Rethinking distance in international trade:World Trade Atlas 1870-2013

Guillermo Garcıa-Perez,1 Marian Boguna,1 Antoine Allard,1 and M. Angeles Serrano1, 2

1Departament de Fısica Fonamental, Universitat de Barcelona, Martı i Franques 1, E-08028 Barcelona, Spain2Institucio Catalana de Recerca i Estudis Avancats (ICREA),

Passeig Lluıs Companys 23, E-08010 Barcelona, Spain(Dated: February 28, 2020)

Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps inwhich distances incorporate the different dimensions that affect international trade, beyond meregeography. The atlas provides us with information regarding the long-term evolution of the interna-tional trade system and demonstrates that, in terms of trade, the world is not flat, but hyperbolic.The departure from flatness has been increasing since World War I, meaning that differences intrade distances are growing and trade networks are becoming more hierarchical. Smaller-scaleeconomies are moving away from other countries except for the largest economies; meanwhile thoselarge economies are increasing their chances of becoming connected worldwide. At the same time,Preferential Trade Agreements do not fit in perfectly with natural communities within the tradespace and have not necessarily reduced internal trade barriers. We discuss an interpretation interms of globalization, hierarchization, and localization; three simultaneous forces that shape theinternational trade system.

When it comes to international trade, the evidence sug-gests that we are far from a distance-free world. Distancestill matters [1] and in many dimensions: cultural, ad-ministrative or political, economic, and geographic. Thisis widely supported by different evidence concerning themagnitude of bilateral trade flows. The gravity model oftrade [2, 3], in analogy to Newton’s law of gravitation,accurately predicts that the volume of trade exchangedbetween two countries increases with their economic sizesand decreases with their geographical separation. Theprecision of that model improves when it is supplementedwith other factors, such as colony–colonizer relationships,a shared common language, or the effects of political bor-ders and a common currency [4]. Despite the success ofthe gravity model at replicating trade volumes, it per-forms very poorly at predicting the existence of a tradeconnection between a given pair of countries [5]; an obvi-ous limitation that prevents it from explaining the strik-ing regularities observed in the complex architecture ofthe world trade web [6–10]. One of the reasons for thisflaw is that the gravity model focuses on detached bi-lateral relationships and so overlooks multilateral traderesistance and other network effects [11].

Another drawback of the classical gravity model is thatgeography is not the only factor that defines distance ininternational trade. Here, we propose a gravity modelfor the existence of significant trade channels betweenpairs of countries in the world, which is based on ef-fective trade distances, such that the closer countriesare in trade space, the greater their chance of becom-ing connected. We estimate this effective trade distancefrom historical data using a systems approach based onnetwork science methodologies [12–15]. In our gravitymodel, trade distances incorporate the different dimen-sions that affect international trade, not only geography,and allow us to represent international trade throughWorld Trade Maps (WTMs) that define a coordinate sys-

tem in which countries are located in relative positionsaccording to the aggregate trade barriers between them.The maps are annual and cover a time span of fourteendecades. The collection as a whole, referred to as theWorld Trade Atlas 1870-2013, is presented via spatialprojections [16, 17] and trade distance matrices [18]. Be-yond the obvious advantages of visualization, the WorldTrade Atlas 1870-2013 significantly increases our under-standing of the long-term evolution of the internationaltrade system and helps us to address a number of im-portant and challenging questions. In particular: Howfar, in terms of trade, have countries traveled in recenthistory? What role does each country play in the mapsand how have those roles evolved over time? Are Prefer-ential Trade Agreements (PTAs) consistent with naturalcommunities as measured by trade distances? Has theformation of PTAs led to lesser or greater barriers totrade within blocs? Is trade distance becoming increas-ingly irrelevant?

The answers to these questions can be summarized byasserting that, in terms of trade, the world is not flat; itis hyperbolic. Differences in trade distances are growingand becoming more heterogeneous and hierarchical; atthe same time as they define natural trade communities—not fully consistent with PTAs. Countries are becomingmore interconnected and clustered into hierarchical tradeblocs than ever before.

