Here we explore the fragility of the global food system using a complex-systems perspective with a particular focus on staple-food trade networks. We address two interrelated questions: (1) Does the global food system have characteristics that are consistent with one that is fragile (i.e., has 'an accelerating sensitivity' to harmful stressors [ 34 ])? (2) How has the global food system changed in terms of global trade flow and interconnectivity? In particular, we hypothesise that the global food system has characteristics consistent with one that has a threshold beyond which a critical change in state could occur. To test this hypothesis, we evaluate the evolving properties of the global food system between 1992–2009 to understand its susceptibility to self-propagating changes [ 35 ] that could interrupt global food trade and threaten country-level staple food supplies. As part of our evaluation, we also use a parsimonious approach to understand the potential impacts of extreme disturbances on the global trade of staple foods. Finally, we discuss strategies that can be used to enhance both local and systemic resilience in the global food system.

The interplay between international food trade and the stability of the global food system is multifaceted. International food trade helps balance supply and demand across different regions and provides protection against regional disturbances [ 3 ]. For example, international trade helped prevent a major food security challenge during Europe's heat wave in 2003 [ 8 ], while its absence was a major reason why severe flooding initiated famine conditions in North Korea during the 1990s [ 32 ]. Enhanced local and regional resilience to food-supply disruptions as a result of international food trade is therefore invaluable. At the same time, we must consider whether the global food system is susceptible to catastrophic changes in state, due to its organization and related feedbacks [ 26 ]. We therefore argue that efficiency-maximising agricultural trade liberalization is not a panacea for the global food system, as its impacts on food-supply resilience may be negative and require nuanced analyses [ 33 ].

Several studies have assessed the temporal evolution of trade networks using a complex systems approach, including recent work on world trade [ 28 ] and on the 'virtual water' trade associated with global agriculture [ 29 , 30 ]. Although these studies did not specifically assess shocks, their insights into the topology of these complex networks are highly valuable. One study on world trade did go further, presenting an extinction analysis to evaluate trade network robustness [ 31 ]. Importantly, the authors found that the world trade network is moving towards a 'robust-yet-fragile' configuration, meaning that the network is resistant to random failures but fragile when key network components are either stressed or fail.

A promising approach emerging in the economics literature to understand the impacts of extreme disturbances is focused on systemic complexity [ 25 , 26 ]. In the context of the global food system, a key source of complexity at the global scale is international food trade because of its numerous interactions and interdependences. Similar systemic complexity is found across a variety of disciplines, where global networks have led to highly interdependent systems that are not understood and cannot be controlled well [ 27 ]. Yet understanding network characteristics and interdependences is crucial, as it allows us to gain insight into the susceptibility of globally interconnected systems to system-wide failures and the policies that would mitigate the likelihood and severity of such failures [ 25 , 27 ].

All else being equal, a spike in global food prices would accompany any significant reduction in food supply. Price shocks, which have long characterized global commodity prices [ 20 , 21 ], alter global food trade [ 22 ], threaten global development, and exacerbate poverty [ 23 ], with particularly severe consequences for developing countries that are heavily dependent on food imports [ 20 ]. Despite the importance of preventing or at least mitigating these negative impacts, the short-run behaviour associated with price spikes (e.g., large-scale governmental intervention, hoarding, panic buying, and precautionary purchases) is poorly understood [ 3 , 24 ].

Weather-related shocks are especially important because of crop sensitivity to weather extremes [ 7 ], including high [ 8 ] and low [ 9 ] temperatures, droughts [ 10 ], and floods [ 11 ]. Beyond these weather-related shocks, crop pests and pathogens [ 12 , 13 ], regional nuclear wars [ 14 – 16 ], agroterrorism [ 17 ], and epidemics [ 18 ] (including the ongoing Ebola outbreak) all represent potential future disruptions to the global food system. Considering that society has been largely ineffective in coping with recent shocks [ 19 ], efforts focused on enhancing resilience in the global food system to such disruptions are critically needed.

Studies of the global food system have typically focused on the challenges associated with matching supply to demand for future climate, environmental, and socioeconomic scenarios [ 1 – 5 ]. These studies provide valuable insight into 'equilibrium' conditions, yet a critical knowledge gap continues to exist on how extreme disturbances or 'shocks' would impact the global food system. Shocks are relevant if they are widespread and severe, impact food-producing regions (especially any of the world's major breadbaskets [ 6 ]), and ultimately lead to substantial reductions in global food supply.

