the complex network of global cargo ship movements

8/13/2019 The Complex Network of Global Cargo Ship Movements

1/12

doi: 10.1098/rsif.2009.0495, 1093-1103 first published online 19 January 201072010J. R. Soc. Interface

Pablo Kaluza, Andrea Klzsch, Michael T. Gastner and Bernd BlasiusThe complex network of global cargo ship movements

Supplementary data

lhttp://rsif.royalsocietypublishing.org/content/suppl/2010/01/19/rsif.2009.0495.DC1.htm

"Data Supplement"

References

http://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#related-urlsArticle cited in:

http://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#ref-list-1

This article cites 40 articles, 13 of which can be accessed free

Email alerting servicehereright-hand corner of the article or click

Receive free email alerts when new articles cite this article - sign up in the box at the top

http://rsif.royalsocietypublishing.org/subscriptionsgo to:J. R. Soc. InterfaceTo subscribe to

on July 29, 2012rsif.royalsocietypublishing.orgDownloaded from
http://rsif.royalsocietypublishing.org/content/suppl/2010/01/19/rsif.2009.0495.DC1.htmlhttp://rsif.royalsocietypublishing.org/content/suppl/2010/01/19/rsif.2009.0495.DC1.htmlhttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#related-urlshttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#related-urlshttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#related-urlshttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#ref-list-1http://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#ref-list-1http://rsif.royalsocietypublishing.org/cgi/alerts/ctalert?alertType=citedby&addAlert=cited_by&saveAlert=no&cited_by_criteria_resid=royinterface;7/48/1093&return_type=article&return_url=http://rsif.royalsocietypublishing.org/content/7/48/1093.full.pdfhttp://rsif.royalsocietypublishing.org/cgi/alerts/ctalert?alertType=citedby&addAlert=cited_by&saveAlert=no&cited_by_criteria_resid=royinterface;7/48/1093&return_type=article&return_url=http://rsif.royalsocietypublishing.org/content/7/48/1093.full.pdfhttp://rsif.royalsocietypublishing.org/cgi/alerts/ctalert?alertType=citedby&addAlert=cited_by&saveAlert=no&cited_by_criteria_resid=royinterface;7/48/1093&return_type=article&return_url=http://rsif.royalsocietypublishing.org/content/7/48/1093.full.pdfhttp://rsif.royalsocietypublishing.org/subscriptionshttp://rsif.royalsocietypublishing.org/subscriptionshttp://rsif.royalsocietypublishing.org/subscriptionshttp://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/subscriptionshttp://rsif.royalsocietypublishing.org/cgi/alerts/ctalert?alertType=citedby&addAlert=cited_by&saveAlert=no&cited_by_criteria_resid=royinterface;7/48/1093&return_type=article&return_url=http://rsif.royalsocietypublishing.org/content/7/48/1093.full.pdfhttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#related-urlshttp://rsif.royalsocietypublishing.org/content/7/48/1093.full.html#ref-list-1http://rsif.royalsocietypublishing.org/content/suppl/2010/01/19/rsif.2009.0495.DC1.html


2/12

The complex network of global cargoship movements

Pablo Kaluza, Andrea Kolzsch, Michael T. Gastner

and Bernd Blasius*

Institute for Chemistry and Biology of the Marine Environment, Carl von OssietzkyUniversitat, Carl-von-Ossietzky-Strae 9-11, 26111 Oldenburg, Germany

Transportation networks play a crucial role in human mobility, the exchange of goods andthe spread of invasive species. With 90 per cent of world trade carried by sea, the globalnetwork of merchant ships provides one of the most important modes of transportation.Here, we use information about the itineraries of 16 363 cargo ships during the year 2007to construct a network of links between ports. We show that the network has several fea-tures that set it apart from other transportation networks. In particular, most ships can be

classified into three categories: bulk dry carriers, container ships and oil tankers. Thesethree categories do not only differ in the ships physical characteristics, but also in theirmobility patterns and networks. Container ships follow regularly repeating paths whereasbulk dry carriers and oil tankers move less predictably between ports. The network of allship movements possesses a heavy-tailed distribution for the connectivity of ports andfor the loads transported on the links with systematic differences between ship types.The data analysed in this paper improve current assumptions based on gravity models ofship movements, an important step towards understanding patterns of global trade andbioinvasion.

Keywords: complex network; cargo ships; bioinvasion; transportation

1. INTRODUCTIONThe ability to travel, trade commodities and shareinformation around the world with unprecedented effi-ciency is a defining feature of the modern globalizedeconomy. Among the different means of transport,ocean shipping stands out as the most energy efficientmode of long-distance transport for large quantities ofgoods (Rodrigue et al. 2006). According to estimates,as much as 90 per cent of world trade is hauled byships (International Maritime Organization 2006). In2006, 7.4 billion tons of goods were loaded at theworlds ports. The trade volume currently exceeds 30trillion ton-miles and is growing at a rate faster thanthe global economy (United Nations Conference onTrade and Development 2007).

The worldwide maritime network also plays a crucialrole in todays spread of invasive species. Two majorpathways for marine bioinvasion are discharged waterfrom ships ballast tanks (Ruiz et al. 2000) and hullfouling (Drake & Lodge 2007). Even terrestrial speciessuch as insects are sometimes inadvertently transportedin shipping containers (Lounibos 2002). In several partsof the world, invasive species have caused dramaticlevels of species extinction and landscape alteration,thus damaging ecosystems and creating hazards for

human livelihoods, health and local economies (Macket al. 2000). The financial loss owing to bioinvasion isestimated to be $120 billion per year in the USAalone (Pimentel et al. 2005).

Despite affecting everybodys daily lives, the ship-ping industry is far less in the public eye than othersectors of the global transport infrastructure. Accord-ingly, it has also received little attention in the recentliterature on complex networks (Weiet al. 2007;Hu &Zhu 2009). This neglect is surprising considering thecurrent interest in networks (Albert & Barabasi 2002;Newman 2003a; Gross & Blasius 2008), especially air-port (Barrat et al. 2004; Guimera & Amaral 2004;

Hufnagel et al. 2004;Guimera et al. 2005), road (Buhlet al. 2006; Barthelemy & Flammini 2008) and trainnetworks (Latora & Marchiori 2002; Sen et al. 2003).In the spirit of current network research, we take herea large-scale perspective on the global cargo shipnetwork (GCSN) as a complex system defined as thenetwork of ports that are connected by links if shiptraffic passes between them.

Similar research in the past had to make strongassumptions about flows on hypothetical networkswith connections between all pairs of ports in order toapproximate ship movements (Drake & Lodge 2004;Tatem et al. 2006). By contrast, our analysis is based

on comprehensive data of real ship journeys allowingus to construct the actual network. We show that ithas a small-world topology where the combined cargocapacity of ships calling at a given port (measured in

*Author for correspondence ([email protected]).

Electronic supplementary material is available at http://dx.doi.org/10.1098/rsif.2009.0495 or viahttp://rsif.royalsocietypublishing.org.

