Modelling the fate of alien species populations and their assignment to different categories of commonness through time for the Gaussian and Cauchy dispersal kernels, for specific combinations of per capita growth rate, dispersal capacity, interception efficacy and synchronisation of cross-boundary management (low, intermediate and maximum over the three columns), using the framework presented in Fig. 1. The lengths of the bars represent the proportion of simulations ending in a given category for a given time step, over the 20 replicates (each replicate being characterised by a different spatial distribution of the patches).