We assess basic network characteristics—including network connectivity, trade flow, and homogeneity of network components—to explore whether the system is conducive to a self-propagating state shift [35] or 'multiplier effect' [36]. We argue here that a critical mechanism for a self-propagating state shift in the global food system is widespread imposition of trade policy interventions due to a severe spike in food prices. In the subsections below, we describe the metrics, data, analyses, and limits of the methodology.

2.1. Network metrics

In our global network analysis, individual countries are nodes and trade between any two countries is a link with an associated weight (defined as trade flows measured in crop equivalents) [28, 31, 37]. We focus on wheat and rice as they are (together with maize) the most critical staple food crops of the global food system. Adapting the nomenclature presented in [37], global trade of these grain commodities is represented as a weighted, directed network designated as the matrix G D . Each element of this matrix contains the export flow from node i to node j. The elements of the principal diagonal for G D are zero, because a country cannot trade with itself. The total global grain trade is then computed as . When we are only concerned about the trade connections (and not the weights), we simplify to matrix A D (the so-called directed adjacency matrix). Its elements are equal to one if an export connection exists (and zero otherwise). A further simplification is to ignore direction for both of these matrices, yielding undirected versions designated as G U and A U . Each element is the total trade between countries (i.e., the sum of exports from country i to country j and from country j to country i), while each element is equal to one if there is trade and zero if not. With these matrices, we identify some standard metrics used in complex systems analysis. First, the degree of node i, k i , refers to the number of connections of that node to other nodes and is computed as . We then distinguish between the number of export connections (export node degree of node i: ) and the number of import connections (import node degree of node i: ). Likewise, we define metrics that take the amount of trade (i.e., weights) into account: the export node strength is and the import node strength is .

2.2. Network data

To analyze the global food trade network for the period 1992 to 2009, we obtain bilateral trade and food supply data from the Statistics Division of the Food and Agriculture Organization (FAOSTAT, http://faostat.fao.org). We aggregate by converting to either wheat or paddy rice equivalent using factors from the FAO's commodity trees [38] and summing the values to obtain the trade matrix G D . (The conversion factors are presented in table S2 of the supplementary data document, available at stacks.iop.org/erl/10/024007/mmedia.) For wheat, we aggregate the following commodities: wheat, flour, macaroni, bread, bulgur, pastries, and breakfast cereals. The rice commodities used here are paddy rice, husked rice, milled rice from imported husked rice, milled paddy rice broken rice, and rice flour. If any discrepancies exist in the trade amounts between two countries, the average is used [37]. However, if one of the two countries reported that no trade occurred, we simply use the single reported value [37]. Although bilateral trade data are available starting in 1986 from FAOSTAT, we focus on data after the dissolution of the Soviet Union (i.e., 1992 onward). From a trade-network perspective, we focus on this post-cold war era as it has been dominated by the rise of globalization. 1992 is also a convenient start year for comparative purposes, as there are only small changes to the set of nodes (i.e., countries) after this point. The analysis ends with 2009 data, because FAOSTAT's commodity balance data were available only through that year at the time of this analysis. These and other data that follow are available at http://data.giss.nasa.gov/impacts/fragile/.