J. R. Soc. Interface(2010) 7, 10931103

doi:10.1098/rsif.2009.0495

Published online19 January 2010

Received11 November 2009Accepted21 December 2009 1093 This journal is q 2010 The Royal Society

mailto:[email protected]://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495http://dx.doi.org/10.1098/rsif.2009.0495mailto:[email protected]


3/12

gross tonnage (GT)) follows a heavy-tailed distribution.This capacity scales superlinearly with the number ofdirectly connected ports. We identify the most centralports in the network and find several groups of highlyinterconnected ports showing the importance ofregional geopolitical and trading blocks.

A high-level description of the complete network,however, does not yet fully capture the networks com-plexity. Unlike previously studied transportationnetworks, the GCSN has a multi-layered structure.

There are, broadly speaking, three classes of cargoshipscontainer ships, bulk dry carriers and oiltankersthat span distinct subnetworks. Ships indifferent categories tend to call at different ports andtravel in distinct patterns. We analyse the trajectoriesof individual ships in the GCSN and develop techniquesto extract quantitative information about characteristicmovement types. With these methods, we can quantifythat container ships sail along more predictable, fre-quently repeating routes than oil tankers or bulk drycarriers. We compare the empirical data with theoreti-cal traffic flows calculated by the gravity model.Simulation results, based on the full GCSN data or

the gravity model, differ significantly in a population-dynamic model for the spread of invasive speciesbetween the worlds ports. Predictions based on thereal network are thus more informative for internationalpolicy decisions concerning the stability of worldwidetrade and for reducing the risks of bioinvasion.

2. DATA

An analysis of global ship movements requires detailedknowledge of ships arrival and departure times at theirports of call. Such data have become available in recent

years. Starting in 2001, ships and ports have beguninstalling the automatic identification system (AIS)equipment. AIS transmitters on board of the shipsautomatically report the arrival and departure times

to the port authorities. This technology is primarilyused to avoid collisions and increase port security, butarrival and departure records are also made availableby Lloyds Register Fairplay for commercial purposesas part of its Sea-web database (www.sea-web.com).AIS devices have not been installed in all ships andports yet, and therefore there are some gaps in thedata. Still, all major ports and the largest ships areincluded, thus the database represents the majority ofcargo transported on ships.

Our study is based on Sea-webs arrival anddeparture records in the calendar year 2007 as well asSea-webs comprehensive data on the ships physicalcharacteristics. We restrict our study to cargo shipsbigger than 10 000 GT that make up 93 per cent ofthe worlds total capacity for cargo ship transport.From these, we select all 16 363 ships for which AISdata are available, taken as representative of theglobal traffic and long distance trade between the 951ports equipped with AIS receivers (for details see elec-tronic supplementary material). For each ship, weobtain a trajectory from the database, i.e. a list ofports visited by the ship sorted by date. In 2007,

there were 490 517 non-stop journeys linking 36 351 dis-tinct pairs of arrival and departure ports. The completeset of trajectories, each path representing the shortestroute at sea and coloured by the number of journeyspassing through it, is shown infigure 1a.

Each trajectory can be interpreted as a smalldirected network where the nodes are ports linkedtogether if the ship travelled directly between theports. Larger networks can be defined by merging tra-jectories of different ships. In this article, weaggregate trajectories in four different ways: the com-bined network of all available trajectories and thesubnetworks of container ships (3100 ships), bulk dry

carriers (5498) and oil tankers (2628). These three sub-networks combinedly cover 74 per cent of the GCSNstotal GT. In all four networks, we assign a weight wijto the link from port i to j equal to the sum of the

5000

journeys

0

1

2

3

>4

betweenness(104)

the 20 most central ports

1 Panama Canal2 Suez Canal3 Shanghai4 Singapore5 Antwerp6 Piraeus7 Terneuzen8 Plaquemines9 Houston10 Ijmuiden

11 Santos12 Tianjin13 New York and New Jersey14 Europoort15 Hamburg16 Le Havre17 St Petersburg18 Bremerhaven19 Las Palmas20 Barcelona

(a)(a) (b)

Figure 1. Routes, ports and betweenness centralities in the GCSN. ( a) The trajectories of all cargo ships bigger than 10 000 GTduring 2007. The colour scale indicates the number of journeys along each route. Ships are assumed to travel along the shortest

(geodesic) paths on water. (b) A map of the 50 ports of highest betweenness centrality and a ranked list of the 20 most central ports.

1094 Complex network of ship movements P. Kaluza et al.

J. R. Soc. Interface (2010)

http://www.sea-web.com/http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://www.sea-web.com/


4/12

available space on all ships that have travelled on thelink during 2007 measured in GT. If a ship made a jour-ney fromito jmore than once, its capacity contributesmultiple times to wij.

3. THE GLOBAL CARGO SHIP NETWORK

The directed network of the entire cargo fleet is notice-ably asymmetric, with 59 per cent of all linked pairs ofports being connected only in one direction. Still, thevast majority of ports (935 out of 951) belongs to onesingle strongly connected component, i.e. for any twoports in this component, there are routes in both direc-tions, though possibly visiting different intermediateports. The routes are intriguingly short: only few stepsin the network are needed to get from one port toanother. The shortest path length lbetween two portsis the minimum number of non-stop connections onemust take to travel between origin and destination. In

the GCSN, the average over all pairs of ports is extre-mely small, kll 2:5. Even the maximum shortestpath between any two ports (e.g. from Skagway,Alaska, to the small Italian island of Lampedusa) isonly of lengthlmax 8. In fact, the majority of all poss-ible origin destination pairs (52%) can already beconnected by two steps or less.

Comparing these findings to those reported for theworldwide airport network (WAN) shows interestingdifferences and similarities. The high asymmetry ofthe GCSN has not been found in the WAN, indicatingthat ship traffic is structurally very different from avia-tion. Rather than being formed by the accumulation of

back-and-forth trips, ship traffic seems to be governedby an optimal arrangement of unidirectional, often cir-cular routes. This optimality also shows in the GCSNssmall shortest path lengths. In comparison, in theWAN, the average and maximum shortest path lengthsarekll 4:4 andlmax 15, respectively (Guimeraet al.2005), i.e. about twice as long as in the GCSN. Similarto the WAN, the GCSN is highly clustered: if a port Xislinked to portsYand Z, there is a high probability thatthere is also a connection from Yto Z. We calculated aclustering coefficient C (Watts & Strogatz 1998) fordirected networks and found C 0.49, whereasrandom networks with the same number of nodes and

links only yieldC 0.04 on average. Degree-dependentclustering coefficients Ck reveal that clusteringdecreases with node degree (see electronic supplemen-tary material). Therefore, the GCSNlike theWANcan be regarded as a small-world network pos-sessing short path lengths despite substantialclustering (Watts & Strogatz 1998). However, the aver-age degree of the GCSN, i.e. the average number of linksarriving at and departing from a given port (in-degreeplus out-degree), kkl 76.5, is notably higher than inthe WAN, where kkl 19.4 (Barrat et al. 2004). Inthe light of the network size (the WAN consists of3880 nodes), this difference becomes even more pro-

nounced, indicating that the GCSN is much moredensely connected. This redundancy of links gives thenetwork high structural robustness to the loss ofroutes for keeping up trade.

