耕地资源是粮食生产的基础要素，保障粮食安全和实现可持续发展的关键。然而，随着人口增长和城市化进程加剧，中国面临着耕地资源供求矛盾，耕地短缺和分布不均问题日益突出。虚拟耕地流动作为一种新型的资源再配置方式，通过粮食贸易实现耕地资源的跨区域流动和再分配，成为研究的热点。本研究聚焦于中国省际粮食贸易中的虚拟耕地流动，以2015—2021年间中国31个省份为研究对象，首先，构建贸易成本最小化线性模型来模拟国内粮食贸易流动，并从生产者角度测算虚拟耕地流动量（实际消耗量），结合标准差椭圆分析和核密度估计法观察虚拟耕地流动的时空格局特征。然后，补充消费者视角测算理想消耗量，基于双视角差异揭示粮食供需均衡下虚拟耕地流动的均衡问题。另构建资源最优节约利用线性模型，对比两种目标模型下虚拟耕地消耗情况，探讨粮食流动路径是否仍有优化空间。最后，从需求、供给以及成本因素三个层面构建影响因素指标，采用泊松伪极大似然估计法（PPML）构建贸易回归模型，实证分析得到2015—2021年省际虚拟耕地流动驱动因素，以期为优化虚拟耕地资源配置，实现耕地可持续利用提供政策参考。本研究的主要结果如下：

（1）虚拟耕地流动格局：虚拟耕地流动格局与粮食贸易格局基本一致，表现出明显的区域不对称特征。虚拟耕地输出区主要集中在黑龙江、吉林、内蒙古、甘肃和新疆等地，其中黑龙江年均输出量占全国总流动量的80%以上。虚拟耕地输入区则主要为广东、福建和浙江等地，广东自2015年起每年输入量占全国总流动量的25%左右。2015年虚拟耕地流动链共计26条，涉及9个输出省，虚拟耕地流动量为2036.38万公顷；到2021年，流动链减少至24条，输出省份减少至8个，虚拟耕地流动量略有变化，降至2029.64万公顷，其中黑龙江—广东始终是最主要的流动路径，年流动量均超过510万公顷。

（2）时空格局的变化：采用标准差椭圆分析和核密度估计法进一步揭示了虚拟耕地流动的时空格局。结果表明，虚拟耕地输出区表现出较为稳定的集聚趋势，而输入区则呈现扩散与两极分化趋势。标准差椭圆分析显示，输出区的空间分布趋于收缩，2021年椭圆面积相比2015年缩小了19.91%，长半轴从13.04千米缩小至11.53千米，短半轴从5.08千米缩小至4.60千米，表现出东北－西南方向上的集聚趋势。核密度估计分析进一步揭示输入区虚拟耕地流动量逐年下降，且出现明显的两极分化趋势。

（3）虚拟耕地资源消耗与优化路径：基于双视角评价了虚拟耕地消耗量与理想消耗量的差距，结果发现虚拟耕地资源消耗始终为负值，资源浪费问题较为严重。2015年消耗为-866.18万公顷，2021年为-849.31万公顷。部分粮食主产区（如黑龙江、吉林）资源利用效率较低，而经济发达的输入省（如广东）资源浪费较为严重。通过与实际流动路径对比，构建的虚拟耕地流动优化路径显示，虚拟耕地浪费减少13.34%，其中2021年减少21.82%。优化后的贸易格局呈现资源优先流入粮食单产高地区趋势，部分消费省份虚拟耕地流入减少，主产区输出对象更加分散，减少了对外部耕地资源的依赖。

（4）虚拟耕地流动的影响因素：省际虚拟耕地流动受供给、需求和成本因素的共同影响，且粮食主产区和主销区对虚拟耕地流动的驱动机制存在差异。供给方面，粮食作物总播种面积、有效灌溉面积和粮食单位面积产量促进虚拟耕地流动，而输出省的地区生产总值和水资源则对其产生抑制作用。需求方面，城镇居民人均可支配收入、输入省地区生产总值与虚拟耕地流动量正相关。成本方面，经济距离与虚拟耕地流动呈正相关，显示较远距离的贸易可能涉及更大规模的虚拟耕地流动。异质性分析发现，有效灌溉面积对虚拟耕地的输入与输出均有正向影响，输出省的地区生产总值对虚拟耕地输入和输出均产生负向影响。城镇居民收入增长能刺激粮食消费需求，进而刺激虚拟耕地输入。

