Transportation networks play a crucial role in human mobility, the exchange of goods and the spread of invasive species. With 90 per cent of world trade carried by sea, the global network 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 2007 to construct a network of links between ports. We show that the network has several features 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. These three categories do not only differ in the ships' physical characteristics, but also in their mobility patterns and networks. Container ships follow regularly repeating paths whereas bulk dry carriers and oil tankers move less predictably between ports. The network of all ship movements possesses a heavy-tailed distribution for the connectivity of ports and for 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 of ship movements, an important step towards understanding patterns of global trade and bioinvasion.

Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the method with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news. Suppose we wish to represent on a map some data concerning, to take the most common example, the human population. For instance, we might wish to show votes in an election, incidence of a disease, number of cars, televisions, or phones in use, numbers of people falling in one group or another of the population, by age or income, or any of very many other variables of statistical, medical, or demographic interest. The typical course under such circumstances would be to choose one of the standard projections for the area of interest and plot the data on it with some color code or similar representation. Such maps, however, can be misleading. A plot of disease incidence, for example, will inevitably show high incidence in cities and low incidence in rural areas, solely because more people live in cities.The obvious cure for this problem is to plot a fractional measure rather than raw incidence data; we plot some measure of the number of cases per capita, binned in segments small enough to give good spatial resolution but large enough to give reliable sampling. This method has its own problems, however, because it discards all information about where most of the cases are occurring. One case per thousand people means something entirely different in Sydney from what it means in Siberia.What we would like is some representation of the data that factors out variations in the population density but, at the same time, shows how many cases are occurring in each region. It appears at first that these two goals are irreconcilable, but this is not the case. On a normal area-preserving or approximately area-preserving projection, such as a Robinson projection or an equal-area conic projection, they are indeed irreconcilable. However, if we can construct a projection in which areas on the map are proportional not to areas on the ground but...

The rate of biological invasions has strongly increased during the last decades, mostly due to the accelerated spread of species by increasing global trade and transport. Here, we combine the network of global cargo ship movements with port environmental conditions and biogeography to quantify the probability of new primary invasions through the release of ballast water. We find that invasion risks vary widely between coastal ecosystems and classify marine ecoregions according to their total invasion risk and the diversity of their invasion sources. Thereby, we identify high-risk invasion routes, hot spots of bioinvasion and major source regions from which bioinvasion is likely to occur. Our predictions agree with observations in the field and reveal that the invasion probability is highest for intermediate geographic distances between donor and recipient ports. Our findings suggest that network-based invasion models may serve as a basis for the development of effective, targeted bioinvasion management strategies.

We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from nongeographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.