The degree distributionP(k) shows that most portshave few connections, but there are some ports linkedto hundreds of other ports ( figure 2a). Similar right-skewed degree distributions have been observed inmany real-world networks (Barabasi & Albert 1999).While the GCSNs degree distribution is not exactlyscale-free, the distribution of link weights, P(w), fol-

lows approximately a power law Pw/ wm

withm 1:71+ 0:14 (95% CI for linear regression,figure 2b, see also electronic supplementary material).By averaging the sums of the link weights arrivingat and departing from port i, we obtain the nodestrength si (Barrat et al. 2004). The strength distri-bution can also be approximated by a power lawPs/ sh with h 1:02+ 0:17, meaning that asmall number of ports handle huge amounts of cargo(figure 2c). The determination of power law relation-ships by line fitting has been strongly criticized (e.g.Newman 2005; Clauset et al. 2009), therefore, weanalysed the distributions with model selection by

Akaike weights (Burnham & Anderson 1998). Ourresults confirm that a power law is a better fit thanan exponential or a lognormal distribution for P(w)and P(s), but not P(k) (see electronic supplementarymaterial). These findings agree well with the conceptof hubsspokes networks (Notteboom 2004) thatwere proposed for cargo traffic, for example, in Asia(Robinson 1998). There are a few large, highly con-nected ports through which all smaller ports transacttheir trade. This scale-free property makes the shiptrade network prone to the spreading and persistenceof bioinvasive organisms (e.g. Pastor-Satorras &Vespignani 2001). The average nearest-neighbour

degree, a measure of network assortativity, addition-ally underlines the hubs spokes property of cargoship traffic (see electronic supplementary material).

Strengths and degrees of the ports are related accord-ing to the scaling relation kskl/ k1:46+0:1 (95% CI forstandardized major axis regression;Wartonet al.2006).Hence, the strength of a port grows generally fasterthan its degree (figure 2d). In other words, highly con-nected ports not only have many links, but their linksalso have a higher than average weight. This obser-vation agrees with the fact that busy ports are betterequipped to handle large ships with large amounts ofcargo. A similar result, kskl/ k1:5+0:1, was found forairports (Barrat et al. 2004), which may hint at a gen-eral pattern in transportation networks. In the light ofbioinvasion, these results underline empirical findingsthat big ports are more heavily invaded because ofincreased propagule pressure by ballast water of moreand larger ships (Williamson 1996; Mack et al. 2000;seeCohen & Carlton 1998).

A further indication of the importance of a node is itsbetweenness centrality (Freeman 1979;Newman 2004).The betweenness of a port is the number of topologi-cally shortest directed paths in the network that passthrough this port. In figure 1b, we plot and list themost central ports. Generally speaking, centrality and

degree are strongly correlated (Pearsons correlationcoefficient: 0.81), but in individual cases other factorscan also play a role. The Panama and Suez canals, forinstance, are shortcuts to avoid long passages around

Complex network of ship movements P. Kaluza et al. 1095


http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/


5/12

South America and Africa. Other ports have a high cen-trality because they are visited by a large number ofships (e.g. Shanghai), whereas others gain their statusprimarily by being connected to many different ports

(e.g. Antwerp).

4. THE NETWORK LAYERS OF DIFFERENTSHIP TYPES

To compare the movements of cargo ships of differenttypes, separate networks were generated for each ofthe three main ship types: container ships, bulk dry car-riers and oil tankers. Applying the network parametersintroduced in the previous section to these three subnet-works reveals some broad-scale differences (table 1).The network of container ships is densely clustered,

C 0.52, has a rather low mean degree, kkl 32:44,and a large mean number of journeys (i.e. number oftimes any ship passes) per link, kJl 24:26. The bulkdry carrier network, on the other hand, is less clustered,

has a higher mean degree and fewer journeys per link(C 0:43,kkl 44:61,kJl 4:65). For the oil tankers,we find intermediate values (C 0:44, kkl 33:32,kJl 5:07). Note that the mean degrees kkl of the sub-networks are substantially smaller than that of the fullGCSN, indicating that different ship types useessentially the same ports but different connections.

A similar tendency appears in the scaling of the linkweight distributions (figure 2b). P(w) can be approxi-mated as power laws for each network, but withdifferent exponents m. The container ships have thesmallest exponent (m 1.42) and bulk dry carriers thelargest (m 1.93) with oil tankers in between (m1.73). In contrast, the exponents for the distribution ofnode strength P(s) are nearly identical in all three sub-networks,h 1.05,h 1.13 andh 1.01, respectively.

These numbers give a first indication that different

ship types move in distinctive patterns. Containerships typically follow set schedules visiting severalports in a fixed sequence along their way, thus provid-ing regular services. Bulk dry carriers, by contrast,

101(a) (b)

(c) (d)

102

103P(k)

104

104

105

106

107

108

104

103

102

101

1 10 102

degree, k link weight, w

102 104

104

105

106

107

108

109

1010

1011

105

106

107

108

109

1010

105 106 107

104 105 106 107 108

101

103

107106105 101 100 1000104

node strength, s degree, k

108

104

1011

1010

109

P(w)

108

107

106

105

1010

109

108P(s)

107

106

105

105 106 107 108

s(k)

Figure 2. Degrees and weights in the GCSN. (a) The degree distributionsP(k) are right-skewed, but not power laws, neither forthe GCSN nor its subnetworks. The degreekis defined here as the sum of in- and out-degree, thusk 1 is rather rare (asterisk, allship types; square, container ships; circle, bulk dry carriers; triangle, oil tankers). ( b) The link weight distributions P(w) revealclear power law relationships for the GCSN and the three subnetworks, with exponents m characteristic for the movement pat-

terns of the different ship types (asterisk, m 1.71+0.14; square,m 1.42+0.15; circle,m 1.93+0.11; triangle,m 1.73+0.25). (c) The node strength distributions P(s) are also heavy tailed, showing power law relationships. The stated exponents arecalculated by linear regression with 95% confidence intervals (similar results are obtained with maximum likelihood estimates, seeelectronic supplementary material) (asterisk, h 1.02+0.17; square, h 1.05+0.13; circle, h 1.13+0.21; triangle, h1.01+0.16). (d) The average strength of a node ks(k)l scales superlinearly with its degree, ks(k)l/ k1.46+0.1, indicating thathighly connected ports have, on average, links of higher weight.





6/12

appear less predictable as they frequently change theirroutes on short notice depending on the currentsupply and demand of the goods they carry. Thelarger variety of origins and destinations in the bulkdry carrier network (n 616 ports, compared withn 378 for container ships) explains the higher averagedegree and the smaller number of journeys for a given

link. Oil tankers also follow short-term market trends,but, because they can only load oil and oil products,the number of possible destinations (n 505) is morelimited than for bulk dry carriers.

These differences are also underlined by the between-ness centralities of the three network layers (seeelectronic supplementary material). While some portsrank highly in all categories (e.g. Suez Canal,Shanghai), others are specialized on certain shiptypes. For example, the German port of Wilhelmshavenranks tenth in terms of its worldwide betweenness for oiltankers, but is only 241st for bulk dry carriers and324th for container ships.

