摘要:据虚拟水概念定义虚拟要素，并将其划分为虚拟资源要素和虚拟生态要素两类，选取虚拟资源要素中的耕地要素和虚拟生态要素中的化肥/农药要素为研究对象，定量分析2002-2016年以粮食贸易为载体的虚拟耕地、虚拟化肥/农药要素的贸易量，构建虚拟要素贸易网络，通过复杂网络的研究方法，结果表明：2002-2016年我国主要农产品虚拟耕地、化肥/农药要素的贸易总量呈下降趋势，降幅分别约25.51%、8.01%；虚拟耕地要素网络节点入度较大的为长江中下游、华南、西南地区，出度较大的为黄淮海和东北地区，虚拟化肥/农药要素网络与之相反；地区间节点强度的差异性大，虚拟耕地要素差值最大可达1459.56万hm²，虚拟化肥/农药要素达61.38万t；二者网络节点度和强度的累积分布均符合幂律分布规律，其尾部的"重尾"现象揭示了节点度和强度的高可变性以及网络结构的脆弱性；虚拟耕地要素的输入区网络同配，输出区网络异配，揭示了地区间耕地要素的流动既呈集聚又有分散的态势，虚拟化肥/农药要素网络节点相关性皆为减函数，网络异配，揭示了虚拟化肥/农药要素在八大区域间联通的状况。网络结构特征分析为研究网络抗毁性特征和网络的优化调控机制奠定基础，为中国粮食贸易格局和粮价制定以及各个地区的农业种植结构调整提供理论依据。



Abstract:We divide virtual elements into two types: virtual resource elements and virtual ecological elements. The virtual farmland elements represented the former and virtual fertilizer/pesticide elements represented the latter; these elements are selected as our research objects. We quantitatively analyzed the trade volume of the virtual elements to establish the trade network. Our research used complex network methods to focus on the total trade volume of virtual farmland and fertilizer/pesticide elements of major agricultural products in China from 2002 to 2016. The results showed downward trends of 25.51% and 8.01% for the farmland and fertilizer/pesticide elements, respectively. The areas of the virtual farmland network with a higher degree of in-node were the middle and lower reaches of the Yangtze River, South China, and Southwest China, while the areas with the higher degree of out-node were Huanghuaihai and Northeast China. The dynamics of the network of virtual fertilizer/pesticides show a clear opposite trend. The node strengths of the virtual elements varied greatly, with a maximum of 14.5956 million hectares and 613,800 tons for the farmland and fertilizer/pesticide elements, respectively. The cumulative distribution of both the node degree and node strength conform to a power law relationship; the "heavy-tailed" phenomenon reveals a high variability of node degree and node strength and the fragility of the network structure. The network of input areas of virtual farmland element are assortative and the output areas are disassortative; specifically, the flow of virtual farmland between regions is both agglomerated and dispersed. The correlation degree of the virtual fertilizer/pesticide element network is a reduction function, and the network is disassortative; this indicates that the flow of virtual fertilizer/pesticide is close between the eight regions. The network structure analysis lays the foundation for studying the invulnerability, optimization, and control mechanism of the network while providing a theoretical basis for a pattern of the grain trade, the establishment of grain prices, and an adjustment of the agricultural planting structure in various regions of China.





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