Time dynamics and invariant subnetwork structures in the world cereals trade network

The development of industrial agriculture has enabled a sharp increase in food trade at the global scale. Worldwide trade underpins food security by distributing food surpluses to food deficient countries. The study of agricultural product flows can provide insights on the complex interactions between exporting and importing countries and the resulting network structures. Commercial partnerships between countries can be modelled using a complex network approach. Based on the detailed trade matrices from FAO covering the period from 1986 to 2013, we present an analysis of the world cereal trade in terms of weighted and directed networks. The network nodes are the countries and the links are the trades of agricultural products in mass. We reveal the changing topology and degree distribution of the world network during the studied period. We distinguish three entangled subnetwork structures when considering the temporal stability of the trades. The three subnetworks display distinct properties and a differential contribution in total trade. Trades of uninterrupted activity over the 28-year study period compose the backbone network which accounts for two thirds of all traded mass and is scale-free. Inversely, two thirds of the trades only have one or two consecutive years of activity and define the transient subnetwork which displays random growth and accounts for very little traded mass. The trades of intermediate duration display an exponential growth both in numbers and in traded mass and define the intermediate subnetwork. The topology of each subnetwork is a time invariant. The identification of invariant structures is a useful basis for developing prospective agri-food network modelling to assess their resilience to perturbations and shocks.

工业化农业的发展推动了全球粮食贸易规模的大幅增长。全球粮食贸易通过将粮食盈余输送至粮食短缺国家，为粮食安全筑牢了根基。对农产品流通的研究，能够揭示进出口国之间的复杂互动关系及其衍生的网络结构。国家间的商业合作关系可借助复杂网络方法进行建模。本研究基于联合国粮食及农业组织（Food and Agriculture Organization, FAO）1986年至2013年的详细贸易矩阵，从加权有向网络（weighted and directed networks）的视角对全球谷物贸易展开分析。该网络以国家为节点，以农产品的实物贸易量为连边。研究揭示了研究周期内全球谷物贸易网络的拓扑结构与度分布的动态演化特征。通过考量贸易的时间稳定性，本研究区分出三类相互交织的子网络结构。这三类子网络各具独特属性，且在总贸易实物量中的占比各不相同。在28年研究周期内持续开展的贸易构成了骨干网络，该网络占总贸易实物量的三分之二，且呈现无标度（scale-free）特性。与之相反，三分之二的贸易仅持续1至2个连续年度，构成了临时子网络，该网络呈现随机增长特征，且仅占极小比例的贸易实物量。持续时长处于中间区间的贸易，在交易数量与贸易实物量上均呈现指数级增长，构成了中间子网络。每一类子网络的拓扑结构均具有时间不变性。识别这类不变结构，可为构建前瞻性农业食品网络模型以评估其应对扰动与冲击的韧性提供重要支撑。