We can gain further insight into the roles of the portsby examining their community structure. Communitiesare groups of ports with many links within the groupsbut few links between different groups. We calculatedthese communities for the three subnetworks with amodularity optimization method for directed networks(Leicht & Newman 2008) and found that they differsignificantly from modularities of correspondingErdosRenyi graphs (figure 3; Guimera et al. 2004).The network of container trade shows 12 communities(figure 3a). The largest ones are located (i) on theArabian, Asian and South African coasts, (ii) on theNorth American east coast and in the Caribbean, (iii)

in the Mediterranean, the Black Sea and on the Euro-pean west coast, (iv) in Northern Europe and (v) inthe Far East and on the American west coast. Thetransport of bulk dry goods reveals seven groups(figure 3b). Some can be interpreted as geographicalentities (e.g. North American east coast, trans-Pacifictrade), while others are dispersed on multiple continents.Especially interesting is the community structure of theoil transportation network that shows six groups(figure 3c): (i) the European, north and west Africanmarket, (ii) a large community comprising Asia,South Africa and Australia, (iii) three groups for theAtlantic market with trade between Venezuela, the

Gulf of Mexico, the American east coast and NorthernEurope and (iv) the American Pacific coast. It shouldbe noted that the network includes the transport ofcrude oil as well as commerce with already refined oil

products so that oil-producing regions do not appearas separate communities. This may be due to thelimit in the detectability of smaller communities bymodularity optimization (Fortunato & Barthelemy2007), but does not affect the relevance of the revealedship traffic communities. Because of the, by definition,higher transport intensity within communities, bioinva-

sive spread is expected to be heavier between ports ofthe same community. However, in figure 3, it becomesclear that there are no strict geographical barriersbetween communities. Thus, spread between commu-nities is very likely to occur even on small spatialscales by shipping or ocean currents between close-byports that belong to different communities.

Despite the differences between the three main cargofleets, there is one unifying feature: their motif distri-bution (Milo et al. 2002). Like most previous studies,we focus here on the occurrence of three-node motifsand present their normalized Z score, a measure fortheir abundance in a network (figure 4). Strikingly,

the three fleets have practically the same motif distri-bution. In fact, the Z scores closely resemble thosefound in the World Wide Web and different social net-works that were conjectured to form a superfamily ofnetworks (Milo et al. 2004). This superfamily displaysmany transitive triplet interactions (i.e. ifX! Y andY! Z, thenX! Z); for example, the overrepresentedmotif 13 infigure 4, has six such interactions. Intransi-tive motifs, like motif 6, are comparably infrequent. Theabundance of transitive interactions in the ship net-works indicates that cargo can be transported bothdirectly between ports as well as via several intermedi-ate ports. Thus, the high clustering and redundancy of

links (robustness to link failures) appear not only in theGCSN but also in the three subnetworks. The similarityof the motif distributions to other humanly optimizednetworks underlines that cargo trade, like social net-works and the World Wide Web, depends crucially onhuman interactions and information exchange. Whileadvantageous for the robustness of trade, the clusteringof links as triplets also has an unwanted side effect: ingeneral, the more clustered a network, the more vulner-able it becomes to the global spread of alien species,even for low invasion probabilities (Newman 2003b).

5. NETWORK TRAJECTORIES

Going beyond the network perspective, the databasealso provides information about the movement

Table 1. Characterization of different subnetworks. Number of ships, total GT (106 GT) and number of ports n in eachsubnetwork; together with network characteristics: mean degree kkl, clustering coefficient C, mean shortest path length k ll,mean journeys per link kJl, power law exponents m and h; and trajectory properties: average number of distinct ports kNl,links kLl, port calls kSlper ship and regularity index kpl. Some notable values are highlighted in bold.

ship class ships MGT n kkl C kll kJl m h kNl kLl kSl kpl

whole fleet 16 363 664.7 951 76.4 0.49 2.5 13.57 1.71 1.02 10.4 15.6 31.8 0.63

container ships 3100 116.8 378 32.4 0.52 2.76 24.25 1.42 1 .05 11.2 21.2 48.9 1.84bulk dry carriers 5498 196.8 616 44.6 0.43 2.57 4.65 1.93 1.13 8.9 10.4 12.2 0.03oil tankers 2628 178.4 505 33.3 0.44 2.74 5.07 1.73 1.01 9.2 12.9 17.7 0.19





7/12

characteristics per individual ship (table 1). The aver-age number of distinct ports per ship kNl does notdiffer much between different ship classes, but con-tainer ships call much more frequently at ports than

bulk dry carriers and oil tankers. This difference isexplained by the characteristics and operationalmode of these ships. Normally, container ships arefast (between 20 and 25 knots) and spend less time

(1.9 days on average in our data) in the ports forcargo operations. By contrast, bulk dry carriers andoil tankers move more slowly (between 13 and 17knots) and stay longer in the ports (on average 5.6

days for bulk dry carriers and 4.6 days for oiltankers).

The speed at sea and of cargo handling, however, isnot the only operational difference. The topology of

(a)

(b)

(c)

Figure 3. Communities of ports in three cargo ship subnetworks. The communities are groups of ports that maximize the numberof links within the groups, as opposed to between the groups, in terms of the modularity Q(Leicht & Newman 2008). In eachmap, the colours represent the c distinct trading communities for the goods transported by (a) container ships (c 12, Q0.605), (b) bulk dry carriers (c 7, Q 0.592) and (c) oil tankers (c 6, Q 0.716). All modularities Qof the examined net-works differ significantly from modularities in ErdosRenyi graphs of the same size and number of links (Guimeraet al. 2004).For the networks corresponding to (a), (b) and (c), values are QER 0.219, QER 0.182 and QER 0.220, respectively.





8/12

the trajectories also differs substantially. Characteristicsample trajectories for each ship type are presented infigure 5a c. The container ship (figure 5a) travels onsome of the links several times during the studyperiod, whereas the bulk dry carrier (figure 5b) passesalmost every link exactly once. The oil tanker

(figure 5c) commutes a few times between some ports,but by and large also serves most links only once.We can express these trends in terms of a regularity

index p that quantifies how much the frequency withwhich each link is used deviates from a random network.Consider the trajectory of a ship callingStimes atNdis-tinct ports and travelling on L distinct links. Wecompare the mean number of journeys per linkfreal S=Lto the average link usage fran in an ensembleof randomized trajectories with the same number ofnodes N and port calls S. To quantify the differencebetween real and random trajectories, we calculate theZscorep freal fran=s(where sis the standard devi-ation of f in the random ensemble). If p

0, the realtrajectory is indistinguishable from a random walk,whereas larger values of p indicate that the movementis more regular. Figure 5df present the distributionsof the regularity index p for the different fleets. For con-tainer ships,p is distributed broadly around p 2, thussupporting our earlier observation that most containerships provide regular services between ports along theirway. Trajectories of bulk dry carriers and oil tankers,on the other hand, appear essentially random with thevast majority of ships near p 0.

6. APPROXIMATING TRAFFIC FLOWSUSING THE GRAVITY MODEL

In this article, we view global ship movements as a net-work based on detailed arrival and departure records.

