Food and nutrition security under global trade: a relation-driven agent-based global trade model — TEI-tagged view

Jiaqi GepersName, J. Gareth PolhillpersName, Jennie I. MacdiarmidpersName, Nuala FittonpersName, Pete SmithpersName, Heather ClarkpersName, Terry DawsonpersName, Mukta AphalepersName (2021date). “Food and nutrition security under global trade: a relation-driven agent-based global trade model.” Royal Society Open Sciencetitle·j.

Object of study — effect of global food trade on countries' macro- and micronutrientterm·key security, in a relation-driventerm·key agent-based modelterm·key

Research question — how to capture trade relationships that price-driven trade models miss

Contribution — an empirically grounded, relation-driventerm·key agent-based global tradeterm·key model linked to a nutrition formula

Full text — tagged

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Food and nutrition securityterm·dom under global tradeterm·key: a relation-driventerm·key agent-based global tradeterm·key model Abstract This paper addresses the highly relevant and timely issues of global tradeterm·key and food securityterm·key by developing an empirically grounded, relation-driventerm·key agent-based global tradeterm·key model. Contrary to most price-driven trade models in the literature, the relation-driventerm·key agent-based global tradeterm·key model focuses on the role of relational factors such as trust, familiarity, trade history and conflicts in countries' trade behaviour. Moreover, the global tradeterm·key model is linked to a comprehensive nutrition formula to investigate the impact of trade on food and nutrition securityterm·dom, including macro and micronutrientsterm·key. Preliminary results show that global tradeterm·key improves the food and nutrition securityterm·dom of countries in Africa, Asia and Latin America. Trade also promotes a healthier and more balanced diet, as countries have access to an increased variety of food. The effect of trade in enhancing nutrition securityterm·dom, with an adequate supply of macro and micronutrientsterm·key, is universal across nutrients and countries. As researchers call for a holistic and multifactorial approach to food securityterm·key and climate change (Hammond and Dubé 2012 Proc. Natl Acad. Sci. USA 109 , 12 356–12 363. ( doi:10.1073/pnas.0913003109 )), the paper is one of the first to develop an integrated framework that consists of socio-economic, geopolitical, nutrition, environmental and agri-food systems to tackle these global challenges. Given the ongoing events of Brexit, the US–China trade war and the global COVID-19 pandemic, the paper will provide valuable insights on the role of trade in improving the food and nutrition securityterm·dom across countries.

Background In 2019, 821.6 million people in the world are hungry and 2 billion people (26.4% of the world's population) are food and nutrition insecure, who lack access to safe, sufficient and nutritious food, according to the State of Food Securityterm·key and Nutrition [ 1 ]. Despite great progress in agri-technology in the last century, hunger is increasing in poor countries, especially during economic slowdowns and downturns. In addition to the degradation of ecosystems and more frequent crop failures due to climate change [ 2 ], recent trade disputes and conflicts among countries, and the outbreak of the COVID-19 pandemic have all posed threat to global food supply and food securityterm·key [ 3 ]. As a result, the world is struggling to meet the WHO nutrition target by 2025 or the UN sustainable development goal's nutrition target by 2030.

Food production and supply concerns more than the agri-food systems. They are deeply coupled with the social, economic and geopolitical systems at both local and global scales. Using a large-scale simulationterm·mth model of land-use change, Brown et al . [ 4 ] show that social and behavioural factors can drastically change local land use and cause severe food shortages of up to 56% without climatic disturbances. Hammond and Dubé [ 5 ] argue that food and nutrition securityterm·dom is driven by complex underlying systems at both local and regional/global scales. The authors call for a systems approach using transdisciplinary modelling tools such as system dynamics and agent-based modelling.

One important mechanism for food allocation is via trade. In 2013, about 23% of the food produced for human consumption was traded internationally [ 6 ], which feeds 2–3 billion people globally and uses 13% of worldwide cropland and pasture [ 7 , 8 ] and the proportion continues to grow annually. As globalization deepens, spatially distant countries become increasingly connected by trade, and so are their agri-food systems, a phenomenon called ‘telecouplingterm·dom’. For example, Challies et al . [ 9 ] show how surging pork demand in Germany caused large-scale deforestation in Brazil, as the latter is a major supplier of soya beans, which are used as pig feed in Germany [ 9 ]. Similarly, Fuchs et al . [ 3 ] discuss how the recent US–China trade war can cause large-scale deforestation in the Amazon, as China switched to Brazil for soya imports. Disputes and conflicts between any two countries can thus lead to a serious disturbance to global tradeterm·key and food securityterm·key.

Price versus relation-driventerm·key trade models Conventional trade models are based on the general equilibriumterm·mth (GEterm·mth) theory in economics, where trade volumes are expressed as mathematical equations of commodity prices. Solutions to the equations are found (analytically or numerically) by adjusting the prices so that supply equals demand (market clearing) in every sector. One of the common methods to derive numerical solutions is computable general equilibriumterm·mth (CGEterm·mth), which is used in models such as global trade analysis projectterm·mth (GTAPterm·mth) [ 10 ]. CGEterm·mth trade models have been used to evaluate the impact of trade policies such as tariffs and trade liberalization (e.g. [ 11 ]). Apart from GEterm·mth models, partial equilibriumterm·mth (PEterm·mth) models are also developed for the agricultural sector, upon which integrated assessment models such as common agricultural policy regionalized impact model (CAPRI) [ 12 ] are based. Both CGEterm·mth and PEterm·mth models are built upon the key assumptions of equilibrium, price elasticities and the market-clearing condition. However, these theoretical frameworks offer limited possibilities for rigorous testing against historical data and experience [ 13 ].

The gravity modelterm·mth of trade, on the other hand, takes an empirical approach, which assumes that trade volume between two countries is proportional to the GDP of the two countries and disproportional to their geographic distance [ 14 , 15 ]. The model has since become one of the most successful empirical models in economics [ 16 , 17 ]. A price mechanism and market clearing, which are central in CGEterm·mth and most macroeconomic trade theories, are not part of the gravity trade model. There is thus a gap between CGEterm·mth model, which is based on theory but lacks predictive power, and the gravity modelterm·mth, which has predictive power but lacks theoretical underpinning.

What conventional price-driven trade models like CGEterm·mth do not consider is other relational factors such as trust, familiarity, conflicts and competition in a trade relationship. For example, evidence shows that countries that share culture, language, religion and institutional structure trade more even after controlling for geographic distance and GDP [ 18 – 25 ]. Trust and familiarity play an important role in trade relationships. Using trade data of 25 countries, Den Butter and Mosch [ 26 ] show that trust explains a large fraction of trade volume between any two countries by reducing transaction costs. Deardorff [ 27 ] argues that increasing trust and reducing unfamiliarity is crucial in establishing new trade relationships, especially for countries culturally high in uncertainty aversion. Huang [ 28 ] shows empirically that transport cost is not the only reason that distant countries trade less. Countries trade also less because they have never traded before and are thus unfamiliar with each other.

