11 The global cargo ship network power law for the deterrence function, f ( d$_{ij}$ ) = d$_{ij}$ − β exp( − d$_{ij}$/κ ). The strongest correla- tion between model and data is obtained for β = 0 . 59 and κ = 4900 km (see Electronic Supplementary Material). At first sight, the agreement between data and model appears indeed impressive. The predicted distribution of travelled distances (Fig. 6a) fits the data far better than a simpler non-spatial model that preserves the total number of journeys, but assumes completely random origins and destinations. A closer look at the gravity model, however, reveals its limitations. In Fig. 6b we count how often links with an observed number of journeys N$_{ij}$ are predicted to be passed F$_{ij}$ times. Ideally all data points would align along the diagonal F$_{ij}$ = N$_{ij}$ , but we find that the data are substantially scattered. Although the parameters β and κ were chosen to minimize the scatter, the correlation between data and model is only moderate (Kendall’s τ = 0 . 433). In some cases, the prediction is off by several thousand journeys per year. Recent studies have used the gravity model to pinpoint the ports and routes central to the spread of invasive species (Drake & Lodge 2004, Tatem et al. 2006). The model’s shortcomings pose the question how reliable such predictions are. For this purpose, we investigated a dynamic model of ship-mediated bioinvasion where the weights of the links are either the observed traffic flows or the flows of the gravity model. We follow previous epidemiological studies (Rvachev & Longini 1985, Flahault et al. 1988, Hufnagel et al. 2004, Colizza et al. 2006) in viewing the spread on the network as a metapop- ulation process where the population dynamics on the nodes are coupled by transport on the links. In our model, ships can transport a surviving population of an invasive species with only a small probability p$_{trans}$ = 1% on each journey between two successively visited ports. The transported population is only a tiny fraction s of the population at the port of origin. Immediately after arriving at a new port, the species experiences strong demo- graphic fluctuations which lead in most cases to the death of the imported population. If however the new immigrants beat the odds of this “ecological roulette” (Carlton & Geller 1993) and establish, the population P grows rapidly following the stochastic logistic equa- tion dP dt = rP (1 − P ) + √$_{P ξ}$$_{(}$$_{t}$$_{) with growth rate}$ r = 1 / year and Gaussian white noise ξ . For details of the model, we refer to the Electronic Supplementary Material. Starting from a single port at carrying capacity P = 1, we model contacts between ports as Poisson processes with rates N$_{ij}$ (empirical data) or F$_{ij}$ (gravity model). As shown in Fig. 7a, the gravity model systematically overestimates the spreading rate, and the difference