Until recently, surveys of seaborne trade had to relyon far fewer data: only the total number of arrivals atsome major ports was publicly accessible, but not theships actual paths (Zachcial & Heideloff 2001). Missinginformation about the frequency of journeys, thus, hadto be replaced by plausible assumptions, the gravity

model being the most popular choice. It posits thattrips are, in general, more likely between nearby portsthan between ports far apart. If dij is the distancebetween portsiand j, the decline in mutual interactionis expressed in terms of a distance deterrence functionf(dij). The number of journeys from i to j then takesthe form Fij aibjOiIjfdij, where Oi is the totalnumber of departures from port i and Ij the numberof arrivals at j (Haynes & Fotheringham 1984). Thecoefficients aiand bjare needed to ensure

PjFij Oi

andP

iFij Ij.How well can the gravity model approximate real

ship traffic? We choose a truncated power law for the

deterrence function, fdij db

ij expdij=k. Thestrongest correlation between model and data isobtained for b 0:59 and k 4900 km (see electronicsupplementary material). At first sight, the agreementbetween data and model appears indeed impressive.The predicted distribution of travelled distances(figure 6a) fits the data far better than a simpler non-spatial model that preserves the total number ofjourneys, but assumes completely random origins anddestinations.

A closer look at the gravity model, however, revealsits limitations. In figure 6b, we count how often linkswith an observed number of journeys Nij are predicted

to be passed Fij times. Ideally, all data points wouldalign along the diagonal Fij Nij, but we find thatthe data are substantially scattered. Although the par-ameters b and kwere chosen to minimize the scatter,

0.75

0.50

0.25

0

0.25normalizedZscore

0.50

0.751 2 3 4 5 6 7

subgraph

8 9 10 11 12 13

Figure 4. Motif distributions of the three main cargo fleets. A positive (negative) normalizedZscore indicates that a motif is more

(less) frequent in the real network than in random networks with the same degree sequence. For comparison, we overlay the Zscores of the World Wide Web and social networks. The agreement suggests that the ship networks fall in the same superfamily ofnetworks (Milo et al. 2004). The motif distributions of the fleets are maintained even when 25, 50 and 75% of the weakest con-nections are removed. Line with open circles, www-1; line with open squares, www-2; line with open diamonds, www-3; line withtriangles, social-1; line with crosses, social-2; line with asterisks, social-3; line with red circles, bulk dry carriers; line with bluesquares, container ships; line with black diamonds, oil tankers.





9/12

the correlation between data and model is only moder-ate (Kendalls t 0.433). In some cases, the predictionis off by several thousand journeys per year.

Recent studies have used the gravity model to pin-point the ports and routes central to the spread ofinvasive species (Drake & Lodge 2004; Tatem et al.2006). The models shortcomings pose the question asto how reliable such predictions are. For this purpose,we investigated a dynamic model of ship-mediatedbioinvasion where the weights of the links are eitherthe observed traffic flows or the flows of the gravity

model.We follow previous epidemiological studies (Rvachev &

Longini 1985;Flahaultet al.1988;Hufnagelet al.2004;Colizza et al. 2006) in viewing the spread on the

network as a metapopulation process where the popu-lation dynamics on the nodes are coupled bytransport on the links. In our model, ships can transporta surviving population of an invasive species with only asmall probability ptrans 1% on each journey betweentwo successively visited ports. The transported popu-lation is only a tiny fraction sof the population at theport of origin. Immediately after arriving at a newport, the species experiences strong demographic fluctu-ations that lead, in most cases, to the death of theimported population. If, however, the new immigrants

beat the odds of this ecological roulette (Carlton &Geller 1993) and establish, the population P growsrapidly following the stochastic logistic equationdP=dt rP1 P ffiffiffiffiPp jt with growth rate r 1

Mina Al Ahmadi4

44

4

1

1Terneuzen Buenos Aires

Montevideo

Jebel Ali

Jubail

Port Rashid

Santos

Kalamaki

YuzhnyPiraeus

Algiers

Rouen

Ghazaouet

Port Jerome

El Dekheila

Ras Laffan

Santos

Antwerp

HamburgRotterdam

Botlek

Vlaardingen

Cuxhaven

Emden

(a) (c)

(b)

21

4

3

2

1

1

1

11

1

1

34

1

1

1

1

11

1

11

1

2

1

1

1

1

1

1

1

2

2

2

Jebel Dhanna/Ruwais

Singapore

(d) (e) (f)3 container ships

2

1

D(p)

00 2 4

p6 8

bulk dry carriers

0 2 4p

6 8

oil tankers

0 2 4p

6 8

Figure 5. Sample trajectories of (a) a container ship with a regularity indexp 2.09, (b) a bulk dry carrier,p 0.098 and (c) anoil tanker,p 1.027. In the three trajectories, the numbers and the line thickness indicate the frequency of journeys on each link.(df) Distribution ofp for the three main fleets.





10/12

per year and Gaussian white noise j. For details of themodel, see the electronic supplementary material.

Starting from a single port at carrying capacityP 1,we model contacts between ports as Poisson processeswith rates Nij (empirical data) or Fij (gravity model).As shown infigure 7a, the gravity model systematicallyoverestimates the spreading rate, and the difference canbecome particularly pronounced for ports that are well

connected, but not among the central hubs in the net-work (figure 7b). Comparing typical sequences ofinvaded ports, we find that the invasions driven bythe real traffic flows tend to be initially confined tosmaller regional ports, whereas in the gravity modelthe invasions quickly reach the hubs. The total out-and in-flows at the ship journeys origin and departureports, respectively, are indeed more strongly positivelycorrelated in reality than in the model (t 0.157versus 0.047). The gravity model thus erases toomany details of a hierarchical structure present in thereal network. That the gravity model eliminates mostcorrelations is also plausible from simple analytic argu-

ments (see electronic supplementary material fordetails). The absence of strong correlations makes thegravity model a suitable null hypothesis if the corre-lations in the real network are unknown, but severalrecent studies have shown that correlations play animportant role in spreading processes on networks(e.g. Boguna & Pastor-Satorras 2002;Newman 2002).Hence, if the correlations are known, they should notbe ignored.

While we observed that the spreading rates for theAIS data were consistently slower than for the gravitymodel even when different parameters or populationmodels were considered, the time scale of the invasion

is much less predictable. The assumption that only asmall fraction of invaders succeed outside their nativehabitat appears realistic (Mack et al. 2000). Further-more, the parameters in our model were adjusted so

that the per-ship-call probability of initiating invasionis approximately 4.4

1024, a rule-of-thumb value

stated by Drake & Lodge (2004). Still, too little isempirically known to pin down individual parameterswith sufficient accuracy to give more than a qualitativeimpression. It is especially difficult to predict how a

0 5000 10000 15000 20000

distance (km)

1

10

102

103

104

105(a) (b)

number

ofjourneys

observed journeys, Nij

0 10 100 1000

predicted

journeys,Fij

01

10

102

103

1

10

102

103

104

number of

links

Figure 6. (a) Histogram of port-to-port distances travelled in the GCSN (navigable distances around continents as indicated infigure 1). We overlay the predictions of two different models. The gravity model (red), based on information about distancesbetween ports and total port calls, gives a much better fit than a simpler model (blue) which only fixes the total number of jour-neys (black line, observed; red line, gravity model; blue line, random traffic). (b) Count of port pairs with Nijobserved and Fij

predicted journeys. The flowsFijwere calculated with the gravity model (rounded to the nearest integer). Some of the worst out-liers are highlighted in blue. Circle, Antwerp to Calais (Nij 0 versus Fij 200); triangle, Hook of Holland to Europoort(16 versus 1895); diamond, Calais to Dover (4392 versus 443); square, Harwich to Hook of Holland (644 versus 0).