For perishable goods such as food and agricultural products, trust, reputation and previous trade relationship is particularly important. Because the conditions of perishable goods are hard to enforce by contract compared with manufactured goods, importers and exporters rely on mutual trust and repeated transactions to assure contractual performance. Macchiavello and Morjaria [ 29 ] show the value of long-term relationships based on trust and reputation in rose exports in Kenya. They find that when supply disturbances occur, exporters have incentives to prioritize delivery to buyers with whom they have traded before to protect their reputation. Similarly, research has found that trust, reputation and a previous trade relationship are particularly important for perishable and non-enforceable goods such as foods and agricultural products [ 30 , 31 ].

Trade can also be driven by geopolitical conflicts and competition among countries. For example, China's decision to buy soya from Brazil and not the US is driven by its relationship with the US rather than any ‘rational’ economic factors. Similarly, Brazil uses soya bean exports to secure land ownership in neighbouring countries, particularly Paraguay and Bolivia, extend political influence in Africa and balance trade with China [ 32 ]. Countries may also engage in (irrational) competition with each other for essential foods, especially in a crisis. Timmer [ 33 ] shows how, in the 2008 rice crises, countries in Southeast Asia competed to secure rice by hoarding and banning exports, causing spikes in rice price far exceeding what classic economic theory would suggest based on the initial (moderate) fall in supply. Timmer [ 34 ] concludes that complex human behaviours, such as loss aversion, time inconsistency and herd behaviour can present significant challenges to a traditional ‘economic optimization’ approach to trade.

In summary, existing price-driven global tradeterm·key models are insufficient to fully capture trade relationships among countries. Relational factors such as trust, familiarity, conflicts and competition are just as important. When trust and a previous trade relationship is needed for trade to happen, countries will miss potential trade opportunities if they don't have trust between them [ 26 ], leaving the market to not clear in reality. We thus need a relation-driventerm·key approach to global tradeterm·key to complement the price-driven one, which this paper will develop.

Countries as agents Although trade activities are carried out by individual firms, most economic global tradeterm·key models such as CGEterm·mth and gravity modelsterm·mth treat countries as the entity of trade. Similarly, many agent-based modelsterm·mth (ABMsterm·mth) of trade and international relations also treat countries as encapsulated agents that interact with each other [ 22 , 35 , 36 ]. In fact, the question ‘what constitutes an agent’ remains open in the ABMterm·mth community. Macal and North [ 37 ] summarize four properties most ‘agents’ in ABMterm·mth have: (i) autonomy (function independently in their environment), (ii) modularity (identifiable, discrete entity), (iii) sociality (interact with other agents), and (iv) conditionality (have a state that varies over time). Entities that meet the above four criteria have been represented as agents in the ABMterm·mth literature, ranging from a biological cell to a person to an organization to a country.

Conceptually, it is appropriate to treat countries as agents if the model aims to study country-wise trade relationships, because a country makes decisions on national trade policies and positions, and behaves as a single entity as it sets up trade barriers, joins trade agreements and engages in trade wars [ 34 , 35 ]. Moreover, a country shares common attributes such as GDP per capita, institutional structure, languages and culture, so it can be treated as a single agent when researchers look at the role of these attributes in trade [ 22 , 23 ]. On the other hand, treating countries as a single unit misses the complex behaviour of and interactions between individual firms that carry out the actual trade. Treating countries as agents also miss the internal trade flows between regions in a country. Hence more other studies have been using firm-level and/or regional-level data to study heterogeneous firm behaviour in trade (e.g. [ 29 ]) and intra-national trade (e.g. [ 38 ]).

Practically, however, most global tradeterm·key data are available at the country level, including the ones from the UN and OECD, which we use in this study. Although some advanced countries have much more detailed trade data at the regional level, such segregated data are not available for all countries in the world, especially the lower income ones that are more prone to food insecurity. Even more scarce are firm-level transaction data, which are often exclusive, almost always incomplete and vary greatly by countries and sectors. The lack and incompleteness of empirical data at lower than the country level severely restricts the types of empirically grounded agent-based modelterm·key researchers can develop, especially if the model aims to include all countries and sectors. Finally, as Geterm·mth and PolhillpersName [ 39 ] have argued, agent representation is rather a narrative concept, and the appropriate agent will depend on the aims and purposes of the study, the research questions, and the constraints imposed by data, ontological complexity and computational capacity.

Multivariate nutrition Most research on food securityterm·key has so far focused on energy consumption (calories). However, having sufficient energy does not guarantee a nutritionally adequate diet. While obesity becomes a problem even in the poorest parts of the world [ 40 ], nutrient deficiency, especially deficiency in micronutrientsterm·key, are still prevalent in both low- and high-income countries [ 41 ]. For example, more than 2 billion people in the world are deficient in iron; 21% of children are deficient in vitamin A, which is the direct cause of 800 000 deaths per year [ 42 ]. In 1996, the Food and Agriculture Organization (FAO) amplified the definition of food securityterm·key to include a sufficient supply of nutrients in the diet. The UN's sustainable development goal (SDG Target 2) ‘Zero Hunger’ aims to meet the nutritional needs of all people, especially those susceptible to micronutrientterm·key deficiency (adolescent girls, pregnant and lactating women and older persons).

Previously the majority of food securityterm·key research has focused on staple foods that are the main sources of calories, such as wheat, rice, soya beans and maize (e.g. [ 43 – 45 ]), although more recent studies have been looking at a larger variety of foods (e.g. [ 46 – 48 ]). To achieve food and nutrition securityterm·dom by FAO and SDG 2 standards, however, one needs a diverse, balanced diet containing a variety of foods, such as those rich in vitamin A (offal, oranges, carrots), iron (e.g. red meat, offal, spinach) and zinc (e.g. meat, seafood, nuts).

This paper develops an empirically grounded, relation-driventerm·key agent-based global tradeterm·key model to study the impact of global tradeterm·key on food and nutrition securityterm·dom of countries across the world. It addresses the highly relevant and timely issues of trade and food securityterm·key given the current debates about trade agreements associated with Brexit and US–China trade dispute. The paper makes several important contributions to the current literature. First, it will develop a relation-driventerm·key global tradeterm·key model to complement the price-driven trade models that dominate the literature. It will provide a more flexible framework to incorporate more complex, relation-driventerm·key trade behaviour of countries. The model developed in this paper can thus enhance our understanding of some trade phenomenon such as repeated trade, preferential treatment in trade and trade conflicts, which are common in the real world but hard to explain using price-driven trade theories. It also relaxes the restrictive assumptions in CGEterm·mth models, including market-clearing and equilibrium condition and price-driven trade behaviour. Second, the trade model will include a comprehensive list of foods and be linked to a nutrition formula based on food consumption to investigate the impact of trade on food and nutrition securityterm·dom. The model can thus be used to identify countries and regions most vulnerable to food and nutrition shortage, and which macro- and micro-nutrition they are likely to lack under different scenarios.

Methods This paper describes the development of an empirical agent-based modelterm·key of global food trade to study the impact of trade and climate change on food and nutrition securityterm·dom of countries across the world. The empirical agent-based modelterm·key is implemented in NetLogoterm·key [ 49 ]. In this section, we will follow the guidelines of Grimm et al .'s overview, design concepts and detailsterm·mth (ODDterm·mth) protocol [ 50 , 51 ] to describe the model.