I. MAPPING THE INTERNATIONAL TRADESYSTEM

Network representations of world trade [6–10] offer aperspective that goes beyond bilateral analysis and al-lows us to uncover stable large-scale patterns such asthe small-world property, heterogeneous distributions ofthe number of trade partners (degree), and high levels of

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transitive relationships (clustering). Our main hypothe-sis is that this architecture is a reflection of the distancesbetween countries in an underlying trade space. We havereconstructed international trade networks using histor-ical aggregate import/export data from two consistentand consecutive databases. For the period 1870–1996,we used data from [19, 20]. We then compiled DatabaseS1 which covers the period from 1997 to 2013 [18]. Inthe reconstructed undirected networks, links representbilateral trade relationships, and the weight of the linkcorresponds to the value of goods exchanged in a givenyear, in current US millions of dollars. World war peri-ods, 1914–1919 and 1939–1947, were avoided due to thelack of reported information.

A. Backbones of significant trade channels

The evolution of trade networks shows trends that areconsistent with globalization [21–23], understood as in-creases in the density of connections, in the total amounttraded, and in the relative average geographic length oftrade channels, Fig. S2. This augmented entanglementobscures patterns and regularities within the networksthat we will need to exploit to infer trade distances. Inparallel, world trade networks display, especially afterWorld War I (WWI), a strong heterogeneity in the globaldistributions of: the number of trading partners, totaltrade per country, and bilateral flows [18]. An increas-ing heterogeneity is also present at the local level in thedistribution of flows between the neighbors of each singlecountry, Fig. 1B and Fig. S3 in [18], which we quantifyusing the disparity measure Y (k) [8, 18, 24, 25]. This in-dicates that, at the same time as countries gained tradepartners, they intensified only a few of their trade con-nections.

These heterogeneities can be exploited to filter out, foreach year, a sparse subnetwork representing the relevantstructure that remains after eliminating the contingentinteractions which overshadow the information containedin the system [13, 18]. These ”backbones”, Fig. 1A andTable S3, retain most of the countries but the numberof trade channels is drastically reduced to the statisti-cally significant ones, Fig. S4 in [18]. At the same time,they preserve pivotal features of the original trade net-works: most of the total trade, global connectedness, thesmall-world property, the heterogeneous degree distribu-tions, and clustering. Interestingly, the correlation be-tween the degrees of countries within the backbones andtheir GDPs is always extremely high, Fig. 1C, meaningthat these backbones of world trade networks reveal eco-nomic size as an underlying variable.

Backbones differ from the unfiltered networks in therelation between geographic distance and trade connec-tions. Overall, the geographic length of connections rela-tive to the geographic distance between all the countries(located at the coordinates of their capitals) shows a sus-tained increase in the unfiltered network. This means

that trade connections become less dependent on dis-tance over time, Fig. S2 in [18]. However, the tradechannels within the backbone are comparatively shorterover the whole period, which means that, despite glob-alization, countries are more likely to choose their moresignificant trade partners from among their closer neigh-bors. The connection probability is almost independentof distance in the unfiltered networks, but it shows aclear power-law decay with a stable exponent in the caseof the backbones, Fig. 1D. Strikingly, the filter that pro-duces the backbones is blind to geography [18]. Hence,compared to the unfiltered networks, trade backbones re-veal economic size—in terms of GDP—as an underlyingvariable, and show that geographic distance plays an in-creasingly important role for the most significant tradechannels.

