordination stage. From 2009 to 2022, the coupling coordination had significant advancement, with an average growth rate of 16.34%. In 2014, the average value of the coupling coordination degree attained 0.596, indicating a favourable progression in the coordination between the efficiency of agricultural carbon emissions and food security. In 2018, the number of provinces exhibiting severe food security discrepancies decreased to zero, with only Liaoning nearing a lagging food security status. Most provinces were in essential coordination, including ten provinces such as Henan and Shandong, which were categorised as lagging in food security coordination. Meanwhile, Heilongjiang province emerged as the frontrunner, advancing into a highly coordinated and synchronous development phase. In 2022, the average coupling coordination degree attained 0.796, with five provinces—Heilongjiang, Henan, Shandong, Inner Mongolia, and Sichuan—entering the stage of highly coordinated development. However, only Heilongjiang sustains the significantly coordinated and synchronous development model, while the other provinces exhibit a lag in food security. Sichuan Province has achieved a high level of coordinated development in agricultural carbon emission efficiency and food security from 1999 to 2022. Consequently, all regions within primary food-producing areas must enhance the safeguarding of arable land, bolster scientific and technological innovation, and establish a diversified food supply system to improve food security levels consistently.

The primary grain-producing regions were categorised based on watersheds, and the Dagum Gini coefficient was utilised to assess the overall disparities in the coupled coordination of agricultural carbon emission efficiency and food security, along with the decomposition results presented in Table 8. The overall Gini coefficient indicates that the spatial disparity in the coupling and coordination of agricultural carbon emission efficiency and food security from 1999 to 2022 exhibits a fluctuating downward trend, with the Gini coefficient in 2022 decreasing by 68.94% compared to 1999, signifying a gradual reduction in regional inequality. This results from the regional coordinated development strategy enacted by the state to effectively mitigate regional development disparities, significantly contributing to the decrease in overall spatial discrepancies in the integration and synchronisation of agricultural carbon emission efficiency and food security.

(1) Disparities within a region. Table 8 illustrates that relative to 1999, the intra-regional Gini coefficients of coupled coordination in the Yangtze River Basin, the Songhua River Basin, and the Yellow River Basin decreased by 83.08%, 31.39%, and 80.29%, respectively, indicating an improvement in the equilibrium of coupled coordination among the three significant basins due to the comprehensive execution of the coordinated regional development strategy. The mean intra-regional difference in the Songhua River basin is 0.115, characterised by a notable alternating rise and fall during 2014–2015, followed by a fluctuating decline from 2015–2022, rendering it the region with the most substantial intra-regional difference among the three principal basins. The average intra-regional disparity in coupling coordination within the Yangtze River Basin is 0.071, exhibiting a generally declining trend. The average intra-regional disparity in the Yellow River basin is 0.077, having increased from 2000 to 2002, followed by a drop from 2002 to 2022 at an average rate of 8.08%.

Figure 7 illustrates the outcomes of the Kernel density estimation about the integrated coordination of agricultural carbon emission efficiency and food security throughout the primary food-producing regions. Figure 7A illustrates that the coupling coordination degree distribution curve in major grain-producing areas from 1999 to 2022 exhibits a consistent rightward shift, signifying a continual optimisation of the coupling coordination mode. The right-dragging tail characteristic of the coupling coordination degree distribution progressively enhances throughout the examination period, culminating in an observable increase in the central peak height and a reduction in wave width, indicating a declining trend in the differentiation of coupling coordination degree across the primary grain-producing regions.