Purpose The purpose of the model is to study the impact of global food trade on food and nutrition securityterm·dom in countries around the world. It will incorporate three main aspects of trade between countries, including a country's wealth, geographic location and its trade relationships with other countries (past and ongoing), and will be used to study food and nutrition securityterm·dom across countries in various scenarios, such as climate change, sustainable intensification, waste reduction and dietary change.

Agent classes and attributes Countries As previously discussed, for both conceptual and practical reasons, we choose to represent countries as agents, which we believe is the most suitable for the study and the research questions we will address, as well as the most practical given the data and computational constraints. Each country in the model has a list of attributes ( table 1 ), including geographic location, population size, GDP, production of (multi-dimensional) food commodities, the country's historic trade relationships with other countries and so on. We include the 165 countries in the world for which complete data of the food supply from the FAO food balance sheetterm·mth are available. The model is spatially explicit in that the countries are represented spatially at a global scale. Table 1. Selected attributes of a country agent. variable description data source (if exogenous) En? a D? b country name name of the country, including variations FAO N N location country location in a global map GIS N N area geographic area GIS N N region and sub-region the region and sub-region a country belongs to UN N N initial GDP In 2000 FAO N N initial population In 2000 FAO N N initial production tonnes of each food commodity produced in the country in 2000 FBSterm·mth N N initial import tonnes of each commodity imported from all other countries in 2000 FBSterm·mth N N initial export tonnes of each commodity exported from this country to all other countries in 2000 FBSterm·mth N N initial domestic supply (DS) DS of all commodities in the country in 2000 (DS = production + import – export – stock = food + feed + processing + loss) FBSterm·mth N N percentage of food in DS percentage of food in DS for each commodity in 2000 (food/DS) derived from FBSterm·mth N N percentage of loss in DS percentage of loss in DS for each commodity in 2000 (loss/DS) derived from FBSterm·mth N N is intermediary c whether a country is a trade intermediary for each commodity derived from FBSterm·mth N N import needed—domestic import needed for domestic consumption for each commodity endogenous Y Y import needed—intermediary import needed for re-export for each commodity (only relevant for intermediaries for the commodity) endogenous Y Y export available export available for each commodity endogenous Y Y import realized import (both domestic and intermediary) realized in each commodity endogenous Y Y export realized export (both domestic and intermediary) realized in each commodity endogenous Y Y current food supply food supply of each commodity in the current year endogenous Y Y current GDP GDP in the current year FAO if year ≤ 2013; OECD projection if year >2013 current population population in the current year FAO if year ≤ 2013; OECD projection if year > 2013 N Y current production production of each commodity in the current year FBSterm·mth if year ≤ 2013; Scenario projection if year > 2013 N Y typical diet c the country's food supply of each commodity in 2000 FBSterm·mth Y Y fortification how the country fortifies its wheat products food fortification initiative http://www.ffinetwork.org/index.html N N household waste c the percentage of household food wasted for each commodity Gustavsson et al . [ 52 ] N N population-level nutrient required per person c population-level nutrient required per person in the given year in macro and micronutrientsterm·key based on the demographic composition WHO recommendations N Y current nutrient supply consumed per person average nutrient supply per person in the given year in macro and micronutrientterm·key endogenous, calculated from food consumption Y Y a If the variable is endogenous (same for all tables in this section). b If the variable is dynamic or will change over time (same for all tables in this section). c More explanations below.

The activities country agents engage in are the production, trade and food intake, which is a multi-dimensional variable consisting of 91 food commodities, consistent with those used in FAO food balance sheetsterm·mth (FBSterm·mth) (see §2.4.3). The production of food commodities in each country is exogenous and changes every year depending on the scenarios. Once the production for the year is revealed or completed, countries trade with each other if they have unfulfilled domestic demand or unconsumed domestic supply. A country's food supply is then a combined outcome of its domestic production and trade with other countries. We do not consider inequalities within a country in access to food, which can be great in some countries. In this study, we focus on the average food intake per capita, which we use to compare with food requirement per capita, as an indicator of a country's food and nutrition securityterm·dom. Indicators of country-specific inequality (such as the GINI index) can be built into the model later on, which is beyond the scope of this study.

Table 1 lists selected attributes of a country agent.

Trade intermediary For a given commodity, an intermediary countryterm·dom is one that imports food for the purpose of re-exporting. As discussed before, intermediary countries are important facilitators of trade. In the model, we define a country as an intermediary for the commodity if the total export of the commodity is more than 80% of the total import (i.e. the majority of import is for re-exporting) in 2000, the baseline year. The motivation and trade behaviour of an intermediary countryterm·dom will be different from other non-intermediary countries that import for domestic consumption.

Typical diet We use the term ‘diet’ in the paper, but this is based on the national supply of food taken from the FAO food balance sheetsterm·mth (FBSterm·mth), adjusted by the proportion that is inedible (e.g. banana peels) and wasted, which differs by region. Typical diet varies across countries and reflects a country's tradition and culture, as well as their natural and land-use conditions. When considering nutrient sufficiency and dietary change, we need to make sure that we do not naively prescribe countries an ‘ideal diet’ (nutritionally adequate) that is unrealistic to implement. In the model, we use the average reported food consumption between 2000 and 2002 (to smooth out fluctuations in any one year) as the baseline for each country's typical diet. The food composition in the typical diet changes every year in proportion to global food production and supply, to reflect the fact that the diet of people changes gradually (not drastically) over time. We assume that a country will aim to obtain the typical diet for its population in the current year; it will import a food commodity if it produces less domestically than is needed in the typical diet and export if it produces more. Some countries may fail to feed their populations with the typical diet; nor does a country's typical diet necessarily guarantee nutrient sufficiency, which reflects the situations in reality.

Fortification In some countries where wheat is refined and stripped of fibre and micronutrientsterm·key, the flour and refined cereals are fortified replacing some of the micronutrientsterm·key. The most commonly fortified food is wheat (flour) [ 53 ]. Hence, when calculating nutrient supply for each country, we need to adjust for the nutrient content of wheat in each country depending on if it is refined or not, then if the refined flour is fortified. This varies by the income of countries, with higher income countries more commonly refining than fortifying with micronutrientsterm·key. The level of fortification also varies by country. The refined flour and cereal, however, will have a lower supply of fibre. Food composition values are derived from the USDA food composition database (2014, release 27) [ 54 ]. Food Fortification Initiative specifies whether food is fortified or not in a country, and the income levels for countries are as specified by the World Bank. 1 Household waste Food waste up to the point of the household is accounted for in the FBSterm·mth, but not waste generated in the household, after production and trade where a certain percentage of food will be wasted. Not accounting for household waste will lead to an overestimation of nutritional intake based on food consumption. The amount of food wasted depends on the type of food and the countries and regions. Generally speaking, countries and regions that are wealthier waste more food at the household level. Note that household waste does not include the part of food that is inedible, such as banana peel, which has already been accounted for in the nutrient calculation. Table 2 shows the percentage of food waste, based on food that could have been eaten, in household consumption by region and food type, which is estimated in Gustavsson et al . [ 52 ]. Table 2. Percentage of food waste in household consumption. region cereals roots & tubers oilseeds pulses nuts fruit veg meat offal fish milk Europe 25 17 4 4 4 19 19 11 11 11 7 North America, Oceania 27 30 4 4 4 28 28 11 11 33 15 industrialized Asia 20 10 4 4 4 15 15 8 8 8 5 sub-Saharan Africa 1 2 1 1 1 5 5 2 2 2 0.1 North Africa, West and Central Asia 12 6 2 2 2 12 12 8 8 4 2 South and Southeast Asia 3 3 1 1 1 7 7 4 4 2 1 Latin America 10 4 2 2 2 10 10 6 6 4 4 Nutrient requirements Because people in different gender–age groups have different nutritional needs, the population-level nutrient requirement per person in a country is based on the demographic composition of its population. Countries with a larger young adult and male population will have a higher nutrient requirement than those with an ageing population. The demographic composition of a country will change over time, and so will the population-level nutrient requirement. An adequate energy intake was estimated using population-weighted average dietary energy requirements (ADERs), calculated using data for each age and sex with assumptions of physical activity level (PAL) being 1.75 and BMI being 21 kg m −2 for adults. The population-level nutrient requirement of a country will be compared with the nutrient supply in the country in any given year to determine a country's level of nutrient sufficiency. The nutrient requirements are from the WHO [ 55 , 56 ].