B. WTM construction: a gravity model forinternational trade channels

World trade backbones are suitable to be mapped ontoan underlying trade space. The simplest metric spacethat can be considered is a circle on which countries areseparated by an angular distance da = min(|∆θ|, 2π −|∆θ|). We propose that the probability that any pair ofcountries i and j are connected in terms of this distanceis

pij =1

1 + xβij, (1)

where xij = da,ij/(µκiκj), such that pij decreases as afunction of da and increases with the expected economicsizes κ [26]. These economic sizes are strongly corre-lated with degrees [15, 27] in the backbone and so withthe corresponding GDPs, Fig. 1A and C. The parame-ters µ and β govern the average degree and clustering,respectively, of the network. Note that β is an elastic-ity measure with respect to trade distances; it calibratesthe coupling between the topology and the underlyingmetric space. Hence, the proposed connection probabil-ity resembles Newton’s law of gravitation and, therefore,the classical gravity model predicting the volume of bi-lateral trade flows. Notice, however, that here pij is notused to predict the volume of trade but the existenceof a significant trade channel; information which has tobe provided a priori in classical gravity models of trade,since they reproduce the existence of a link along withits weight very badly [5].

The model defined by Eq. (1) is isomorphic to a purelygeometric network model in the hyperbolic plane [14, 18].In the hyperbolic version, nodes are distributed withina hyperbolic disk of radius R. The angular coordi-nates are the same as before, whereas the radial coor-dinates, r ∈ [0, R], depend on the economic sizes ofthe countries, with power-law distribution p(κ) ∼ κ−γ

and average κ. The mapping κ = κ0e(R−r)/2 with

R = 2 ln (2/µκ20) and κ0 = κ(γ − 2)/(γ − 1) transforms

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1FIG. 1: Backbones of International Trade. A: Backbone for the year 2013. Nodes represent countries and their sizes areproportional to the logarithm of the number of trade partners in the backbone. Nodes are colored according to the logarithmof GDP values. B: Evolution of the local heterogeneity level. C: Pearson correlation coefficient, r, between the GDPs ofcountries and their degrees in the backbone. In the unfiltered network, values of r are in the range r ≈ 0.3 − 0.4 after WWII.D: Probability of trade as a function of geographic distance for the year 2013. It follows a power law, p(d) ∼ d−ν , with ν ≈ 0.7in the backbones; whereas it is almost independent of distance in the unfiltered networks.

the distance term in Eq. (1) into xij = e12 (dh,ij−R), where

dh,ij ≡ dh,ij(ri, rj , da,ij) is the hyperbolic distance be-tween two countries, and can be measured from the co-ordinates using the hyperbolic law of cosines [18]. Theembedding method uses statistical inference techniquesto identify the coordinates of each country in a back-bone which maximize the likelihood that the backboneis reproduced by the model [18]. Inferred angular dis-tances represent a measure of trade likelihood, except forthe (economic) sizes of the countries. This means thattwo small countries need to be close in terms of angulardistance to increase their chance of becoming connected.The inferred hyperbolic distance, however, incorporatessize effects; that is, two countries can be close in hyper-bolic space just because of their size. In particular, largecountries are in general closer to the rest of the world.

In this way, we apply our mapping method [18] toannual networks of world trade from 1870 to 2013 andobtain 129 World Trade Maps that conform the WorldTrade Atlas 1870-2013. For visualization purposes, weuse a single embedding for each year [16], Fig. 2 andTable S5; while for the computation of distances, we av-

erage over a hundred realizations [18], Table S6. Fig. 3Ademonstrates the excellent agreement between the em-pirical and the theoretical probability of connection asa function of the hyperbolic distance between countries.As a further demonstration of the quality of the embed-ding, Fig. 3B displays the characteristic receiver oper-ating characteristic (ROC) curve of the model for theyear 2013 and, in the inset, the temporal evolution ofthe area under the ROC curve: the AUC statistics [18].Finally, a key observation is that the correlation betweenembedding distances and geographic distances, as shownin Fig. 3C, is significant over the whole period, but farfrom one; meaning that trade distances encode more thanpurely geographical information.