0

100

200

300

400

0 10 20 30 40 50

time (years)

0

200

400

meann

umberofinvadedports

(a)

(b)

Figure 7. Results from a stochastic population model for thespread of an invasive species between ports. (a) The invasionstarts from one single, randomly chosen port. (b) The initialport is fixed as Bergen (Norway), an example of a well-connected port (degreek 49) which is not among the centralhubs. The rate of journeys from port ito jper year is assumedto be Nij (real flows from the GCSN) or Fij(gravity model).Each journey has a small probability of transporting a tiny frac-tion of the population from origin to destination. Parameterswere adjusted (r 1 per year, ptrans 0.01 and s 4 1025)to yield a per-ship-call probability of initiating invasion ofapproximately 4.4 1024 (Drake & Lodge 2004; see electronicsupplementary material for details). Plotted are the cumulativenumbers of invaded ports (population number larger than halfthe carrying capacity) averaged over (a) 14000 and (b) 1000simulation runs (standard error equal to line thickness).Black line, real traffic flows; grey line, gravity model.





11/12

potential invader reacts to the environmental con-ditions at a specific location. Growth rates certainlydiffer greatly between ports depending on factors suchas temperature or salinity, with respect to the habitatrequirements of the invading organisms. Our resultsshould, therefore, be regarded as one of many differentconceivable scenarios. A more detailed study of bioinva-

sion risks based on the GCSN is currently underway(H. Seebens & B. Blasius 2009, unpublished data).

7. CONCLUSION

We have presented a study of ship movements based onAIS records. Viewing the ports as nodes in a networklinked by ship journeys, we found that global cargo ship-ping, like many other complex networks investigated inrecent years, possesses the small-world property as well asbroad degree and weight distributions. Other features,like the importance of canals and the grouping of portsinto regional clusters, are more specific to the shippingindustry. An important characteristic of the network aredifferences in the movement patterns of different shiptypes. Bulk dry carriers and oil tankers tend to move in aless regular manner between ports than container ships.This is an important result regarding the spread of invasivespecies because bulk dry carriers and oil tankers often sailempty and therefore exchange large quantities of ballastwater. The gravity model, which is the traditionalapproach to forecasting marine biological invasions, cap-tures some broad trends of global cargo trade, but formany applications its results are too crude. Future strat-egies to curb invasions will have to take more details into

account. The network structure presented in this articlecan be viewed as a first step in this direction.

We thank B. Volk, K. H. Holocher, A. Wilkinson, J. M. Drakeand H. Rosenthal for stimulating discussions and helpfulsuggestions. We also thank Lloyds Register Fairplay forproviding their shipping database. This work was supportedby German VW-Stiftung and BMBF.

REFERENCES

Albert, R. & Barabasi, A.-L. 2002 Statistical mechanics ofcomplex networks. Rev. Mod. Phys. 74, 4797. (doi:10.1103/RevModPhys.74.47)

Barabasi, A.-L. & Albert, R. 1999 Emergence of scaling inrandom networks. Science 286, 509512. (doi:10.1126/science.286.5439.509)

Barrat, A., Barthelemy, M., Pastor-Satorras, R. &Vespignani, A. 2004 The architecture of complex weightednetworks. Proc. Natl Acad. Sci. USA 101, 37473752.(doi:10.1073/pnas.0400087101)

Barthelemy, M. & Flammini, A. 2008 Modeling urban streetpatterns. Phys. Rev. Lett. 100, 138 702. (doi:10.1103/PhysRevLett.100.138702)

Boguna, M. & Pastor-Satorras, R. 2002 Epidemic spreading incorrelated complex networks. Phys. Rev. E 66, 047 104.(doi:10.1103/PhysRevE.66.047104)

Buhl, J., Gautrais, J., Reeves, N., Sole, R. V., Valverde, S.,Kuntz, P. & Theraulaz, G. 2006 Topological patterns instreet networks of self-organized urban settlements. Eur.Phys. J. B49, 513 522. (doi:10.1140/epjb/e2006-00085-1)

Burnham, K. P. & Anderson, D. R. 1998Model selection andmultimodel inference. A practical information-theoreticapproach. New York, NY: Springer.

Carlton, J. T. & Geller, J. B. 1993 Ecological roulette:the global transport of nonindigenous marine organisms.Science261 , 7882. (doi:10.1126/science.261.5117.78)

Clauset, A., Shalizi, C. R. & Newman, M. E. J. 2009 Power-law distributions in empirical data. SIAM Rev. 51,

661703. (doi:10.1137/070710111)Cohen, A. N. & Carlton, J. T. 1998 Accelerating invasion rate

in a highly invaded estuary. Science 279, 555 558.(doi:10.1126/science.279.5350.555)

Colizza, V., Barrat, A., Barthelemy, M. & Vespignani, A. 2006The role of the airline transportation network in the pre-diction and predictability of global epidemics. Proc. NatlAcad. Sci. USA 103, 20152020. (doi:10.1073/pnas.0510525103)

Drake, J. M. & Lodge, D. M. 2004 Global hot spots of biologi-cal invasions: evaluating options for ballast-watermanagement. Proc. R. Soc. Lond. B 271, 575 580.(doi:10.1098/rspb.2003.2629)

Drake, J. M. & Lodge, D. M. 2007 Hull fouling is a risk factor

for intercontinental species exchange in aquatic ecosys-tems. Aquat. Invasions2, 121131. (doi:10.3391/ai.2007.2.2.7)

Flahault, A., Letrait, S., Blin, P., Hazout, S., Menares, J. &Valleron, A. J. 1988 Modelling the 1985 influenza epidemicin France. Stat. Med. 7, 11471155. (doi:10.1002/sim.4780071107)

Fortunato, S. & Barthelemy, M. 2007 Resolution limit in com-munity detection. Proc. Natl Acad. Sci. USA 104, 3641.(doi:10.1073/pnas.0605965104)

Freeman, L. C. 1979 Centrality in social networks I: concep-tual clarification. Soc. Netw. 1, 215239. (doi:10.1016/0378-8733(78)90021-7)

Gross, T. & Blasius, B. 2008 Adaptive coevolutionary net-

works: a review. J. R. Soc. Interface5, 259 271. (doi:10.1098/rsif.2007.1229)Guimera, R. & Amaral, L. A. N. 2004 Modeling the world-

wide airport network. Eur. Phys. J. B 38, 381 385.(doi:10.1140/epjb/e2004-00131-0)

Guimera, R., Sales-Pardo, M. & Amaral, L. A. N. 2004Modularity from fluctuations in random graphs andcomplex networks. Phys. Rev. E70, 025 101(R). (doi:10.1103/PhysRevE.70.025101)

Guimera, R., Mossa, S., Turtschi, A. & Amaral, L. A. N. 2005The worldwide air transportation network: anomalous cen-trality, community structure, and cities global roles.Proc.Natl Acad. Sci. USA 102, 77947799. (doi:10.1073/pnas.0407994102)

Haynes, K. E. & Fotheringham, A. S. 1984 Gravity and spatialinteraction models. Beverly Hills, CA: Sage.