Trade relationships between countries As previously said, the trade model will be relation-driventerm·key, which means that trade decisions will depend on previous bilateral trade relationships between countries as they engage in trade repeatedly over time, in addition to their geographic location and ability to pay. We assume countries rank each other with different trade priorities to determine whom to trade with (assuming there are multiple competing buyers or sellers). Trade priority will depend on four elements: (i) GDP per capita, (ii) geographic distance, (iii) historic trade relationship, and (iv) emergent trade relationshipterm·dom.

The first element, GDP per capita, serves as a proxy for a country's ability to pay for a commodity. Priority is given to countries with a higher GDP per capita or high ability to pay. The second element, geographic distance between the two trading countries, is an important factor in predicting trade volumes: countries close to each other tend to trade more. One reason is the lower transport cost. Another reason is that countries close to each other are also more familiar with each other, and more likely to have a similar culture, customs and languages, all of which facilitate trade [ 28 ].

The third element, historic trade relationship, is measured by trade volume of all commodities in the year 2000. We use trade volume as an indicator of the existing trade relationships established between the two countries. As research has shown, countries that are more familiar with each other (via common language, religion, institutional structure and other social and cultural characteristics) trade more often [ 19 , 20 , 57 ]. While geographic proximity is one cause for enhanced familiarity and trust between countries, there are other non-geographic factors, such as historic connections (e.g. former colony, commonwealth) [ 58 ] and international organizations or trade unions (e.g. OECD, EEA, Trans-Pacific Partnership), that could cause some countries to have closer connections and thus trade more. Historic trade volume will reflect these non-GDP and non-geographic factors. We distinguish trade volumes by exports and imports because they represent different roles in trade relationships.

The last element, emergent trade relationshipterm·dom, allows new trade to emerge endogenously and to influence subsequent trade development in a path-dependent way. While the first three elements are exogenous to the model and deterministic, the last element is endogenous and stochastic. Trade relationship that evolved from the model has an impact on future trade decisions. Two countries low on each other's trade priority (due to low GDP per capita, long geographic distance or few trade records before) can start a new trade relationship in a year when they fail to trade with their usual partners (e.g. due to crop failure or market disturbances). Such an ‘incidental’ new trade between the two countries will increase their ranks in each other's trade priority, which will in turn increase the chances that they trade again in the future.

The trade priority (for importing and exporting partners) assigned by countries to one another is a weighted average of the four elements above. The weights are calibrated using actual trade and consumption data. We allow the weight to be zero in the search space, so that if any of the above elements do not have a significant impact on trade patterns in the empirical data, it will not have an effect in the model either. Although the second and third elements may be correlated (e.g. many countries that trade often are also geographically close), they do not coincide. For example, countries that have developed historical trade links may not be geographically close, such as the commonwealth countries; on the other hand, geographically close countries may not trade as much, such as the US and Cuba. Hence, we should still be able to distinguish the effect of the four elements when calibrating the weights for the elements using empirical data.

In this model, we do not try to emulate price dynamics or predict future prices. Although prices are not explicitly modelled, the price mechanism to allocate commodities among countries will be partially incorporated in the ranking and matching process of trade partners through countries' GDP per capita, geographic location, production, consumption and dietary preferences. A country's GDP per capita and dietary preference determine its purchasing power and willingness to pay for a product. Moreover, a country's production reflects its overall productivity and production costs of the food; its consumption reveals a country's budget, dietary habits and preferences; its location is a proxy for transportation costs. Therefore, although the model does not include the price mechanism directly, it does implicitly incorporate the information that prices contain.

Table 3 shows the attributes of the trade relationship class. Table 3. Attributes of a trade relationship. variable data source if not endogenous En? a D? b GDP per capita FAO (year <=2013); OECD projection (year > 2013) N Y distance GIS N N historic trade relationship—import FAO FBSterm·mth data for years 2000–2002 N N historic trade relationship—export FAO FBSterm·mth data for years 2000–2002 N N emergent trade relationshipterm·dom—import Y Y emergent trade relationshipterm·dom—import Y Y a If the variable is endogenous (same for all tables in this section). b If the variable is dynamic or will change over time (same for all tables in this section).

Food and nutrients As was discussed before, we must look at a more comprehensive food list than a few major crops to gain a better understanding of the nutrient sufficiency, especially micronutrientterm·key sufficiency across countries. In this study, we include 91 food categories as in FAO's FBSterm·mth. Countries will produce, trade and consume a different amount in each food category, which we then use to calculate macro and micronutrientsterm·key. The aggregated groups to which each food category belongs are as follows: ‘Cereals – Excluding Beer’, ‘Starchy Roots’, ‘Sugar Crops’, ‘Sugar & Sweeteners’, ‘Pulses’, ‘Treenuts’, ‘Oilcrops’, ‘Vegetable Oils’, ‘Vegetables’, ‘Fruits – Excluding Wine’, ‘Spices’, ‘Stimulants’, ‘Alcoholic Beverages’, ‘Meat’, ‘Offal’, ‘Animal fats’, ‘Eggs’, ‘Milk – Excluding Butter’, ‘Fish; Seafood’, ‘Aquatic Products’ and ‘Other (e.g. Infant food and miscellaneous)’.

The mapping of food to nutrients is based on data from the GENuS project [ 59 ]. For a detailed description of the methodology see [ 46 ]. Each of the 91 food categories, which are made up of many food items, was disaggregated to individual food items. Each food commodity was then mapped to the nutrient composition. A weighted mean of the nutrient composition for the food items was used when the data were aggregated back to the food commodity groups. This was based on the global production of each food item within that group (FAO production data). If there were no production data for food items in a food commodity, an unweighted average was used. The nutrient data came primarily from the USDA food composition data. 2 If any food item was not in the USDA tables, the composition was taken from other regional food composition tables. In this study, we exclude the nutrients for which the mapping involves large uncertainties, leaving the following: calories (energy, kcal), protein, fat, vitamin C, vitamin A, folate, calcium, iron, zinc, dietary fibre, thiamin, riboflavin, niacin, vitamin B6 and saturated fat.

