Context. The toxic cane toad (Rhinella marina) has invaded over 50 countries and is a serious conservation issue in Australia. Because the cane toad has taken several decades to colonise northern Australia, due to the large size of the continent and the east-west invasion axis, there is scope for making testable predictions about how toads will invade new areas. The western toad invasion front is far from linear, providing clear evidence for heterogeneity in invasion speed. Aims. Several ad hoc hypotheses have been offered to explain this heterogeneity, including the evolution of traits that could facilitate dispersal, and spatial heterogeneity in climate patterns. Here an alternative hypothesis is offered, and a prediction generated for the spatiotemporal pattern of invasion into the Kimberley Region-the next frontier for the invading toads in Australia. Methods. Using observations of spatiotemporal patterns of cane toad colonisation in northern Australia over the last 15 years, a conceptual model is offered, based on the orientation of wet season river flows relative to the invasion axis, as well as toad rafting and floating behaviour during the wet season. Key results. Our model predicts that toads will invade southern areas before northern areas; an alternative model based on rainfall amounts makes the opposite prediction. The models can now be tested by monitoring the spread of invasion front over the next 5-10 years. Conclusions. Our conceptual models present a pleuralistic approach to understanding the spatiotemporal invasion dynamics of toads; such an approach and evaluation of the models could prove useful for managing other invasive species. Implications. Although control of cane toads has largely proved ineffective, knowledge of the spatiotemporal pattern of the toad invasion in the Kimberley could: (1) facilitate potential management tools for slowing the spread of toads; (2) inform stakeholders in the local planning for the invasion; (3) provide researchers with a temporal context for quantifying toad impacts on animal communities; and (4) reveal the mechanism(s) causing the heterogeneity in invasion speed.