2.3. Network properties

In networks where nodes can flip between two possible states and the interactions are susceptible to a multiplier effect, high heterogeneity and low connectivity tend to impede changes [35, 39]. This means, for example, that countries decide whether to export at different prices, and the imposition of export restriction by one country only affects a relatively small number of countries. Conversely, for a network in which most countries are similar and are highly connected, countries impose export restrictions at similar prices, and these restrictions impact many countries throughout the network. Such a network would be susceptible to a self-propagating trade disruption. To understand the interconnectivity of the global food trade network, we present the network 'backbone' [37] in figure 1, which shows the largest trade links that together account for 80% of total trade in 2009 for each network. The importance of a handful of wheat producers (USA, Canada, France, Germany, Russia, Ukraine, etc) and rice producers (Thailand, USA, Pakistan, Vietnam, India, etc) is evident. Also, we see the expected influence of geopolitics on the trade connections. For example, we find substantial interconnectivity among traditional trade partners of the USA and Russia, among European countries, and between European and African countries in the wheat trade network. Figure 1. Wheat and rice trade networks, showing the largest export links that together account for 80% of the total trade for each network (i.e. the network 'backbone' [37]). Plots were produced using Cytoscape [40]. Line widths are proportional to the trade flow volume, while the size of the nodes is proportional to the average export degree (k out, i ) of the node. Note: the three-letter country codes are listed in table S1 of the supplementary data document. Download figure: Standard image High-resolution image Export PowerPoint slide We next want to understand how similar (i.e., homogeneous) countries are in terms of their dependencies on other countries to assess whether the global food system is vulnerable to self-propagating trade disruptions. The self sufficiency ratio (SSR)—a measure of a country's ability to meet its own food requirements without imports—is useful in this regard. That is, we are particularly interested in the similarity of countries during times of food scarcity on the global food markets, as this similarity provides insight into their trade-policy behaviour for those times. We expect that most countries, especially those with low or marginal self-sufficiency, would be under substantial pressure to impose trade interventions to protect their domestic markets. SSR is computed as the ratio of domestic production to domestic consumption [41, 42], so we have for country i: where P i is production, I i is imports, E i is exports, and is change in reserves (or stocks) for country i. To be consistent with FAOSTAT's designation, we take to be positive if a commodity was consumed from country's i reserves in a given year (leading to a net stock decrease). To compute SSR, we expand our analyses to consider other major staple foods in addition to the aforementioned wheat- and rice-derived commodities, because we use this metric to understand the self-sufficiency status of individual countries (nodes) in the network. (In contrast, we are interested in network connectivity and trade flows in our analyses with global wheat and rice trade data.) Specifically, we include other staple cereals as well as starchy roots following [42], because these crops are the foundation of most diets throughout the world. FAOSTAT has prepared two aggregated items that are useful in this regard: 'cereals—excluding beer' and 'starchy roots'. The cereals group includes wheat, maize, rice (milled equivalent), barley, rye, sorghum, oats, millet, and an 'other cereals' category, while the starchy roots group consists of potatoes, sweet potatoes, yams, cassava, and an 'other roots' category. Starchy roots are converted to cereal equivalent assuming 0.26 tonnes of cereals are equivalent to 1 tonne of starchy roots [42, 43].

2.4. Trade restrictions as a disruption mechanism

The events of the 2008 global food crisis provide (circumstantial) evidence that food trade interventions may result in a fragile global food system. For example, in response to the 2008 food-price spike, 6 out of the top 17 wheat exporters (accounting for 90% of total trade) imposed some degree of trade restrictions, while 4 out of the top 9 rice exporters did so (figure 2). Such trade interventions to protect domestic markets represent a collective-action problem that amplifies food-price volatility [44]. A recent analysis referred to this amplification as a 'multiplier effect' [36]. A multiplier effect, in this context, refers to the situation where a country imposes export restrictions, which lead to higher global prices that trigger additional export restrictions by other countries and, therefore, further price increases in the global markets [36]. Those authors analysed data on 29 food products for the period 2008–2010, finding empirical evidence to support the existence of this multiplier effect. Figure 2. Trade restrictions for wheat and rice in response to the global food crisis of 2008. (Top) wheat exports and (bottom) rice exports by country that account for 90% of total trade averaged over the period 2004–2006 (based on data from FAOSTAT). The asterisk indicates that the country imposed trade restrictions [45]. Download figure: Standard image High-resolution image Export PowerPoint slide Export restrictions, together with import subsidies, represent trade policy interventions that governments traditionally have used to shield domestic agricultural markets from extreme fluctuations in international prices [36, 46]. Studies have shown that trade interventions accompanied recent surges in food prices, including the food spike of 2008 global food crisis [24, 36, 44, 46, 47] and afterwards in 2011 and 2012 [46]. In complex networks like the global food system, such interventions may ultimately be ineffective and may actually contribute to price spikes (as indicated by recent empirical findings [24, 36]).