Process overview and scheduling Each step in the simulationterm·mth represents a year in real time. We choose an annual time step because it is appropriate for the production cycle and the time-scale of the model (2000–2050), and also because data on trade, production, GDP and population are only available annually. The starting year of the model was 2000, which is also the baseline year.

At the beginning of each year, countries receive the production of all food from last year, which is the amount available for domestic consumption and trade. If a country has produced more than it needs for domestic consumption of the typical diet, it will try to export the excess; if a country has produced less than it needs for domestic consumption, it will try to import the deficiency. Also, if a country is an intermediary of a food commodity, it will want to import food for re-export, even though it may have a sufficient amount for domestic consumption.

After countries decide on their trade positions (whether to import or export, and the amount to import or export), they will start looking for trade partners. Importers will first send buying offers to potential exporters. If there are multiple exporters of the food on the market, importers will send the offer to the country with the highest trade priority on their lists (see §2.2.2). After importers have sent offers, exporters will decide to whom they will sell their commodity, if they receive multiple buying offers. Similarly, exporters will evaluate importers' priorities and sell only to the ones with the highest priority until all the available food for export is sold. Importers whose buying offers are not satisfied in this round will repeat the same process in the next round until their import demand is satisfied or there is nothing left to buy. To prevent some large countries with high demand from flooding and dominating the market, we limit each trade transaction to a maximum amount, so that smaller countries can compete with larger countries. We emphasize that it is not the maximum amount a country can trade in each commodity in total; it is the maximum amount a country can trade in each commodity per round , and the trade of a commodity can take several rounds (on average 5–20) to finish ( figure 1 ). Hence, countries with a large demand will try to buy again in subsequent rounds until their demand is fulfilled. We have conducted a sensitivity analysis using different values for the maximum amount per round, and the results are not sensitive to the parameter. Figure 1. The trade procedure: the ranking and matching of importers and exporters.

It will take several rounds for the market to clear and all the trade opportunities are realized, depending on the total trade volume and the matching process. The same process will then repeat for the next food commodity until all food categories have been traded. For simplicity, we assume that the trading outcome of one food category does not affect that of the other. Figure 1 illustrates the ranking and matching process of trade among countries.

One important factor in the model is trade saturationterm·mth, which is the rate between realized and maximum trade amounts. Trade saturationterm·mth ranges from 0% to 100%, which we vary in the computer experiments. When trade saturationterm·mth is 100%, all trade opportunities are realized. Countries will keep trading until either there are no more importers with remaining demand or exporters with remaining supply. There will be no missed trading opportunities, which can be regarded as an ideal case. When trade saturationterm·mth is less than 100%, not all potential trade opportunities are realized. Countries at the bottom of the trade priority may not be able to trade, even though there are outstanding buyers and sellers of the same commodity. This ‘less than ideal’ case may be closer to reality, as factors such as to risk avoidance, market failure, lack of time (for perishable food), lack of information, communication or facilitators can prevent potential trade opportunities from being realized. The higher the trade saturationterm·mth, the higher percentage of trade opportunities are realized. Later we examine the impact of trade saturationterm·mth on food and nutrient security across countries.

Design concepts Interaction The countries interact with each other via trade. Links and connections are created between countries when one offers to buy from or sell to another. A country's decision to trade with another does not only affect the two countries involved in the trade, but it also indirectly affects other countries because once the food commodity has been traded, there will be less available on the market. Countries also interact with each other via their rankings of each other on trade priority. Their past interactions (trade) with other countries will influence the ranking as familiarity increases, which will in turn affect the way they interact/trade with others in the future.

Emergence Trade relationships can emerge through repeated interactions among countries. Countries who have never traded before (and thus are low on each other's trade priority) can start a trade relationship by chance, for example, due to the lack of available trade partners at the time. The trade experience will then encourage the countries to trade more with each other in the future, thus the emergence of new trade relationships. The nutrients available per capita in each country emerge from the trade.

Stochasticity The main source of randomness in the model comes from the matching of trade partners: the sequence of the countries matters when they send each other a buying offer. The random sequence of agents to execute functions is internal in NetLogoterm·key. To account for that internal stochasticity, we run the model 30 times for each parameter combination and look at the variance in results. As we can see in tables 15 to 21 in the Appendix, the variances caused by the internal stochasticity are very small. Apart from that, the model is data-driven and has not drawn other random parameters from distributions.

Initialization and data The initialization of the model is based on empirical data or estimates from existing research. The 165 countries are created with initial GDP, population, production, food consumption using the average value of the years 2000, 2001 and 2002 in FAO's FBSterm·mth data to smooth out any anomalies in any particular year. The past trade relationship is derived from FAO's trade data of all commodities. The geographic location and area of countries are initialized using a GIS world map. The regions and sub-regions to which countries belong are according to UN categorization and consistent with Müller et al . [ 44 ]. The typical diet for each country is initialized as the food consumption in 2000 from FBSterm·mth. The income categories and the corresponding fortification type is derived from The World Bank and Food Fortification Initiative, respectively. The avoidable waste rate is initialized using estimates from estimation in Gustavsson et al . [ 52 ].

Input data The current model runs from 2000 to 2013. Each year is input from data from FAO to update the GDP, population and production for all countries. The FAO FBSterm·mth data is available until 2013. Table 4 shows the input data for model running from 2000 to 2013. For scenario analysis in the future, the model will use projected data for production, GDP and population between 2014 and 2050. Table 4. Input data for model running from 2000 to 2013. variable data source years GDP UN GDP of countries 2000–2013 population UN GDP of countries 2000–2013 production (multivariate) FAO food balance sheetterm·mth: production 2000–2013 Model calibration Calibration The parameters to be calibrated are the weights given to each of the four elements (GDP per capita, distance, historic and emergent trade relationshipsterm·dom) in the countries' evaluation of trade partner priorities, which cannot be observed in empirical data. Because the ranking of countries is relative, we lose one degree of freedom, and hence we fix the weight for distance at 1 and allow the other three parameters to vary. The sampling of the parameters is twofold: first, we draw a sample of 10 000 random parameters from a three-dimensional Latin hypercube sampling ranging between 0 and 1; second, we transform the random sample using an exponential transformation to account for the ratio relationships (i.e. relative importance) between the weights, so that the parameters range from 0.05 to 20. In other words, relative to distance (which has a fixed weight 1), the weight for the other parameters range from 0.05 (1/20 as important) to 20 (20 times as important).

We then run the model on the 10 000 sampled parameter combinations. The empirical data we use for calibration and validation is FAO FBSterm·mth on import and export volume and food consumption, and trade data from the United Nation Comtrade Database. 3 The data for validation and calibration is available between 2001 and 2013 (the model is initialized in 2000), of which the first seven years (2001–2007) is used for calibration, and the latter six years (2008–2013) for validation.