II. LONG-TERM EVOLUTION OF THEINTERNATIONAL TRADE SYSTEM

The World Trade Atlas 1870-2013 is displayed as a se-quence of frames [16] and as an interactive tool [17]. Itallows us to visualize the evolution of the international

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FIG. 2: World Trade Map for 2013. The native representation of the hyperbolic plane. The radial and angular coordinatesof countries define the trade distances between them. Symbol sizes are proportional to the logarithm of the degrees of thecountries and colors represent communities revealed by the critical gap method presented in Sec. II B. See [18] for the countryassociated with each acronym.

trade system over fourteen decades. During the 19th cen-tury, the atlas shows a sparsely populated trade spacewith the hegemonic UK at its core; and it reflects the riseof Germany, France and the USA as they move towardsthe center prior to WWI. During the interwar period, theatlas presents a central triangle formed by the UK, theUSA and Germany; with the USA then progressively be-coming the new hegemonic economy during the secondpart of the 20th century. In the 1960s, decolonizationintroduces many new countries and at the same time theupper intermediate region becomes more populated byactors such as France, Italy, Japan, and the Netherlands;

together with, in less prominent positions, India, Rus-sia, Spain and Belgium, among others. In the 1990s, theEuropean Community starts its process of construction,with Germany, Italy and France coming closer; while theSoviet Bloc remains very close to Russia. During the lastfew years, China has moved towards a more central posi-tion, as a new pretender to superpower status; while theUSA, the European Community and Japan have movedto less central positions following the decline of their rel-ative dominance.

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FIG. 3: Quality of the Embeddings. A: The empiricalconnection probability as a function of hyperbolic distance,measured using the coordinates of the embedding for the year2013. The empirical probability is compared to Eq. (1). B:The ROC curve of the model [18]. The inset shows the tem-poral evolution of the area under the ROC curve: AUC. C:The Pearson correlation coefficient between hyperbolic andangular distances, dh and da, and geographical distance dg.

A. Hierarchical organization of the trade system

Notice that small economies—low-degree countries—are always located at the periphery of the disk, whilelarge economies—with high degrees—tend to settle at itscenter. This radial stratification is a sign of the hierar-chical organization of the trade system. A rough measureof the hierarchical position of a node is given by its ra-dial coordinate, and so by its degree, as compared to

the radius, R, of the trade space. This latter measuresthe hyperbolicity of the whole system or, equivalently,its departure from flatness, Fig. 4A. R grows until reach-ing a stationary value at the end of the interwar period,around which it fluctuates thereafter. Interestingly, theopposite behavior is observed for the elasticity parame-ter, β, Fig. 4C and Table S4. Larger values of R implythat differences in trade distances are more important forperipheral nodes; that is, they connect to each other lessfrequently.

To study this issue further, we define the level of hi-erarchy as a scalar, H, based on angular distances. Foreach non-leaf country i with radius ri—a non-leaf coun-try has at least one trading partner j whose economy issmaller, i.e, with a radial position such that rj > ri—

we measure the average angular separation da,i with itstrading partners for which r > ri, and define its hierar-chical level as hi = 1− 2da,i/π, Fig. 4B. If the neighborshave exactly the same angular coordinates as i, hi = 1;whereas hi = 0 for random angular positions. The globalhierarchy level, H, is obtained by averaging hi over allnon-leaf countries. In the long run, H increases from be-low 0.7 in the 19th century to very close to 0.9 in 2013,Fig. 4D inset. This represents a substantial increase andsituates the system at extremely high levels of hierarchy.The evolution of H as a function of the number of non-leaf countries, Fig. 4D, is even more revealing. Even if thenumber of non-leaf countries has increased noticeably inthe last decades, H has not decreased but has increased.This indicates an expansion of the depth of the hierar-chy, from a quasi star-like organization before WWI toa deeper hierarchical structure after WWII, with morecountries at intermediate layers acting as local economichubs.