Hu, Y. & Zhu, D. 2009 Empirical analysis of the worldwidemaritime transportation network. Phys. A 388, 20612071. (doi:10.1016/j.physa.2008.12.016)

Hufnagel, L., Brockmann, D. & Geisel, T. 2004 Forecast andcontrol of epidemics in a globalized world. Proc. NatlAcad. Sci. USA 101, 1512415 129. (doi:10.1073/pnas.0308344101)

International Maritime Organization. 2006 International ship-ping and world trade. Facts and figures. See http://www.imo.org/.

Latora, V. & Marchiori, M. 2002 Is the Boston subway asmall-world network? Phys. A 314, 109113. (doi:10.1016/S0378-4371(02)01089-0)

Leicht, E. A. & Newman, M. E. J. 2008 Community structurein directed networks. Phys. Rev. Lett. 100, 118 703.(doi:10.1103/PhysRevLett.100.118703)



http://dx.doi.org/doi:10.1103/RevModPhys.74.47http://dx.doi.org/doi:10.1103/RevModPhys.74.47http://dx.doi.org/doi:10.1103/RevModPhys.74.47http://dx.doi.org/doi:10.1103/RevModPhys.74.47http://dx.doi.org/doi:10.1126/science.286.5439.509http://dx.doi.org/doi:10.1126/science.286.5439.509http://dx.doi.org/doi:10.1126/science.286.5439.509http://dx.doi.org/doi:10.1073/pnas.0400087101http://dx.doi.org/doi:10.1073/pnas.0400087101http://dx.doi.org/doi:10.1073/pnas.0400087101http://dx.doi.org/doi:10.1103/PhysRevLett.100.138702http://dx.doi.org/doi:10.1103/PhysRevLett.100.138702http://dx.doi.org/doi:10.1103/PhysRevLett.100.138702http://dx.doi.org/doi:10.1103/PhysRevE.66.047104http://dx.doi.org/doi:10.1103/PhysRevE.66.047104http://dx.doi.org/doi:10.1103/PhysRevE.66.047104http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1126/science.261.5117.78http://dx.doi.org/doi:10.1126/science.261.5117.78http://dx.doi.org/doi:10.1126/science.261.5117.78http://dx.doi.org/doi:10.1137/070710111http://dx.doi.org/doi:10.1126/science.279.5350.555http://dx.doi.org/doi:10.1126/science.279.5350.555http://dx.doi.org/doi:10.1126/science.279.5350.555http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1098/rspb.2003.2629http://dx.doi.org/doi:10.1098/rspb.2003.2629http://dx.doi.org/doi:10.1098/rspb.2003.2629http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.1073/pnas.0605965104http://dx.doi.org/doi:10.1073/pnas.0605965104http://dx.doi.org/doi:10.1073/pnas.0605965104http://dx.doi.org/doi:10.1016/0378-8733(78)90021-7http://dx.doi.org/doi:10.1016/0378-8733(78)90021-7http://dx.doi.org/doi:10.1016/0378-8733(78)90021-7http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1016/j.physa.2008.12.016http://dx.doi.org/doi:10.1016/j.physa.2008.12.016http://dx.doi.org/doi:10.1016/j.physa.2008.12.016http://dx.doi.org/doi:10.1073/pnas.0308344101http://dx.doi.org/doi:10.1073/pnas.0308344101http://dx.doi.org/doi:10.1073/pnas.0308344101http://dx.doi.org/doi:10.1073/pnas.0308344101http://www.imo.org/http://www.imo.org/http://www.imo.org/http://www.imo.org/http://www.imo.org/http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://dx.doi.org/doi:10.1103/PhysRevLett.100.118703http://dx.doi.org/doi:10.1103/PhysRevLett.100.118703http://dx.doi.org/doi:10.1103/PhysRevLett.100.118703http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://dx.doi.org/doi:10.1103/PhysRevLett.100.118703http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://dx.doi.org/doi:10.1016/S0378-4371(02)01089-0http://www.imo.org/http://www.imo.org/http://www.imo.org/http://dx.doi.org/doi:10.1073/pnas.0308344101http://dx.doi.org/doi:10.1073/pnas.0308344101http://dx.doi.org/doi:10.1016/j.physa.2008.12.016http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1073/pnas.0407994102http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1103/PhysRevE.70.025101http://dx.doi.org/doi:10.1140/epjb/e2004-00131-0http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1098/rsif.2007.1229http://dx.doi.org/doi:10.1016/0378-8733(78)90021-7http://dx.doi.org/doi:10.1016/0378-8733(78)90021-7http://dx.doi.org/doi:10.1073/pnas.0605965104http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.1002/sim.4780071107http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.3391/ai.2007.2.2.7http://dx.doi.org/doi:10.1098/rspb.2003.2629http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1073/pnas.0510525103http://dx.doi.org/doi:10.1126/science.279.5350.555http://dx.doi.org/doi:10.1137/070710111http://dx.doi.org/doi:10.1126/science.261.5117.78http://dx.doi.org/doi:10.1140/epjb/e2006-00085-1http://dx.doi.org/doi:10.1103/PhysRevE.66.047104http://dx.doi.org/doi:10.1103/PhysRevLett.100.138702http://dx.doi.org/doi:10.1103/PhysRevLett.100.138702http://dx.doi.org/doi:10.1073/pnas.0400087101http://dx.doi.org/doi:10.1126/science.286.5439.509http://dx.doi.org/doi:10.1126/science.286.5439.509http://dx.doi.org/doi:10.1103/RevModPhys.74.47http://dx.doi.org/doi:10.1103/RevModPhys.74.47


12/12

Lounibos, L. P. 2002 Invasions by insect vectors of human dis-ease. Annu. Rev. Entomol. 47, 233266. (doi:10.1146/annurev.ento.47.091201.145206)

Mack, R. N., Simberloff, D., Lonsdale, W. M., Evans, H.,Clout, M. & Bazzaz, F. A. 2000 Biotic invasions: causes,epidemiology, global consequences, and control. Ecol.Appl. 10, 689 710. (doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2)

Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii,D. & Alon, U. 2002 Network motifs: simple building blocksof complex networks.Science298, 824 827. (doi:10.1126/science.298.5594.824)

Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S.,Ayzenshtat, I., Sheffer, M. & Alon, U. 2004 Superfamiliesof evolved and designed networks. Science 303,15381542. (doi:10.1126/science.1089167)

Newman, M. E. J. 2002 Assortative mixing in networks. Phys.Rev. Lett. 89, 208701. (doi:10.1103/PhysRevLett.89.208701)

Newman, M. E. J. 2003aThe structure and function of com-plex networks. SIAM Rev. 45, 167 256. (doi:10.1137/S003614450342480)

Newman, M. E. J. 2003b Properties of highly clusterednetworks. Phys. Rev. E 68, 026 121. (doi:10.1103/PhysRevE.68.026121 )

Newman, M. E. J. 2004 Who is the best connected scien-tist? A study of scientific coauthorship networks. InComplex networks (eds E. Ben-Naim, H. Frauenfelder &Z. Toroczkai), pp. 337370. Berlin, Germany: Springer.