The evaluation of the model results is based on two dimensions: trade volume and trade partners. Trade volume compares the actual import, export and food consumption (in FAO FBSterm·mth) in each country with the simulated results from the model. Because the simulated figures will almost surely not be the same as the observed ones (factors unaccounted for in the model, factors unobserved, errors in model specification, errors in input data, errors in empirical/validation data), we use a threshold to determine ‘match’: if the simulated volume is within ±20% of the actual volume (of import, export and food in each country), it is regarded as a match. The first dimension, trade volume, measures the percentage of simulated trade volumes (import, export, food) that falls within the range of the actual volume between 2001 and 2007.

The second dimension, trade partners, compares the actual bilateral trade between two countries in each food category with the simulated ones. If for a specific food category, the importer and exporter in the empirical data match that in the simulated data (regardless of trade volume), it is marked as a match. The trade partner index is the percentage of simulated trade records that matches the actual one of all trade records between 2001 and 2007. Because the FAO trade data does not contain information on bilateral trade partners or is not commodity-specific, we use the Comtrade data from the United Nations to calibrate and validate the bilateral trade results. The Comtrade data, however, does not cover all food categories in FAO. Of the 91 food categories, 42 are available in the Comtrade data.

To account for internal stochasticity, we run the model 30 times for each parameter combination and calculate the average matching rate. Figure 2 shows the 10 000 parameter combinations (consisting of three weights) plotted by the two evaluation dimensions: average matching rate for trade volume and trade partners. The higher the matching rate in each dimension, the better the model with that parameter combination performs. Tables 13 and 14 in Appendix show a small subset or example of the simulated trade volume and partners from the calibrated model (versus actual data), which we use to calculate the matching rate. The full simulationterm·mth results for the calibrated model are available in the electronic supplementary material, due to the large size of the data. Figure 2. The Pareto frontterm·mth of the 10 000 parameter combinations.

Figure 2 shows the Pareto frontterm·mth (the red line connecting the points) of the parameter combinations. The Pareto frontterm·mth represents the set of optimal parameters in that the model performance cannot be improved on one dimension without lowering the performance on the other dimension. There are 10 points on the Pareto frontterm·mth, as shown (in red and green) in figure 2 . There is a big gap in the graph, which shows that a group of parameter combinations (those to the right of the gap) does significantly better in matching trade volumes than the rest. The data used to generate the graph, i.e. the mean match rate of trade partners and trade volumes for all 10 000 parameter combinations is available in the electronic supplementary material, data.

By definition, all the points on the Pareto frontterm·mth are incomparable and can only be partially ordered. Since we value the two performance dimensions equally, we would like to choose a parameter combination that does relatively well in both dimensions. We then calculate the average of the two dimensions (i.e. give equal weight to each) and pick the point with the highest average (in green in figure 2 ), which will be the parameters for the calibrated ABMterm·mth. The calibrated values of the weight for GDP, distance (fixed at 1 as the bench market), historic and emergent trade (in trade priority evaluation) are listed in table 5 . We see that GDP and Historic trade have higher weights than distance and emergent trade, indicating a relatively bigger influence in countries' ranking of trade partners. However, the other two elements are also significantly different from zero, which means they also play a role. There are two caveats concerning the validation method. First, the parameters are the same for all countries (lack of parametrization per country). Second, there are potential although not linear correlations between the four elements in the ranking of trade partners as discussed in §2.2.2. However, they are not an issue for the study, which includes the prediction trade volumes among countries based on their trade relationships. Table 5. Calibrated weights for GDP, distance, historic and emergent trade in trade priority evaluation. GDP distance (fixed) historic trade emergent trade 1.40 1 1.40 0.72 Discussion on calibration and validation To save space, the validation results are presented in appendix A.1. Overall, we find that the model has a better predictive power for trade partners than trade volumes, which is unsurprising partly because the calibrated parameters are in the functions of countries to rank and match trade partners. Moreover, the errors in input data for the volume of trade are likely to be larger than that for trade partners. As a result, we expect the validation results for volume to be less accurate than that for trade partners. We also find that the predictive power of the model decreases over time from 2008 to 2013. As the model moves away from the original year it is initialized (2000), and the years on which is it calibrated (2001–2007), we expect its predictive power to go down, and the variances among parallel models to go up as the effects of stochasticity and random events from previous periods accumulate over time (i.e. being path-dependent).

While using empirical data to initialize, input, calibrate and validate the global tradeterm·key model, we notice that the data availability varies greatly across countries, and it is the dataset available to all countries (the common denominator) that determines the data the model can use for input and validation. While some countries (e.g. UK, US) have more detailed or accurate data for trade and nutritional intake, the same data is not available for all countries, especially some countries in Africa, which largely restricts the data available for the global ABMterm·mth. In some models, the problem is mitigated by grouping countries into regions and sub-regions, so missing data for some countries do not necessarily cause issues in the aggregated models. In ABMterm·mth, however, because individual countries are modelled on their own, there is a higher demand for the same type of data with the same content, quality and format to be available for all countries. We identify the issue of data inequality across countries as one of the challenges in building an empirically grounded global ABMterm·mth.

Finally, we find that a Pareto frontterm·mth can be a useful visual tool to show and compare the performance of models when the evaluation criteria are multi-dimensional. Not only can it identify a set of models with the ‘best’ performance (partially ordered), it can also reveal patterns of model performance in the evaluation space, especially when the number of candidate models is large. In this study, we select a model on the Pareto frontterm·mth by giving equal weights to the two evaluation criteria and pick the one with the highest weighted average. In the future, more sophisticated methods can be developed to select a model in the Pareto set; or one can include all models in the Pareto set and develop predictions based on multiple Pareto models, based on which new approaches can be developed towards model optimization, selection and prediction, which we leave for future research.

Preliminary results The impact of trade on macro and micronutrientterm·key sufficiency in 2015 In this section, we show preliminary results on the impact of trade (saturation) on micro and macronutrient sufficiency. For each nutrient, we will compare the nutrition securityterm·dom of countries when trade saturationterm·mth is low (60%, i.e. 60% of all potential trade opportunities are realized), medium (80%, i.e. 80% of all potential trade opportunities are realized) and high (100%, i.e. all potential trade opportunities are realized). Trade saturationterm·mth is an exogenous intervention parameter that we will vary in the experiment. In reality, trade saturationterm·mth can be influenced by countries' trade policies, trade conflicts and other factors such as a global pandemic. We will vary the level of trade saturationterm·mth by low, medium and high in the computer experiment and study its impact on trade and food securityterm·key.

As we discussed before in §2.2.1, the population-level nutrient intake (average per person) is calculated based on food consumption after production and trade, which we compare with nutrient requirement (average per person), which is based on the demographic compositions (age and sex) and varies across countries. If a country's average nutrient intake per person is higher than its average nutrient requirement per person, the country is considered secure in the specific nutrient, and vice versa.