The economic significance of this effect can be exploredfurther by analyzing the evolution of trade distances be-tween countries classified according to their economicsize. We rank countries in decreasing order of GDP anddivide them into three groups: the top 10%, the mid-dle 40%, and the bottom 50%, Fig. 4E. Fig. 4F, G and Hshows the evolution of: the average angular distance (be-tween connected pairs); the average hyperbolic distance;and the average connection probability, for all pairs ofcountries within the same group and in the differentgroups. Hyperbolic and angular distances are normalizedby the diameter of the space, 2R and π, respectively, sothat different years are comparable. There is a sharp andpersistent stratification according to economic group, de-noting a positive correlation between trade distance, orconnection probability, and economic status. The aver-age angular distance strongly correlates with economicsize. Interestingly, we observe the opposite behavior forthe average hyperbolic distance: it is greater, the lowerthe economic size. This reversal reflects the different in-terpretations of the two trade distance measures: thelatter governs the formation of trade channels, and theformer is an indicator of clusterization. The hyperbolicdistance between economic groups has been steadily in-

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1FIG. 4: Hierarchy in World Trade Maps. A: Two hyperbolic disks with different radii (rescaled). Within each disk, wedraw two circles of the same radius but centered at different locations. For small radius, the two inner circles appear to be closeto Euclidean disks; whereas for large radius, the inner circles are strongly distorted. B: Sketch illustrating the definition of thehierarchy level, H, of two different nodes. Leaf nodes appear in gray. C: Evolution of the radius, R, of the hyperbolic disk andof the elasticity parameter, β. D: Evolution of the hierarchy level, H, as a function of the number of non-leaf countries andof time (inset). Note that the number of non-leaf countries has grown (with some fluctuations) over time, so that the increaseof NNL along the x-axis is roughly chronological. E: Evolution of the fraction of total GDP accumulated by the top 10%,40%, and 50% of countries by economic size. F–G–H: Evolution of: the average normalized angular distance (only connectedcountries), the average normalized hyperbolic distance, and the average connection probability, between countries within thesame group and in the different groups defined in E.

creasing since the 1960’s; and this increase has been morepronounced for the large economies. In contrast, the an-gular distance between groups, fluctuating until the endof WWII, has remained very low or decreased over time.This denotes a trend towards concentration of countriesin specific regions of the trade space.

Placed in historical perspective, these results indicatethat small countries at the bottom of the hierarchy arefar from the rest of the world in terms of trade distance.

They therefore encounter greater difficulties establishingtrade channels with other countries, except for the largesteconomies at the top of the hierarchy, which have morechances of becoming connected worldwide. At the sametime, the increase in hyperbolic distance may be a con-sequence of the increase in hierarchy and of market com-petition effects; while the decrease in angular distanceindicates the formation of better-defined trading blocsthat form communities in the trade space.

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B. Natural communities based on trade distances

A precise definition of communities in trade space canbe given to subsets of countries that form densely popu-lated zones separated by void angular sectors. We use acritical gap method [27] (CGM) to search for communi-ties in the WTMs [18]. The method works by groupingcountries in the same community if the angular separa-tion between pairs is smaller than a critical angular dis-tance, which fixes a unique partition into non-overlappingcommunities. We select the critical gap that yields themaximum congruency with topological communities inthe backbone (as measured by modularity [18, 28], Q,giving the quality of the division into clusters). Fig. 2shows the CGM communities in the WTM for the year2013; see also Table S7. The evolution of the number ofCGM communities is shown in Fig. 5A, as compared tothose obtained by applying the Louvain algorithm [18].In terms of modularity, Fig. 5B, the two methods coin-cide to an extremely high degree. However, the numberof communities discovered by CGM is typically twice thatof the Louvain method, since Louvain modules may inte-grate smaller CGM communities. Both modularity andthe number of communities increase over time, reachinga maximum at the beginning of the last economic crisisaround 2007, with a minor downturn afterwards.

