Quantifying the temporal stability of international fertilizer trade networks

Abstract The importance of fertilizers to agricultural production is undeniable, and most economies rely on international trade for fertilizer use. The stability of fertilizer trade networks is fundamental to food security. However, quantifying the temporal stability of a fast-growing system, such as the international fertilizer trade, requires a multi-dimensional perception. Therefore, we propose a new method, namely the structural inheritance index, to distinguish the stability of the existing structure from the influence of the growing process. The well-known mutual information and Jaccard index are calculated for comparison. We use the three methods to measure the temporal stability of the overall network and different functional sub-networks of the three fertilizer nutrients N, P and K from 1990 to 2018. The international N, P and K trade systems all have a trend of increasing stability with the process of globalization. The existing structure in the fertilizer trading system has shown high stability since 1990, implying that the instability calculated by the Jaccard index in the early stage comes from the emergence of new trade. The stability of the K trade network is concentrated in large sub-networks, meaning that it is vulnerable to extreme events. The stable medium sub-network helps the N trade become the most stable nutrient trade. The P trade is clearly in the role of a catch-up player. Based on the analysis of the comparisons of three indicators, we concluded that all three nutrient trade networks enter a steady state.