For all graphs in this section except for ‘fat’, countries that are nutrient secure are in blue, and countries that are nutrient insecure are in red. Grading with the colours illustrates how far the country is from achieving nutrition securityterm·dom. The darker the shade of blue, the more secure the country is in that nutrient (intake ≫ maximum recommendation) and the darker the shade of red, the more insecure the country is in that nutrient (intake ≪ lower recommendation). For the nutrient ‘fat’, because the recommendation is within a range, there is a lower and upper limit (too little and too much fat can be can have negative health consequences), we use three colour schemes to show fat: red for below the lower recommendation, green for healthy, and yellow for over-consumption. In this section, we show the nutrient sufficiency in 2015 under low, medium and high trade saturationsterm·mth for calories, fat, vitamin A, iron and zinc, the latter three are important micronutrientsterm·key, and in the Appendix, we will show that for folate, niacin, riboflavin, thiamine and vitamin C (figures 8 – 12 ).

Figure 3 shows the impact of trade on the consumption of calories. We see that with low to medium trade saturationterm·mth, a handful of countries in Africa, Asia and South America will suffer from the lack of calories (or energy). The problem, however, can be solved by increasing trade saturationterm·mth to 100%, meaning that the world can produce food to feed the population with enough calories, as long as all trade opportunities are realized. Figure 3. Calories sufficiency under low, medium and high trade saturationterm·mth (blue = sufficient, red = insufficient).

Figure 4 shows the impact of trade on the consumption of fat. We see that sufficient trade not only increases fat intake to within the healthy range in some countries in Africa, Asia and South America, and it also brings the fat intake down for some countries (e.g. Russia, Southeast Asian countries) and makes them healthier. The reasons that countries reduce fat intake when the trade is fully realized is that trade allows them to access a more diverse diet from a global supply. Figure 4. Fat sufficiency and over-consumption under low, medium and high trade saturationterm·mth (green = healthy, red = insufficient, yellow = over-consumption).

Figure 5 shows the impact of trade saturationterm·mth on vitamin A supply. We see more countries including developed ones such as the UK becoming deficient in vitamin A, an essential micronutrientterm·key, under low to medium trade saturationterm·mth. Increasing trade saturationterm·mth reduces the level of vitamin A deficiency to a large extent, especially in African countries. It does not, however, eliminate vitamin A deficiency altogether. Moreover, some countries that are not vitamin A deficient under low and medium trade saturationterm·mth such as Brazil and Indonesia become so under full trade saturationterm·mth, because some vitamin A-rich foods consumed domestically under low and medium trade can now be exported when trade saturationterm·mth increases. Hence for vitamin A, although trade reduces the extent of deficiency in many countries, it alone cannot eliminate deficiency. Figure 5. Vitamin A sufficiency under low, medium and high trade saturationterm·mth (blue = sufficient, red = insufficient).

Figure 6 shows the impact of trade saturationterm·mth on iron deficiency. As with vitamin A, more countries become deficient for iron than for calories, including some Scandinavian countries under the different levels of trade. The result shows that increasing trade saturationterm·mth significantly reduces the level of iron deficiency, especially in countries in Africa, Asia and South America. However, trade does not eliminate iron deficiency in Scandinavia countries or Mongolia, although it makes them less deficient (light shade in red). As with vitamin A, other measures such as improving diet and increasing production and consumption of certain foods will be needed to eliminate iron deficiency. Figure 6. Iron sufficiency under low, medium and high trade saturationterm·mth (blue = sufficient, red = insufficient).

Figure 7 shows the impact of trade saturationterm·mth on zinc deficiency. It shows that increasing trade saturationterm·mth from low or medium to high can eliminate zinc deficiency. Figure 7. Zinc sufficiency under low, medium and high trade saturationterm·mth (blue = sufficient, red = insufficient).

The results show that deficiency in micronutrientsterm·key such as vitamin A and iron is much more common than that in macronutrients such as calories and fat. The latter is found only in developing countries in Africa, Asia and South America while the former can be found in both developed and developing countries, which signifies the importance of including both macro and micronutrientsterm·key in the study of food and nutrition securityterm·dom.

We see that trade plays a positive role in improving food and nutrition securityterm·dom in almost all cases. A fully realized trade eliminates calories deficiency in all countries, compared with low trade and makes fat intakes more balanced across countries. For some micronutrientsterm·key (e.g. niacin and zinc, see Appendix), high trade saturationterm·mth has successfully eliminated deficiency in all countries, compared with low and medium trade saturationterm·mth; for others, deficiency still exists even under fully realized trade, but to a lesser degree. It will require other measures, such as change increasing production and alternative trade scenarios of food rich in the micronutrientsterm·key to eliminate nutrient deficiency in those micronutrientsterm·key. In many developing countries currently use supplementation to correct the deficiencies. In almost all cases, we observe that trade at least reduces the level of nutrient deficiency across countries, if not eliminates it. The effect of trade is most prominent in countries most vulnerable to food and nutrition insecurity, including those in Africa, Asia and South America.

Finally, table 6 lists the nutrition intake per capita of the 20 most populous countries in 2013, which together account for more than two-thirds of the world population; also table 22 in the Appendix for the full list of countries. Note that the nutrient requirement per capita will vary slightly by countries due to the different population composition in each country (e.g. a younger/higher male percentage population will require more nutrient). Table 6. Nutrition intake per capita a of the 20 most populous countries in 2013, which together account for more than two-thirds of the world population (also table 22 in the Appendix for the full list of countries). country pop, millions calories protein fat vitamin C vitamin A folate iron zinc thiamine riboflavin niacin saturated FA China 1384 2750 89.9 85.7 275.4 1686.9 575.9 26.3 12.3 2.60 2.06 23.77 25.32 India 1296 2543 62.4 55.3 91.4 568.3 392.8 17.0 8.3 1.63 1.27 14.23 19.73 United States 329 3869 105.1 188.6 103.1 741.6 752.1 20.0 14.3 2.64 3.38 32.18 63.68 Indonesia 262 2967 65.7 63.8 84.5 546.2 410.8 22.9 10.4 2.83 1.33 26.53 28.92 Brazil 208 3503 99.7 131.6 95.7 572.2 790.5 22.3 13.2 2.75 2.53 29.57 48.94 Pakistan 207 2738 72.4 82.5 39.6 794.9 258.8 10.4 8.1 0.94 1.66 10.24 31.98 Nigeria 203 3158 72.2 64.9 181.8 674.6 703.5 23.0 11.4 2.90 1.37 25.53 20.84 Bangladesh 159 2387 53.4 29.0 40.1 331.9 187.9 19.3 8.5 2.25 0.86 19.34 9.31 Russia 142 3347 93.7 117.0 102.5 810.5 314.4 13.5 10.7 1.39 2.04 18.99 36.70 Japan 126 2525 75.3 93.6 89.9 712.5 314.1 17.3 10.1 1.61 1.81 17.67 26.39 Mexico 125 3295 93.4 103.6 102.5 787.1 618.1 21.9 14.4 2.76 2.46 29.24 34.04 Ethiopia 108 2108 66.6 33.3 37.8 443.7 417.1 18.4 11.8 1.92 1.15 18.13 9.48 Philippines 105 2710 63.2 56.0 108.5 486.7 375.3 19.9 9.1 2.63 1.42 25.07 24.68 Egypt 99 3247 91.2 57.2 127.7 712.6 386.6 20.4 11.4 1.86 1.70 20.99 16.86 Vietnam 97 2823 80.1 71.3 155.0 885.4 451.3 27.4 11.7 3.11 1.68 27.14 24.26 Congo 85 2306 48.2 46.8 163.7 583.2 583.1 12.9 6.4 2.08 0.95 20.89 14.38 Iran 83 3478 98.9 82.0 217.3 997.7 553.7 20.9 10.8 1.83 1.87 19.67 21.87 Turkey 81 3956 111.6 129.1 174.2 1177.6 582.0 20.5 13.1 1.75 2.65 19.23 38.42 Germany 80 3787 94.8 180.8 100.3 998.6 298.8 12.8 12.0 1.65 2.87 19.32 63.85 Thailand 68 2786 60.6 57.7 120.2 624.9 244.6 21.5 8.8 1.95 1.20 19.57 21.43 a nutrition intake per capita will be compared with the nutrition required per capita in the country, which depends on the country's demographic composition to determine a country's food and nutrition securityterm·dom.

