24 The global cargo ship network 0 100 200 300 400 0 10 20 30 40 50 time (years) 0 200 400 mean number of invaded ports real traffic flows gravity model (a) invasion starting at random port (b) invasion starting in Bergen, Norway FIG. 7: Results from a stochastic population model for the spread of an invasive species between ports. (a) The invasion starts from one single, randomly chosen port. (b) The initial port is fixed as Bergen (Norway), an example of a well-connected port (degree k = 49) which is not among the central hubs. The rate of journeys from port i to j per year is assumed to be N$_{ij}$ (real flows from the GCSN) or F$_{ij}$ (gravity model). Each journey has a small probability of transporting a tiny fraction of the population from origin to destination. Parameters were adjusted ( r = 1 / year, p$_{trans}$ = 0 . 01, s = 4 · 10 − $^{5}$) to yield a per-ship-call probability of initiating invasion of ≈ 4 . 4 · 10 − 4 (Drake & Lodge 2004, see Electronic Supplementary Material for details). Plotted are the cumulative numbers of invaded ports (population number larger than half the carrying capacity) averaged over (a) 14 , 000, (b) 1000 simulation runs (standard error equal to line thickness).