This tendency towards localism in trade space seemsconsistent with the proliferation, since the late 1980’s, ofPTAs as formal trading blocs [29, 30], Fig. 5A. We usethe WTO’s Regional Trade Agreements Information Sys-tem (RTA-IS) [31] to list all plurilateral PTAs in force in2013 and compare them with natural CGM trade com-munities. To measure their similarity, we used normal-ized mutual information [32] (MI), which takes a valueof 1 when the two compared partitions are identical and0 when there is no more than random matching. Overthe entire period, natural communities are noticeablymore congruent with PTAs than those identified by theLouvain method, Fig. 5C. However, the overlap betweenPTAs and natural communities is not perfect.

This poses a question regarding the progression of bar-riers to trade within each PTA, which can be assessedfrom the evolution of the average normalized angularand hyperbolic distances—〈da〉 and 〈dh〉, respectively—between its members [18]. We focus in PTAs with at leastten years of history—31 trading blocs in 2013—for whichwe find different patterns of evolution; see representativeexamples in Fig. 5D-I and [18] for the full set. Both aver-age normalized angular and hyperbolic distances remainstable over time in about half (17) of the PTAs, with 〈da〉typically close but above the geographic value. In someblocs, 〈da〉 and 〈dg〉 are extremely congruent, specificallyin PTAs with a worldwide composition, Fig. 5D; or, atthe other extreme, with a strong geographical orienta-tion, Fig. 5E. Strikingly, the value of 〈da〉 is found tobe below the geographical average in PTAs interconnect-ing Russia and the republics of the former Soviet Union,which denotes communities with reduced trade barriers,

even below levels expected given their geographical dis-persion, Fig. 5F.

Distances in the rest of the PTAs show mixed pro-gressions. An interesting case is the Asia-Pacific TradeAgreement (APTA), Fig. 5G. For the APTA, 〈dh〉 hasbeen steadily decreasing since its inception, even afterthe accession of China in 2002; whereas 〈da〉 has re-mained fairly stable. This implies a significant increasein the internal connectivity of the PTA, which may berelated to the increasing economic size of their members.In other interesting cases, both distances present a slightbut clear increase; denoting a trend towards trade di-version among their members, as in the South PacificRegional Trade and Economic Cooperation Agreement(SPARTECA), Fig. 5H, mainly formed of small islandsin the Pacific Ocean.

The European Community (EC) Treaty is the largestand most complex of all the PTAs, accounting for 23.6%of world GDP in 2013. Its evolution has moved throughthree different stages, Fig. 5I. The first lasted from its in-ception until 1972, just before the accession of Denmark,Ireland, and the UK. During this period, both angularand hyperbolic distances reduced significantly and theinternal connectivity increased, which indeed indicatesan important reduction of barriers to trade. The afore-mentioned accessions in 1973 reversed the trend, whichindicates that the new members were not natural part-ners of the treaty before they entered the agreement.During the second stage, 1973–2003, many medium/largeeconomies joined, but internal distances remained stablesince these new countries were, de facto, natural tradepartners of the treaty. Between 2003 and 2004, anothertransition took place with the accession of a large numberof small economies, mainly in Eastern Europe. Duringthe transition, 〈da〉 decreased significantly at the same

time as 〈dh〉 increased, and so the internal connectivitydecreased. Before joining the EC these newly adjoinedcountries already had members of the EC as their maintrading partners. After joining the EC, these new coun-tries kept the same main trading partners but, due totheir small size, did not increase trade with them. So,the effect has been augmented internal barriers to tradein the last decade, as the increased localization due tothe addition of small economies could not be compen-sated for due to the heterogeneity in economic sizes ofthe members.