Newman, M. E. J. 2005 Power laws, Pareto distributions andZipfs law. Contemp. Phys. 46, 323351. (doi:10.1080/00107510500052444)

Notteboom, T. E. 2004 Container shipping and ports: anoverview. Rev. Netw. Econ. 3, 86106. (doi:10.2202/1446-9022.1045)

Pastor-Satorras, R. & Vespignani, A. 2001 Epidemic spread-

ing in scale-free networks. Phys. Rev. Lett. 86,32003203. (doi:10.1103/PhysRevLett.86.3200 )Pimentel, D., Zuniga, R. & Morrison, D. 2005 Update on the

environmental costs associated with alien-invasive species

in the United States. Ecol. Econ. 52, 273288. (doi:10.1016/j.ecolecon.2004.10.002)

Robinson, R. 1998 Asian hub/feeder nets: the dynamics ofrestructuring. Marit. Policy Manag. 25, 2140. (doi:10.1080/03088839800000043)

Rodrigue, J.-P., Comtois, C. & Slack, B. 2006 The geographyof transport systems. London, UK: Routledge.

Ruiz, G. M., Rawlings, T. K., Dobbs, F. C., Drake, L. A.,

Mullady, T., Huq, A. & Colwell, R. R. 2000 Globalspread of microorganisms by ships. Nature 408, 4950.(doi:10.1038/35040695)

Rvachev, L. A. & Longini Jr, I. M. 1985 A mathematicalmodel for the global spread of influenza. Math. Biosci.75, 3 22. (doi:10.1016/0025-5564(85)90064-1)

Sen, P., Dasgupta, S., Chatterjee, A., Sreeram, P. A.,Mukherjee, G. & Manna, S. S. 2003 Small-world propertiesof the Indian railway network. Phys. Rev. E67, 036 106.(doi:10.1103/PhysRevE.67.036106)

Tatem, A. J., Hay, S. I. & Rogers, D. J. 2006 Global trafficand disease vector dispersal. Proc. Natl Acad. Sci. USA103, 62426247. (doi:10.1073/pnas.0508391103)

United Nations Conference on Trade and Development. 2007

Review of maritime transport. See http://www.unctad.org/en/docs/rmt2007_en.pdf.Warton, D. I., Wright, I. J., Falster, D. S. & Westoby, M.

2006 Bivariate line-fitting methods for allometry. Biol.Rev. 81, 259291. (doi:10.1017/S1464793106007007)

Watts, D. J. & Strogatz, S. H. 1998 Collective dynamics ofsmall-world networks. Nature 393, 440442. (doi:10.1038/30918)

Wei, T., Deng, G. & Wu, P. 2007 Analysis of network effect inport and shipping system characterized by scale-freenetwork. In Proc. Int. Conf. on Intelligent Systems andKnowledge Engineering. Amsterdam, The Netherlands:Atlantic Press.

Williamson, M. 1996 Biological invasions. London, UK:

Chapman and Hall.Zachcial, M. & Heideloff, C. 2001 ISL shipping statistics year-book 2001. Technical report, Institute of ShippingEconomics and Logistics, Bremen, Germany.



http://dx.doi.org/doi:10.1146/annurev.ento.47.091201.145206http://dx.doi.org/doi:10.1146/annurev.ento.47.091201.145206http://dx.doi.org/doi:10.1146/annurev.ento.47.091201.145206http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1126/science.298.5594.824http://dx.doi.org/doi:10.1126/science.298.5594.824http://dx.doi.org/doi:10.1126/science.298.5594.824http://dx.doi.org/doi:10.1126/science.1089167http://dx.doi.org/doi:10.1126/science.1089167http://dx.doi.org/doi:10.1126/science.1089167http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1137/S003614450342480http://dx.doi.org/doi:10.1137/S003614450342480http://dx.doi.org/doi:10.1137/S003614450342480http://dx.doi.org/doi:10.1103/PhysRevE.68.026121http://dx.doi.org/doi:10.1103/PhysRevE.68.026121http://dx.doi.org/doi:10.1103/PhysRevE.68.026121http://dx.doi.org/doi:10.1080/00107510500052444http://dx.doi.org/doi:10.1080/00107510500052444http://dx.doi.org/doi:10.1080/00107510500052444http://dx.doi.org/doi:10.2202/1446-9022.1045http://dx.doi.org/doi:10.2202/1446-9022.1045http://dx.doi.org/doi:10.2202/1446-9022.1045http://dx.doi.org/doi:10.1103/PhysRevLett.86.3200http://dx.doi.org/doi:10.1103/PhysRevLett.86.3200http://dx.doi.org/doi:10.1103/PhysRevLett.86.3200http://dx.doi.org/doi:10.1016/j.ecolecon.2004.10.002http://dx.doi.org/doi:10.1016/j.ecolecon.2004.10.002http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1038/35040695http://dx.doi.org/doi:10.1038/35040695http://dx.doi.org/doi:10.1038/35040695http://dx.doi.org/doi:10.1016/0025-5564(85)90064-1http://dx.doi.org/doi:10.1016/0025-5564(85)90064-1http://dx.doi.org/doi:10.1016/0025-5564(85)90064-1http://dx.doi.org/doi:10.1103/PhysRevE.67.036106http://dx.doi.org/doi:10.1103/PhysRevE.67.036106http://dx.doi.org/doi:10.1103/PhysRevE.67.036106http://dx.doi.org/doi:10.1073/pnas.0508391103http://dx.doi.org/doi:10.1073/pnas.0508391103http://dx.doi.org/doi:10.1073/pnas.0508391103http://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://dx.doi.org/doi:10.1017/S1464793106007007http://dx.doi.org/doi:10.1017/S1464793106007007http://dx.doi.org/doi:10.1017/S1464793106007007http://dx.doi.org/doi:10.1038/30918http://dx.doi.org/doi:10.1038/30918http://dx.doi.org/doi:10.1038/30918http://dx.doi.org/doi:10.1038/30918http://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/http://dx.doi.org/doi:10.1038/30918http://dx.doi.org/doi:10.1038/30918http://dx.doi.org/doi:10.1017/S1464793106007007http://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://www.unctad.org/en/docs/rmt2007_en.pdfhttp://dx.doi.org/doi:10.1073/pnas.0508391103http://dx.doi.org/doi:10.1103/PhysRevE.67.036106http://dx.doi.org/doi:10.1016/0025-5564(85)90064-1http://dx.doi.org/doi:10.1038/35040695http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1080/03088839800000043http://dx.doi.org/doi:10.1016/j.ecolecon.2004.10.002http://dx.doi.org/doi:10.1016/j.ecolecon.2004.10.002http://dx.doi.org/doi:10.1103/PhysRevLett.86.3200http://dx.doi.org/doi:10.2202/1446-9022.1045http://dx.doi.org/doi:10.2202/1446-9022.1045http://dx.doi.org/doi:10.1080/00107510500052444http://dx.doi.org/doi:10.1080/00107510500052444http://dx.doi.org/doi:10.1103/PhysRevE.68.026121http://dx.doi.org/doi:10.1103/PhysRevE.68.026121http://dx.doi.org/doi:10.1137/S003614450342480http://dx.doi.org/doi:10.1137/S003614450342480http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1103/PhysRevLett.89.208701http://dx.doi.org/doi:10.1126/science.1089167http://dx.doi.org/doi:10.1126/science.298.5594.824http://dx.doi.org/doi:10.1126/science.298.5594.824http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2http://dx.doi.org/doi:10.1146/annurev.ento.47.091201.145206http://dx.doi.org/doi:10.1146/annurev.ento.47.091201.145206

the complex network of global cargo ship movements

Documents