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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. [ABSTRACT FROM AUTHOR]

The Russia-Ukraine conflict is a growing concern worldwide and poses serious threats to regional and global food security. Using monthly trade data for maize, rice, and wheat from 2016/1 to 2023/12, this paper constructs three international crop trade networks and an aggregate international food trade network. We aim to examine the structural changes following the occurrence of the Russia-Ukraine conflict. We find significant shifts in the number of edges, average in-degree, density, and efficiency in the third quarter of 2022, particularly in the international wheat trade network. Additionally, we have shown that political reasons have caused more pronounced changes in the trade connections between the economies of the North Atlantic Treaty Organization and Russia than with Ukraine. This paper could provide insights into the negative impact of geopolitical conflicts on the global food system and encourage a series of effective strategies to mitigate the negative impact of the conflict on global food trade.

The temporal rich club (TRC) phenomenon is widespread in real systems, forming a tight and continuous collection of the prominent nodes that control the system. However, there is still a lack of sufficient understanding of the mechanisms of TRC formation. Here we use the international N-nutrient trade network as an example of an in-depth identification, analysis, and modeling of its TRC phenomenon. The system exhibits a statistically significant TRC phenomenon, with eight economies forming the cornerstone club. Our analysis reveals that node degree is the most influential factor in TRC formation compared to other variables. The mathematical evolution models we constructed propose that the TRC in the N-nutrient trade network arises from the coexistence of degree-homophily and path-dependence mechanisms. By comprehending these mechanisms, we introduce a different perspective on TRC formation. Although our analysis is limited to the international trade system, the methodology can be extended to analyze the mechanisms underlying TRC emergence in other systems.