III. DISCUSSION

The connectivity gravity law not only models the vol-ume of flows in bilateral trade, but also, as we haveproved, the large-scale architecture of the connectionswithin the international trade system. This law worksin a trade space in which distance represents an aggre-gated measure which brings together and integrates thedifferent dimensions—economic, administrative and po-litical, geographical, and cultural—that shape interna-

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FIG. 5: Natural Communities vs. Preferential Trade Agreements. A: Evolution of the number of communitiesfound by the Louvain method and the critical gap method, along with the evolution of the number of PTAs. B: Evolutionof the modularity, Q, for the two methods. C: Mutual information between critical gap method or Louvain communities andPTAs. D–I: Evolution of normalized angular and hyperbolic distances between countries in representative PTAs, along withthe average geographic distance and the average connection probability within each PTA. Dashed vertical lines indicate theaccession of new countries. The dashed horizontal red line indicates the 0.5 level, which, in the case of angular distances,corresponds to a random distribution of points.

tional trade networks. We have proved that the naturalgeometry within which to embed these networks is hyper-bolic space, which we used to construct the World TradeAtlas 1870-2013 that summarizes international trade his-tory between these dates. Most importantly, as statedbefore by others in an interesting discussion of globaliza-tion [33–35]: the world is not flat. We claim, on scientificgrounds, that it is hyperbolic.

In contrast to the widespread perception that glob-alization has led to a decrease in the importance ofdistance, we observe that countries preferentially select

their significant trade partners from geographically closeneighbors, in line with general statistics [36]. Accordingto the World Trade Atlas 1870-2013, the role of trade dis-tance has not decreased but increased over time, drivenby two main forces. First, we report an increased hier-archical organization related to a persistent stratificationby economic size, so that not all global trade market com-petitors have equal opportunities. It was reported previ-ously that elasticity with respect to distance of bilateraltrade between high-income countries fell in the period1962-1996 [37], with no trend for the group of low-income

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countries. The portrait that emerges from our maps ismore dire. Differences in trade distances are becomingmore important, particularly for small economies at thebottom of the hierarchy, which are moving away from therest of the world. The small economies are encounteringmore difficulties in establishing trade channels, except forthose with the largest economies at the top of the hier-archy, which have more chance of becoming connectedworldwide.

Second, we observe a movement towards localism—already encountered before in the context of economicgeography [38, 39]—as a tendency to concentrate withinnatural trade communities. Interestingly, this trendseems to have been reverted since 2009, maybe as a con-sequence of the fast rise of China as a new commercialpower and due to the effects of the economic crisis. De-spite the proliferation of PTAs as formal trading blocs,we only found a moderate overlap with natural communi-ties. Indeed, PTAs have not necessarily reduced barriersto trade between their members, as measured by hyper-bolic and angular distances. These results reveal PTAsas a tool that may serve purposes other than trade in eco-nomics or politics, so that their ambiguous consequenceson the creation or steering of trade depend upon severalother conditions [29, 40]. In our framework, we observethat the localization effect is entangled with that of hier-archization; that is, with the formation of intermediatehubs that dominate well-delimited angular regions as thenumber of layers in the hierarchy grows. Both effects, as

two sides of the same coin, may have been exacerbatedby trade liberalization policies with uneven effects amongnon-equals [41].

Our discussion has focused on revealing, through a sin-gle historical picture, globalization, hierarchization, andlocalization as the main forces shaping the trade space,which far from being flat is hyperbolic. The World TradeAtlas 1870-2013 can help to shed light on a number ofother questions based on trade distances, for instance,those regarding the specific composition of natural com-munities in trade space, or it can facilitate a new ap-proach to the analysis of the relationship between tradeand other economic factors.

IV. ACKNOWLEDGMENTS

This work was supported by: a James S. McDon-nell Foundation Scholar Award in Complex Systems; theICREA Academia award, funded by the Generalitat deCatalunya; the MINECO project no. FIS2013-47282-C2-1-P; the Generalitat de Catalunya grant no. 2014SGR608;and the European Commission FET-Proactive ProjectMULTIPLEX (grant 317532).

V. AUTHOR CONTRIBUTIONS

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(1964).[26] M. A. Serrano, D. Krioukov, and M. Boguna, Phys. Rev.

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VI. SUPPLEMENTARY MATERIALS

Materials and Methods available upon request.World Trade Atlas 1870-2013 interactive tool at

http://morfeo.ffn.ub.edu/wta1870-2013