Arable land resources are the fundamental factor for food production and a key to ensuring food security and achieving sustainable development. However, with population growth and the intensification of urbanization, China is facing a conflict in the supply and demand for arable land resources, with issues of land scarcity and uneven distribution becoming increasingly prominent. Virtual land flow, as a new form of resource reallocation, enables the cross-regional flow and redistribution of arable land resources through food trade, becoming a hot research topic. This study focuses on the virtual land flow in China's interprovincial food trade, using data from 31 provinces of China from 2015 to 2021. Firstly, a linear model minimizing trade costs is constructed to simulate domestic food trade flow, and the virtual land flow (actual consumption) is calculated from the perspective of producers. Standard deviation ellipse analysis and kernel density estimation are used to observe the spatial-temporal patterns of virtual land flow. Secondly, the ideal consumption is calculated from the consumer's perspective, and the equilibrium issue of virtual land flow under balanced food supply and demand is revealed based on the differences between the two perspectives. Another linear model is constructed to optimize resource-efficient use, and the virtual land consumption under the two goal models is compared to explore whether there is room for optimizing food flow paths. Finally, from the perspectives of demand, supply, and cost factors, indicators affecting virtual land flow are constructed, and a trade regression model is established using the Poisson pseudo-maximum likelihood (PPML) method to empirically analyze the driving factors of interprovincial virtual land flow from 2015 to 2021, aiming to provide policy references for optimizing virtual land resource allocation and achieving sustainable land use. The main results of this study are as follows:

(1) Virtual land flow pattern: The virtual land flow pattern is consistent with the food trade pattern, exhibiting significant regional asymmetry. Virtual land export areas are mainly concentrated in Heilongjiang, Jilin, Inner Mongolia, Gansu, and Xinjiang, with Heilongjiang accounting for over 80% of the total annual export volume. The main input regions for virtual land are Guangdong, Fujian, and Zhejiang, with Guangdong's annual input volume accounting for about 25% of the national total since 2015. In 2015, there were 26 virtual land flow chains involving 9 exporting provinces, with a total flow of 20.36 million hectares. By 2021, the number of flow chains decreased to 24, the number of exporting provinces decreased to 8, and the total virtual land flow slightly decreased to 20.30 million hectares, with the Heilongjiang-Guangdong flow path remaining the most significant, with annual flows exceeding 5.10 million hectares.

(2) Changes in spatial-temporal patterns: Standard deviation ellipse analysis and kernel density estimation were used to further reveal the spatial-temporal patterns of virtual land flow. The results show that virtual land export areas exhibited a relatively stable aggregation trend, while input areas showed a diffusion and bipolarization trend. Standard deviation ellipse analysis showed that the spatial distribution of export areas contracted, with the ellipse area shrinking by 19.91% in 2021 compared to 2015. The major semi-axis shrank from 13.04 km to 11.53 km, and the minor semi-axis shrank from 5.08 km to 4.60 km, showing an aggregation trend in the northeast-southwest direction. Kernel density estimation revealed that the virtual land flow in input areas declined year by year, showing a clear bipolarization trend.

(3) Virtual land resource consumption and optimization path: Based on the dual-perspective evaluation of the gap between actual and ideal consumption, the results show that virtual land resource consumption has consistently been negative, indicating significant resource waste. In 2015, consumption was -8.66 million hectares, and in 2021, it was -8.49 million hectares. Some major grain-producing areas (e.g., Heilongjiang, Jilin) showed low resource efficiency, while economically developed input provinces (e.g., Guangdong) exhibited significant resource waste. By comparing the actual flow paths with the optimized virtual land flow paths, the research shows a 13.34% reduction in resource waste, with a 21.82% reduction in 2021. The optimized trade pattern shows that virtual land resources flow preferentially into areas with high grain yield, while virtual land flow into some consumption provinces decreases. The output sources from major production regions become more dispersed, reducing dependence on external land resources.

Inter-provincial virtual arable land flow is jointly influenced by supply, demand, and cost factors, and the driving mechanisms differ between major grain-producing areas and major grain-consuming areas. On the supply side, total sown area of grain crops, effective irrigation area, and grain yield per unit area promote virtual arable land flow, while the GDP and water resources of output provinces exert inhibitory effects. On the demand side, urban residents' per capita disposable income and the GDP of input provinces are positively correlated with the volume of virtual arable land flow. Regarding cost, economic distance is positively correlated with virtual arable land flow, indicating that trade over longer distances may involve larger-scale virtual arable land flow. Heterogeneity analysis shows that effective irrigation area positively affects both virtual arable land inputs and outputs, while the GDP of output provinces negatively impacts both inputs and outputs of virtual arable land. Growth in urban residents’ income stimulates grain consumption demand, thereby driving an increase in virtual arable land inputs.

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