2.5. Simulated disturbances

As our interest is in fragility of the global food system, we investigate network interactions when a shock causes a reduction in the global food supply. We are less interested in the specifics of the disturbance (aside from the countries affected) and more focused on the response of our highly interconnected global food system to the shock—whatever the origin. In the complex systems literature, a disturbance affecting a critical network node (i.e., a major food producing region) has been referred to as a 'targeted network attack'; in contrast, a 'random network attack' affects a node of random importance [31]. We focus on the former, because, although such events are rare, their impacts are potentially catastrophic. Plausible shocks, as mentioned earlier, include weather extremes, epidemics, civil conflict, or the spread of a major crop disease (e.g., wheat stem rust, known as Ug99, is present in African and Middle Eastern wheat fields and can lead to 100% crop losses in most modern varieties [13]). In this study, we select large-scale weather anomalies as our example 'disturbances', because crop production, and hence our global food system, is particularly sensitive to weather extremes [7]. In particular, we assess how two pan-continental weather anomalies, 1816's 'Year Without a Summer' and the Great Drought of 1876–1878, would impact wheat and rice trade, respectively, for the 1992–2009 networks. The spatial extent of these events is comparable to more recent events including the European heat wave of 2003 [8] and 2012s pan-continental drought in the United States during the summer of 2012 [48], respectively. However, the impacts of 1816's cold temperatures were more severe due to widespread crop failure [50], while the Great Drought was a particularly intense drought that extended over multiple years (unlike the 2012 US drought) [54, 55]. For these two disturbances, we characterize nodes (i.e., countries) as being in one of two alternate states, exporting or non-exporting. We then impose export bans only in directly affected countries (rather than in all exporting countries). Thus, we are conservative in this estimate, as we do not consider the more severe case where trade restrictions propagate throughout the entire network (i.e., the 'multiplier effect'). (Additional limits of the methodology are discussed in the following section.) The 'Year Without a Summer' of 1816 (figure 3, left panel), a result of the 1815 Mount Tambora volcano eruption in Indonesia [49–51], had abnormally low daily average temperatures from late spring through early fall, which led to severe drops in crop yield and a devastating famine in Europe [50]. We simulate a disturbance impacting most of Europe based on this event by overlaying the temperatures experienced in the 'Year Without a Summer' of 1816 and computing the differences between 1816 temperatures and the 1971–2000 averages for June, July, and August (JJA) [52, 53]. Wheat exports are then set to zero for European countries (in the 1992–2009 networks) with a cooling anomaly in half or more of their present-day territory. Figure 3. Continental-scale weather disturbances. (Left panel) temperature anomalies for the 'Year Without a Summer' of 1816. The anomalies are 1816 temperatures relative to the 1971–2000 average for June, July, and August (JJA) [52, 53]. (Right panel) the average Palmer Drought Severity Index (PDSI) for JJA during the Great Drought of 1876–1878 [55], where negative PDSI values indicate drought conditions. Download figure: Standard image High-resolution image Export PowerPoint slide The other disturbance, the late Victorian Great Drought of 1876–1878 (figure 3, right panel), was associated with one of the most severe El events of the last 150 years. It affected most of Monsoon Asia, with particularly catastrophic impacts (more than 30 million famine deaths worldwide) [54, 55]. We use the Palmer Drought Severity Index (PDSI) [55] during JJA to identify the extent of drought during this event. As with the European disturbance, we simulate a shock affecting most of monsoon Asia based on this event by overlaying PDSI for the Great Drought. Rice exports in the 1992–2009 networks are set to zero for Asian countries with a negative PDSI in half or more of present-day countries. Our approach is a parsimonious one for simulating network response to disturbance, as exports are banned only in the directly affected countries. We assess imports lost from each country using two end-member scenarios: (1) Static accounting: no reallocation of remaining commodities on the global market.

(2) Dynamic accounting: reallocation using a gross domestic product (GDP) ranking. The static approach is used to understand the baseline vulnerability to disturbances that exists through trade connections. This baseline allows us then to assess the relative impacts of commodity reallocation. For dynamic accounting, we approach the reallocation problem from the perspective that wealthier countries will use their financial resources and influence to obtain additional food in times of scarcity on the global markets (at the expense of other nations). That is, we preferentially allocate the remaining commodities to wealthy countries using a GDP ranking based on data from the United Nations' National Accounts Main Aggregates Database (http://unstats.un.org/unsd/snaama/introduction.asp). The underlying assumption is that higher GDP countries have more financial resources and influence to mitigate both supply losses and spikes in domestic food prices. In contrast, poor countries have neither the financial resources nor the influence to obtain commodities during times of food scarcity on the global markets. Lastly, we quantify the ratio of lost wheat or rice commodities (due to each disturbance) to the total staple food supply consumed. This ratio is helpful for understanding how important the lost imports are relative to the total amount of staple foods consumed in each country. Total staple food supply consumed for country i ( ) is computed as where is expanded to include aggregated cereals and starchy roots data as done with the SSR computations. We pay particular attention to losses of least developed countries (LDCs), because they are the most vulnerable to disruptions given their limited financial resources. The latest FAOSTAT list of least developed countries (LDCs) (as of February 2014, the list includes 48 countries) is used here. We note, however, that South Sudan and Djibouti are excluded from the LDC assessment. South Sudan is excluded, because our analyses end before it was established. Djibouti is excluded due to major discrepancies in wheat trade between the food balance sheets and the bilateral trade data in FAOSTAT.

2.6. Limits of methodology