Figure 7B illustrates the Kernel density estimation findings for the coupling coordination degree of the Yangtze River Basin. The trajectory of the Yangtze River Basin from 1999 to 2022 has a multi-peak distribution, signifying multi-polar polarisation phenomena, necessitating rapid resolution of the spatial imbalance issue. Over time, the position of the wave peak exhibits a consistent rightward shift, with a notable increase in the peak since 2018, accompanied by a narrowing of the wave peak’s width. This indicates an enhancement in the coupling coordination of the Yangtze River Basin, as evidenced by a reduction in the absolute difference of the coupling coordination. Figure 7C illustrates that the primary peak of the Songhua River basin distribution curve consistently shifted to the right from 1999 to 2009, exhibiting an overall upward trend, while the width of the primary peak progressively narrowed. The elevation of the primary peak diminished considerably from 2009 to 2022. Still, the breadth expanded greatly, suggesting that the coupling coordination degree of the Songhua River basin has progressively enhanced in terms of differentiation. Figure 7D illustrates that the primary peak of the kernel density of the coupling coordination degree in the Yellow River Basin exhibits a general rightward shift over the examination period, signifying an overall increase in the coupling coordination degree of the Yellow River Basin. The data showed a bimodal distribution that transitioned to an unimodal peak between 2018 and 2019, signifying a gradual diminishment of two-level differentiation in the Yellow River Basin. Concurrently, the wave peaks exhibited enhancement while their widths contracted, suggesting a trend towards reduced disparities.

The synergistic enhancement of agricultural carbon emission efficiency and food security in principal food-producing regions results from the intricate interplay of environmental, social, and economic factors and cross-scale connectivity. Based on the research of scholars like Liu et al. (2023) and Sun et al. (2024b), nine indicators representing natural conditions, economic development, and governmental actions in primary grain-producing regions were chosen to examine the driving factors behind the synergistic development of agricultural carbon emission efficiency and food security. The indicators are delineated below:

(1) Arable land extent (X1). The extent of cultivated land is a fundamental resource for food production, directly linked to food production and supply. The rapid urbanisation and population expansion have resulted in a decline of arable land, presenting a significant challenge to food security. Moreover, arable land is both a source of carbon emissions and a crucial mechanism for carbon sequestration. The carbon storage potential of arable land systems can be enhanced by optimising farming practices and advancing ecological agriculture, thus diminishing agricultural carbon emissions. The configuration and organisation of agricultural output can be improved through strategic planning and utilisation of arable land, increasing agricultural carbon emissions’ efficiency. Defined by the aggregate expanse of cultivable land in primary grain-producing regions.

The fundamental factors influencing the synergistic development of the two systems and their intensity were assessed using geo-detectors. All nine indicators demonstrated significance at the 1% level. The primary determinants were the agricultural disaster rate (X2), urbanisation level (X5), financial support for agriculture (X8), and soil erosion control (X9). Figure 8 illustrates the interaction effect of each driving component on the coupling coordination degree of agricultural carbon emission efficiency and food security. The explanatory capacity of the nine driving factors, following two-by-two interactions, is nonlinearly augmented or enhanced by two factors to varying extents, signifying that the degree of coupling coordination between agricultural carbon emission efficiency and food security in primary grain-producing regions is influenced by the interplay of multiple factors. The primary interacting determinants are rural human capital, financial assistance for agriculture, urbanisation rate, soil erosion control, and the power of agricultural machinery concerning soil erosion management. This suggests that economic development, natural resources, and governmental actions in primary food-producing regions must be harmonised to create a reciprocal synergy of internal transformation and external influence, thereby attaining the multiplier effect of synergistic development between the two systems.

Spatio-temporal spatially weighted regression was utilised to examine the spatial heterogeneity of the factors influencing the linked coordination degree of agricultural carbon emission efficiency and food security. Before executing the regression, covariance analysis was conducted on the nine drivers to ascertain the model’s validity. Consequently, the VIF for each factor was below 10, signifying the absence of covariance issues and confirming the validity of the regression results. The R2 of the GTWR model is 0.973, and the AICc is −1119.57, signifying a solid fit of the GTWR model. Consequently, the driving factor coefficients for each spatial unit element were computed utilising the GTWR model and hierarchically represented by the natural breakpoint approach, with the results illustrated in Figure 9.

(1) The cultivated land area is inconsistent with the degree of coupling coordination. The areas of positive value are predominantly located in the Songhua River and Yellow River Basins, with the Yellow River Basin experiencing the most significant beneficial impact. Areas with negative values are predominantly located in the Yangtze River Basin. The spatial peaks in the north and troughs in the south suggest that increasing arable land in the northern region enhances agricultural carbon emission efficiency and fosters harmonious food security development. In contrast, provinces in the Yangtze River Basin should pursue moderate arable land expansion.