Discussion The preliminary results from the model demonstrate the impact of increasing trade on improving macro and micronutrientterm·key sufficiency across countries in the world. For all nutrients included in §4.1, fully realized global tradeterm·key can help ensure a sufficient supply of nutrients and enables countries to have a healthier diet. The reason is quite straightforward: trade allows the countries to access a larger variety of food, thus enabling them to have a more nutritionally balanced diet. Trade is even more important when considering micronutrientterm·key sufficiency because they tend to be more concentrated in specific foods than macronutrients such as calories and fat, so the diet needs to contain more diverse food items to supply sufficient micronutrientsterm·key. The role of increasing trade in improving nutrition securityterm·dom is found to be universal across all macro and micronutrientsterm·key, but more pronounced in micronutrientsterm·key. Results from this study agree with previous studies in that global tradeterm·key can balance food supply and demand across regions and smooth out nutrient intake across countries [ 60 ]. It also confirms the previous conclusion that the focus of food securityterm·key should shift from calories to critical micronutrientsterm·key, in which many regions will continue to have inadequacies [ 41 ].

A criticism of global food trade is that free trade penalizes the poorest and most vulnerable countries [ 61 , 62 ]. This is largely true: the results show that low-income countries are the first to fall into food and nutrition insecurity as trade saturationterm·mth goes from high to medium to low, partly because they are often ranked lower on countries' trade priority due to their low GDP per capita and remote location. However, the results also suggest that the solution is not trade-protectionism. This is very important for countries where diets need to diversity to achieve nutrition securityterm·dom. We need to further remove any trade barriers and increase trade saturationterm·mth so that all potential trade opportunities can be used and the demand for the most vulnerable countries can be met. Preliminary results show that increasing trade saturationterm·mth always improves the nutrition securityterm·dom of countries. For some nutrients, trade alone can eliminate food and nutrition insecurity for all countries altogether. The poor and vulnerable countries also benefit from trade. Because they are lower on the priority rank, they benefit the most from additional trade liberalization and opportunities. Pradhan et al . [ 63 ] estimate that in 2000 about 1 billion people from Asia and Africa require cross-continental agricultural trade to be food secure, and by 2050 the number of people depending on trade for food securityterm·key will be between 1.5 and 6 billion. Any hindrance to trade will put these people at high risk of food insecurity.

The model presented in the study is the first step towards a holistic approach to the grand challenge of food and nutrition securityterm·dom under global tradeterm·key and climate change. There are many ways to extend the model in the future. First, the dimension and factors of countries’ trade relationships included in the model are far from complete. Apart from GDP, distance, and historic and emergent trade relationshipsterm·dom, many factors can affect the trade relationships between countries. For example, the trade war between the US and China in 2019 was motivated by complex economic and political reasons. The flexibility of the ABMterm·mth, however, means that the model can be easily adapted to implement additional factors to increase the dimension of the trade relationship. The relation-driventerm·key trade model developed in this paper will be a framework to which these relation-driventerm·key dimensions and motivations can be added to analyse its impact on trade and food securityterm·key.

Moreover, so far we have only considered the average nutrition intake in a country. We have not considered the inequality and distribution within a country. A country may have enough food for its population overall, but is still food insecure because of unequal internal allocation. This is especially important for countries with unequal developments across regions, where a minority of the population has more than adequate access to food and nutrition while the majority do not. Since the global model cannot model each country in such details due to computational constraints, one approach is to use a measure of inequality of access to food within a country as used by the FAO, such as in the FEEDME model [ 64 , 65 ], which uses a country-level measure of inequality (income and food access inequality) to determine the percentage of a population in each country which is undernourished. Another approach is to couple the global model with individual country models for the country of interest. For example, we can couple the individual country model of China or Brazil with the global tradeterm·key model developed in this paper, which allows us to position the internal dynamics and interactions between different regions and firms under the background of global tradeterm·key, without having to acquire the same level of detailed data for all countries. This is particularly useful for countries like Brazil where global food trade plays a crucial role in its domestic agri-food systems.

Concluding remarks In an increasingly connected world, a country's ability to secure food concerns more than what is produced on the ground, but also its relationships with other countries. The issue is particularly relevant and timely given the current debates about Brexit, US–China trade war and the global COVID-19 pandemic. This paper develops an empirically grounded, relation-driventerm·key model of global tradeterm·key to study the impact of trade on the food and nutrition securityterm·dom of countries around the world, complementing existing price-driven trade models in the literature. It makes several important contributions. First, it provides a flexible modelling framework that focuses on country-wise relationships in trade. The framework can be used to study more complex and relation-driventerm·key behaviour when trading with each other, such as trust, familiarity, history and conflicts. Second, the global tradeterm·key model is linked with a comprehensive nutrition formula based on food consumption to investigate the impact of trade on food and nutrition securityterm·dom. As researchers have been constantly calling for a holistic and multifactorial approach to these global challenges, the model is one of the first attempts to develop an integrated framework consisting of socio-economic, geopolitical, nutrition, environmental and agri-food systems to tackle these global challenges.

Preliminary results show that global tradeterm·key has a significant impact on food and nutrition securityterm·dom across countries. Increasing trade improves the nutritional security of almost all countries, especially countries in Africa, Asia and Latin America susceptible to food insecurity. For some nutrients such as calories, niacin and zinc, trade alone can eliminate nutrition insecurity for all countries; for others such as vitamin A, folate, riboflavin and iron, trade improves nutrition securityterm·dom but is insufficient to achieve food securityterm·key. Other measures such as dietary changes may be needed. We also find that trade allows countries to have a healthier and more balanced diet, due to the increased variety of food enabled by trade: it decreases fat intake in countries that previously consume too much fat and vice versa. Overall, we find that the effect of trade on enhancing nutrition balance and security is universal across all macro and micronutrientsterm·key and countries.

In the future, the global tradeterm·key model developed in the study can be coupled with individual country models to include more detailed regional dynamics, firm interactions and inequality within countries. It offers a way to link models of individual country's agri-food system with a dynamic global tradeterm·key system, which is particularly useful for countries like Brazil where global food trade plays a crucial role. Finally, the model will be used to systemically conduct scenario analysis on food securityterm·key under various scenarios of climate change, dietary change and de-globalization.

Supplementary Material