Spatiotemporal complexity of biological invasion in a space- and time-discrete predator-prey system with the strong Allee effect

► We consider invasion scenarios in a space- and time-discrete system, which have rarely been studied in literature. ► Species spread is shown to occur through patchy invasion, multiple traveling bands or traveling front with pattern formation in the wake. ► The alien species can invade over the space even when it would not be viable in the corresponding homogeneous (non-spatial) system. ► Biocontrol strategy is predicted to be least effective when the predator's dispersal rate is in the intermediate range.